Richard Rodriguez

Richard Rodriguez Theme in Hunger of Memory: Scholarship Boy Theme in Hunger of Memory: Scholarship Boy The author, Richard Rodriguez uses his education background as a central theme in his work to depict how his private life is different from his public life. He particularly revolves around language and education illustrating how they influenced his transition from childhood to adulthood. During his school years, English was enforced as the mode of communication. At his early days, he was a poor performer and this caught the attention of his teachers. However, this was not the case as he becomes a book warmer and English becomes the preferred mode of communication. The student who did not understand a single English word at the age of six, twenty years later, can proudly summarize his education career with one sentence. He progresses through life in a mindset of achievement to become a renowned individual in the same thing that he poorly performed (the English language). Being of a Spanish origin, Rodriguez quest for education tears him apart from his native culture. This is particularly seen as he laments of the success he gained at the expense of his family ties. From one level of education to the next, he would receive awards and everyone congratulated him saying â€Å"Your parents must be very proud†. This, however, made him feel guilty and sleazy as he remembered that the relationship with his parents and siblings was not that tight. He had forfeited their relationship at the expense of his education. The boy had an intimate relationship with his books. His parents were even worried about his social life. On the other hand, his siblings would make jokes about him and his reading habits. Despite his success, the author feels to have attained it in an odd way. He had the feeling that he was a bad scholarship student.   Being a member of the Spanish speaking countries, his endeavors alienated him from his cultural heritage. The members of his society felt betrayed by him acquiring formal education and his criticism to both bilingual education and affirmative action (Rodriguez 1983). Rodriguez ability of retracing his childhood memories brings to his attention the inevitable reality. School had challenged him for the better. Although it had taken him many years to come to terms with the truth, it finally hit him that the primary reason for his success in the classroom was that he enjoyed that kind of life as opposed to his former. Through this, Richard Rodriguez is able to display the power of education and extensive use of language. The hero attributes these two aspects as the greatest pillars contributing to his transition to adulthood. Although he criticizes education, he does it in a peculiar way that depicts his appreciation of the role the subject played in transforming him from the past to the present. His lack of knowledge in the subject matter during his early schooling days made him dormant and a sleeping dog in the classroom. The author, however, rose from setbacks and insecurities as a child to a strong and educated individual. Rodriguez depicts that he was to become an ugly person and had a mentality of viewing himself as ugly. As a child he struggles after the discovery that his dark completion is similar to those of poor in the streets, servants who served at his friend’s houses and various workers of the field. It was because of the education that Rodriguez begins to define himself as a respected person and stops taking into account his skin color. Despite the view from his parents and community that dark is ugly, he is able to see the difference between him and the other people whom he used to compare himself with. The difference was brought about by a change of his attitude, imagination and view of himself. The realization that the inner self is what makes him dawns on him and he determines what he can achieve. After these thoughts, the author realizes that people around him do not picture him as ugly. The change in the mindset of the author culminates the main purpose of the book. It highlights how Rodriguez attain s more confident and better person with a positive view. All these changes are primarily based on education. The theme of education is further rooted in the text as the hero depicts becoming alienated from his family as his desire for education grew. The different phases of Rodriguez life including his early days at the Catholic Church indicate the pain that he was going through as an individual. The most important point to consider is his outright rejection in the staunchest manner. This is why the author criticizes affirmative action. This is expressed in the most candid and vivid ways. However, they do not end as nobody pays attention to what the teacher has to say in the ghetto classroom. Rodriguez rejection is aimed at alleviating racial and ethnic minorities in America. Being engrossed in his educational transition, he views everyone as unable to understand him. Rodriguez argues that he experiences difficulties in separating his classroom life from that of home. The rejection can also be seen as arising from Richard. For example, when his father could not assist him with an assignment , he resolves in doing everything alone henceforth. He seems to forget that his parents had limited education and, therefore, views them as not understanding him (Marquez 1984). The more he quests for education, the more the gap between him and his family widens. From an intellectual point of view, this gap loosens the family and social values that were once held in common. The scholarship betters his life at the expense of his family and culture. The mindset that it offers clearly indicates that this is the central point of the book. The transformation of Rodriguez from a private to a public life can be attributed to the opportunities that most Americans enjoy today. This is from the affirmative action that the author criticizes. He elevates his success as a minority student and illustrates the requirements needed for attaining a successful stature in the American society. It is, however, ironical seeing, the author criticizes the very same thing that enabled him to rise to the public domain (Rivera 1984). Like majority ego-centric individuals, Rodriguez fails to see how the bilingual system has clouded his judgment and philosophy. His criticism is biased a s he speaks with contempt towards the very same nature of the Spanish culture, which he is a part of. The author tries to deny his roots and culture and his social place of America’s minorities. Rodriguez forgets he is part of the minorities that are criticized by him as a result of the success. Despite this, his appreciation of the importance of language is a vivid expression in his work. He, therefore, strives to disassociate himself with the poor class of the uneducated. From Rodriguez point of view, assimilation occurs due to the bilingual system that offered him the chance that hasn’t been prompt to many American minorities. In conclusion, Rodriquez is, however, of the view that education, success and chances that accompanied it, is the root for his alienation from his family, relations and culture. This clearly shows how the book has advanced in the exploration of the theme of education. â€Å"Haunted by the knowledge that one chooses to become a student, education is not an inevitable or natural step in growing up†. The author recounts and regrets how his choice separated him from the life once loved and enjoyed. His view indicates that he would have preferred being in the monolingual system (Sollors 1986). live CHAT

Characterize the Daily Life of a Woman in the West Essays

Characterize the Daily Life of a Woman in the West Essays Characterize the Daily Life of a Woman in the West Essay Characterize the Daily Life of a Woman in the West Essay Facts About the West- Where Are the Black Folks Or, for That Matter Where Is the Vaquero the Essential By learnings unit Three Chapter 18 Writing Assignment During the late sasss to early SASS women In the west were valued In their work In the home, on the streets and some women during this time played the same roles as men being Cowgirls. However, women mainly held their responsibilities In the home. Women played the role of a wife, a mother, a seamstress and often nurses. Their domestic duties Including gassing their children, farm work, gathering food and milk along with utilizing their sewing skills. These women had much to do while often their husband is out looking for gold, working from dusk to dawn laboring and doing the other duties that were not as common for the wives to be doing. Often there was so much work to be done in the home that women would have their children assist them with household duties and work on the farm by age nine. Women of this time spent many hours at home and away from their husbands. Labor Jobs seemed to be an excellent job during the right season. The Cowboy and the migrant worker; Mexicans, Chinese, and even African Americans would round up cattle. In return of the labor of walking thousands of miles and herding asss of cattle they would get paid a hefty amount of money. There were about 25% of black cowboys that would work as Cowboys during the years of 1870-1885. Some African Americans were so skilled that one particularly Bill Pickett being called the Greatest Cowboy winning competitions with the reputation of his tricks and stunts. Many of these cowboys during this time were making a lot of money. With the money that they would make they would often go Into town and spend or blow their money on working women. Many women now have en tired of working in the home and not feeling respected. They were tired of not being paid the amount they felt was necessary to survive. Many teens and younger unmarried women would work the streets and be paid per visit by another man, usually a cowboy. Women that were predominantly In the Mexican communities were quickly entering a new era close to the end of the century. Selling produce, working as seamstresses and laundresses was how they were able to make ends meet. However, It was shortly after when women lost status wealth the community. Mexicans found fewer options and quickly they were making below what was average pay for that time. Even though these times were tough, Mexicans still manage to preserve their heritage and religious beliefs which kept their community and heritage growing and strong. Although it appears that women mainly stayed at home, there was a portion of the population where the women fought just as hard as the men. These women built reputations of being the wildest of them all. With a quo KC craw or Just as Drive as a man, teen would ROR Tanks or ROR ten roll to gain power and support of their needs for their families. Some women were so talented that they were able to travel and put on shows like Anne Oakley. This was the new rend of what was consider a win in the war. There was entertainment and celebrations of Winning of the West. At the turn of the century, many American imagined this land as a promise for opportunities. Even with this positive movement, there were still many outlaws that fled towns and caused havoc. The outlaws played another percentage in history that included Women to be involved in. These women were also outlaws and running from the law taking their families and traveling state to state once they feared of being caught. Overall, women were still not as respected and times were still ahead of fighting to have be treated more equal.

Curriculum Development Assignment Essay Example | Topics and Well Written Essays - 7000 words

Curriculum Development Assignment - Essay Example Prior studies have acknowledged that GCSE students have a limited knowledge of science (i.e., concerning medicine and drugs) with no positive reception of the responsibility played by scientists ideas in guiding inquiry. Therefore, this study tests the argument that the GCSE students can make significant progress in developing a more refined, constructivist epistemology of science, if given a Kagan structure was used in school science curriculum (Kagan, 2004,p.1606). In this essay I chose to objectively discuss the Kagan structure on cooperative learning versus independent learning. In this case, the two class units taught will be medicine and drugs using the two methods to determine which one is more effective (Kagan, 2008,p.5). This will help to provide information concerning how GCSE students can further progress in methods of teaching. On the same note, the essay will helps one to identify aims of what is to be discovered and achieved. Also there will be a reflective account and discussions of findings and data analysis based on engagement, attitude and motivation. The rationale behind this Kagan structure is that those teachers who try it find it easy to make their students understand learning procedures and it also make it easier for teachers teach. Teachers confess that the structures have made more difference that any other innovation in teaching methods. Students on the other hand say that they are a fun to use while administrators report that it has led to positive outcomes to their schools and districts. In fact, the structures foster wide range of skills and virtues allowing learners to function successfully and with dignity in all in all of their life situations. This has helped in developing the whole student by inculcating thinking skills, social character and societal skills into the learners. In this regard, mission is to prepare students with the relationship

System of Structuring Cities and Understanding Interactions between Essay

System of Structuring Cities and Understanding Interactions between Individual Components within Sets - Essay Example Jane Jacobs illustrates this point most clearly in her chapter in The Death and Life of Great American Cities, â€Å"Uses of Sidewalks: Safety.† In this chapter, Jacobs attempts to analyze the ways in which sidewalks serve as a safety network for various cities. They do this in several ways, from the most basic, elevating and separating pedestrians from bikes and cars which could be dangerous to them, to much more complex systems. It is incredibly important, however, that Jacobs recognizes that the sidewalks in and of themselves do very little to create or destroy a safe environment. Jacobs indicates that people are not merely â€Å"passive beneficiaries of safety or helpless victims of danger† on sidewalks (30), but rather, everyone who participates in the interactions involved on sidewalks, from people in houses and businesses bordering the sidewalk, to the cars bordering the other side, to the pedestrians actually on the sidewalk, all have an important part to play i n keeping these sidewalks safe. She then identifies the human factors that help to keep a feeling of safety or un-safety on sidewalks. Things like high turnover of housing, little community feeling and empty streets with occasional traffic but easy access all lead to feeling (and reality) of un-safety – people are not likely to intervene on each other’s behalf and there is not a high enough mass of people and inter-person respect to provide a feeling of safety. But Jacobs is quick to point out that this safety is not merely a reflection of population density, because if it was, Los Angeles, which is nearly entirely suburban, would have a low rather than high crime rate (32). She also makes it very clear that police cannot solve this problem, and that in fact places with high police presence tend to be the most dangerous – police cannot solve the problems of unsafe cities (31). So to Jacobs the problems of creating safety in cities must rest with people – how to create public spaces in streets and sidewalks that discourage feelings of un-safety while encouraging feelings of community that create a safer environment for everyone. The idea of people being the fundamental unit of architecture appears in the works of Christopher Alexander and Le Corbusier as well, though they take almost opposite tracks to understanding how to fascilitate people’s use of cities. Both recognize very clearly that the living, breathing city is created by people – not the physical spaces, but the people that inhabit them. Alexander takes a natural view of cities, using semilattice and set theory to describe the ways a cities parts interact, through people. He strongly dislikes artificial cities, saying that there is something necessarily missing from them, and that artificial cities tend to create a â€Å"tree† system, where each component is only interrelated to each other through its connection to the whole (80). Each leaf is only conn ected to each other leaf because they are connected to the tree – not because they have any particular relationship to each other.

How Smoking in Public Places Is Harmful Essay Example for Free

How Smoking in Public Places Is Harmful Essay Many studies and surveys have been researched and prove rather or not smoking in public places can be harmful to others. Studies have proven that smoking is hazardous to our health. When the person who smokes is active that makes the person that’s near him and inhale the smoke passive smokers However, people have been smoking for many years smoking draws people in by using some type’s advertisement to draw them to smoking. Smoking is not a good habit smoking causes serious health issue to the smokers and also the people around them that inhale the smoke. Cigarette also contains ammonia and other carbons which could cause other respiratory infection and lung cancer. The particles from smoke may cause cancers, emphysema and other side affects. Blood vessels raise blood pressure and give the effects the nervous system, which can lead to reproductive disorders in the long run. Smoking in public places can be harmful to the heart by banding smoking in public places you significantly reduce the risk of heart attacks among the young people and young people and nonsmokers. Studies have proven that by banning smoking in public places that rate of people having heart attacks have been reduced by 26 percent per year. Studies have really proven that smoking in public places can be harmful to our health in many ways even breathing in low doses of cigarette smoke can increase one’s risk of heart attack. Second hand smoke really increases the chance o heart attacks. Smoking in public places is not only harmful for people that don’t smoke nut harmful, to young children and older people. Second hand smoke is extremely harmful to older people and young children. Smoking can be dangerous and deadly rather it’s first hand or second hand smoke the laws banning smoking might convince some people to quit smoking. In conclusion smoking in the public really causes bad health issues. Heart attacks, strokes and other health problem. Smoking cigarettes can be deadly. Cigarettes are known as the silently killer. Smoking should be banned in some public places to help prevent heart attacks and other health issues. Studies have researched and shown how smoking in public places can be harmful to your health.

Protestantism vs. Catholicism in XVII Century England :: Religion Essays

Protestantism vs. Catholicism in XVII Century England â€Å"The English nation grew increasingly more Protestant during the XVII century, while the monarchy moved ever closer to Rome.† The keen train spotter—spotting trains of thought rather than locomotives—will certainly spot a good deal of redundancy in this unequivocal statement, for it is, beyond doubt, a proclamation framed by the historian rather than the philosopher. The Stuarts—certainly some more than others—were Catholics not in the manner that Henry VIII took his mid-life faith, but rather in the manner that Elizabeth was always a Protestant. Similarly, the general population of the land viewed their faith as they viewed their nation: with pride. We should perhaps initially note that religion was, to those of the 17th century, something cognate to sex to the present day paramour, charity to the philanthropist, money to the niggard: it was a serious business. In the seventeenth century, Protestantism in England was as safe as houses: secure with a firm chronological and doctrinal and popular foundation. Within the larger European context, however, the established National religion was exposed to the rigours of Catholic tempest and seemed far from fixed. It is in this respect that we might tackle the monarchical populous split. The English Restoration was no minor re-establishment of monarchy: it was rather a restatement of the national character. Regicide was abhorrent to most—we need only peruse the emotive power of Macbeth or Hamlet to gain some understanding of the general sentiment—and the execution of Charles I was an extreme act of an extreme sub-minority. The arrival of Charles II, therefore, was not only a restoration of the natural and Godly order, but, in effect, an appeasement of the national conscience; a way to bury the crisis of revolution once and for all. With so much at stake, it was no simple task to recreate the circumstances of the revolution, but this is precisely what Charles II and James II managed. It is certainly an oversimplification to suggest that this came about solely from religious discord, but similarly it is erroneous to suggest that this was not—if we might resort to religious terminology—the â€Å"prime mover.† Charles II had spent mu ch of his life upon the continent, and was, therefore, more a continental than an Englishman. In terms of religion, particularly, his views were consummately European: cosmopolitan and decidedly Catholic.

Bag of Bones CHAPTER TEN

Around nine o'clock, a pickup came down the driveway and parked behind my Chevrolet. The truck was new a Dodge Ram so clean and chrome-shiny it looked as if the ten-day plates had just come off that morning but it was the same shade of off-white as the last one and the sign on the driver's door was the one I remembered: WILLIAM ‘BILL' DEAN CAMP CHECKING CARETAKING LIGHT CARPENTRY, plus his telephone number. I went out on the back stoop to meet him, coffee cup in my hand. ‘Mike!' Bill cried, climbing down from behind the wheel. Yankee men don't hug that's a truism you can put right up there with tough guys don't dance and real men don't eat quiche but Bill pumped my hand almost hard enough to slop coffee from a cup that was three-quarters empty, and gave me a hearty clap on the back. His grin revealed a splendidly blatant set of false teeth the kind which used to be called Roebuckers, because you got them from the catalogue. It occurred to me in passing that my ancient interlocutor from the Lakeview General Store could have used a pair. It certainly would have improved mealtimes for the nosy old fuck. ‘Mike, you're a sight for sore eyes!' ‘Good to see you, too,' I said, grinning. Nor was it a false grin; I felt all right. Things with the power to scare the living shit out of you on a thundery midnight in most cases seem only interesting in the bright light of a summer morning. ‘You're looking well, my friend.' It was true. Bill was four years older and a little grayer around the edges, but otherwise the same. Sixty-five? Seventy? It didn't matter. There was no waxy look of ill health about him, and none of the falling-away in the face, principally around the eyes and in the cheeks, that I associate with encroaching infirmity. ‘So're you,' he said, letting go of my hand. ‘We was all so sorry about Jo, Mike. Folks in town thought the world of her. It was a shock, with her so young. My wife asked if I'd give you her condolences special. Jo made her an afghan the year she had the pneumonia, and Yvette ain't never forgot it.' ‘Thanks,' I said, and my voice wasn't quite my own for a moment or two. It seemed that on the TR my wife was hardly dead at all. ‘And thank Yvette, too.' ‘Yuh. Everythin okay with the house? Other'n the air conditioner, I mean. Buggardly thing! Them at the Western Auto promised me that part last week, and now they're saying maybe not until August first.' ‘It's okay. I've got my Powerbook. If I want to use it, the kitchen table will do fine for a desk.' And I would want to use it so many crosswords, so little time. ‘Got your hot water okay?' ‘All that's fine, but there is one problem.' I stopped. How did you tell your caretaker you thought your house was haunted? Probably there was no good way; probably the best thing to do was to go at it head-on. I had questions, but I didn't want just to nibble around the edges of the subject and be coy. For one thing, Bill would sense it. He might have bought his false teeth out of a catalogue, but he wasn't stupid. ‘What's on your mind, Mike? Shoot.' ‘I don't know how you're going to take this, but ‘ He smiled in the way of a man who suddenly understands and held up his hand. ‘Guess maybe I know already.' ‘You do?' I felt an enormous sense of relief and I could hardly wait to find out what he had experienced in Sara, perhaps while checking for dead lightbulbs or making sure the roof was holding the snow all right. ‘What did you hear?' ‘Mostly what Royce Merrill and Dickie Brooks have been telling,' he said. ‘Beyond that, I don't know much. Me and mother's been in Virginia, remember. Only got back last night around eight o'clock. Still, it's the big topic down to the store.' For a moment I remained so fixed on Sara Laughs that I had no idea what he was talking about. All I could think was that folks were gossiping about the strange noises in my house. Then the name Royce Merrill clicked and everything else clicked with it. Merrill was the elderly possum with the gold-headed cane and the salacious wink. Old Four-Teeth. My caretaker wasn't talking about ghostly noises; he was talking about Mattie Devore. ‘Let's get you a cup of coffee,' I said. ‘I need you to tell me what I'm stepping in here.' When we were seated on the deck, me with fresh coffee and Bill with a cup of tea (‘Coffee burns me at both ends these days,' he said), I asked him first to tell me the Royce Merrill-Dickie Brooks version of my encounter with Mattie and Kyra. It turned out to be better than I had expected. Both old men had seen me standing at the side of the road with the little girl in my arms, and they had observed my Chevy parked halfway into the ditch with the driver's-side door open, but apparently neither of them had seen Kyra using the white line of Route 68 as a tightrope. As if to compensate for this, however, Royce claimed that Mattie had given me a big my hero hug and a kiss on the mouth. ‘Did he get the part about how I grabbed her by the ass and slipped her some tongue?' I asked. Bill grinned. ‘Royce's imagination ain't stretched that far since he was fifty or so, and that was forty or more year ago.' ‘I never touched her.' Well . . . there had been that moment when the back of my hand went sliding along the curve of her breast, but that had been inadvertent, whatever the young lady herself might think about it. ‘Shite, you don't need to tell me that,' he said. ‘But . . . ‘ He said that but the way my mother always had, letting it trail off on its own, like the tail of some ill-omened kite. ‘But what?' ‘You'd do well to keep your distance from her,' he said. ‘She's nice enough almost a town girl, don't you know but she's trouble.' He paused. ‘No, that ain't quite fair to her. She's in trouble.' ‘The old man wants custody of the baby, doesn't he?' Bill set his teacup down on the deck rail and looked at me with his eyebrows raised. Reflections from the lake ran up his cheek in ripples, giving him an exotic look. ‘How'd you know?' ‘Guesswork, but of the educated variety. Her father-in-law called me Saturday night during the fireworks. And while he never came right out and stated his purpose, I doubt if Max Devore came all the way back to TR-90 in western Maine to repo his daughter-in-law's Jeep and trailer. So what's the story, Bill?' For several moments he only looked at me. It was almost the look of a man who knows you have contracted a serious disease and isn't sure how much he ought to tell you. Being looked at that way made me profoundly uneasy. It also made me feel that I might be putting Bill Dean on the spot. Devore had roots here, after all. And, as much as Bill might like me, I didn't. Jo and I were from away. It could have been worse it could have been Massachusetts or New York but Derry, although in Maine, was still away. ‘Bill? I could use a little navigational help if you ‘ ‘You want to stay out of his way,' he said. His easy smile was gone. ‘The man's mad.' For a moment I thought Bill only meant Devore was pissed off at me, and then I took another look at his face. No, I decided, he didn't mean pissed off; he had used the word ‘mad' in the most literal way. ‘Mad how?' I asked. ‘Mad like Charles Manson? Like Hannibal Lecter? How?' ‘Say like Howard Hughes,' he said. ‘Ever read any of the stories about him? The lengths he'd go to to get the things he wanted? It didn't matter if it was a special kind of hot dog they only sold in L.A. or an airplane designer he wanted to steal from Lockheed or Mcdonnell-Douglas, he had to have what he wanted, and he wouldn't rest until it was under his hand. Devore is the same way. He always was even as a boy he was willful, according to the stories you hear in town. ‘My own dad had one he used to tell. He said little Max Devore broke into Scant Larribee's tack-shed one winter because he wanted the Flexible Flyer Scant give his boy Scooter for Christmas. Back around 1923, this would have been. Devore cut both his hands on broken glass, Dad said, but he got the sled. They found him near midnight, sliding down Sugar Maple Hill, holding his hands up to his chest when he went down. He'd bled all over his mittens and his snowsuit. There's other stories you'll hear about Maxie Devore as a kid if you ask you'll hear fifty different ones and some may even be true. That one about the sled is true, though. I'd bet the farm on it. Because my father didn't lie. It was against his religion.' ‘Baptist?' ‘Nosir, Yankee.' ‘1923 was many moons ago, Bill. Sometimes people change.' ‘Ayuh, but mostly they don't. I haven't seen Devore since he come back and moved into Warrington's, so I can't say for sure, but I've heard things that make me think that if he has changed, it's for the worse. He didn't come all the way across the country 'cause he wanted a vacation. He wants the kid. To him she's just another version of Scooter Larribee's Flexible Flyer. And my strong advice to you is that you don't want to be the window-glass between him and her.' I sipped my coffee and looked out at the lake. Bill gave me time to think, scraping one of his workboots across a splatter of birdshit on the boards while I did it. Crowshit, I reckoned; only crows crap in such long and exuberant splatters. One thing seemed absolutely sure: Mattie Devore was roughly nine miles up Shit Creek with no paddle. I'm not the cynic I was at twenty is anyone? but I wasn't naive enough or idealistic enough to believe the law would protect Ms. Doublewide against Mr. Computer . . . not if Mr. Computer decided to play dirty. As a boy he'd taken the sled he wanted and gone sliding by himself at midnight, bleeding hands not a concern. And as a man? An old man who had been getting every sled he wanted for the last forty years or so? ‘What's the story with Mattie, Bill? Tell me.' It didn't take him long. Country stories are, by and large, simple stories. Which isn't to say they're not often interesting. Mattie Devore had started life as Mattie Stanchfield, not quite from the TR but from just over the line in Motton. Her father had been a logger, her mother a home beautician (which made it, in a ghastly way, the perfect country marriage). There were three kids. When Dave Stanch-field missed a curve over in Lovell and drove a fully loaded pulptruck into Kewadin Pond, his widow ‘kinda lost heart,' as they say. She died soon after. There had been no insurance, other than what Stanchfield had been obliged to carry on his Jimmy and his skidder. Talk about your Brothers Grimm, huh? Subtract the Fisher-Price toys behind the house, the two pole hairdryers in the basement beauty salon, the old rustbucket Toyota in the driveway, and you were right there: Once upon a time there lived a poor widow and her three children. Mattie is the princess of the piece poor but beautiful (that she was beautiful I could personally testify). Now enter the prince. In this case he's a gangly stuttering redhead named Lance Devore. The child of Max Devore's sunset years. When Lance met Mattie, he was twenty-one. She had just turned seventeen. The meeting took place at Warrington's, where Mattie had landed a summer job as a waitress. Lance Devore was staying across the lake on the Upper Bay, but on Tuesday nights there were pickup softball games at Warrington's, the townies against the summer folks, and he usually canoed across to play. Softball is a great thing for the Lance Devores of the world; when you're standing at the plate with a bat in your hands, it doesn't matter if you're gangly. And it sure doesn't matter if you stutter. ‘He confused em quite considerable over to Warrington's,' Bill said. ‘They didn't know which team he belonged on the Locals or the Aways. Lance didn't care; either side was fine with him. Some weeks he'd play for one, some weeks t'other. Either one was more than happy to have him, too, as he could hit a ton and field like an angel. They'd put him at first base a lot because he was tall, but he was really wasted there. At second or shortstop . . . my! He'd jump and twirl around like that guy Noriega.' ‘You might mean Nureyev,' I said. He shrugged. ‘Point is, he was somethin to see. And folks liked him. He fit in. It's mostly young folks that play, you know, and to them it's how you do, not who you are. Besides, a lot of em don't know Max Devore from a hole in the ground.' ‘Unless they read The Wall Street Journal and the computer magazines,† I said. ‘In those, you run across the name Devore about as often as you run across the name of God in the Bible.' ‘No foolin?' ‘Well, I guess that in the computer magazines God is more often spelled Gates, but you know what I mean.' ‘I s'pose. But even so, it's been sixty-five years since Max Devore spent any real time on the TR. You know what happened when he left, don't you?' ‘No, why would I?' He looked at me, surprised. Then a kind of veil seemed to fall over his eyes. He blinked and it cleared. ‘Tell you another time it ain't no secret but I need to be over to the Harrimans' by eleven to check their sump-pump. Don't want to get sidetracked. Point I was tryin to make is just this: Lance Devore was accepted as a nice young fella who could hit a softball three hundred and fifty feet into the trees if he struck it just right. There was no one old enough to hold his old man against him not at Warrington's on Tuesday nights, there wasn't and no one held it against him that his family had dough, either. Hell, there are lots of wealthy people here in the summer. You know that. None worth as much as Max Devore, but being rich is only a matter of degree.' That wasn't true, and I had just enough money to know it. Wealth is like the Richter scale-once you pass a certain point, the jumps from one level to the next aren't double or triple but some amazing and ruinous multiple you don't even want to think about. Fitzgerald had it straight, although I guess he didn't believe his own insight: the very rich are different from you and me. I thought of telling Bill that, and decided to keep my mouth shut. He had a sump-pump to fix. Kyra's parents met over a keg of beer stuck in a mudhole. Mattie was running the usual Tuesday-night keg out to the softball field from the main building on a handcart. She'd gotten it most of the way from the restaurant wing with no trouble, but there had been heavy rain earlier in the week, and the cart finally bogged down in a soft spot. Lance's team was up, and Lance was sitting at the end of the bench, waiting his turn to hit. He saw the girl in the white shorts and blue Warrington's polo shirt struggling with the bogged handcart, and got up to help her. Three weeks later they were inseparable and Mattie was pregnant; ten weeks later they were married; thirty-seven months later, Lance Devore was in a coffin, done with softball and cold beer on a summer evening, done with what he called ‘woodsing,' done with fatherhood, done with love for the beautiful princess. Just another early finish, hold the happily-ever-after. Bill Dean didn't describe their meeting in any detail; he only said, ‘They met at the field she was runnin out the beer and he helped her out of a boghole when she got her handcart stuck.' Mattie never said much about that part of it, so I don't know much. Except I do . . . and although some of the details might be wrong, I'd bet you a dollar to a hundred 1 got most of them right. That was my summer for knowing things I had no business knowing. It's hot, for one thing '94 is the hottest summer of the decade and July is the hottest month of the summer. President Clinton is being upstaged by Newt and the Republicans. Folks are saying old Slick Willie may not even run for a second term. Boris Yeltsin is reputed to be either dying of heart disease or in a dry-out clinic. The Red Sox are looking better than they have any right to. In Derry, Johanna Arlen Noonan is maybe starting to feel a little whoopsy in the morning. If so, she does not speak of it to her husband. I see Mattie in her blue polo shirt with her name sewn in white script above her left breast. Her white shorts make a pleasing contrast to her tanned legs. I also see her wearing a blue gimme cap with the red W for Warrington's above the long bill. Her pretty dark-blonde hair is pulled through the hole at the back of the cap and falls to the collar of her shirt. I see her trying to yank the handcart out of the mud without upsetting the keg of beer. Her head is down; the shadow thrown by the bill of the cap obscures all of her face but her mouth and small set chin. ‘Luh-let m-me h-h-help,' Lance says, and she looks up. The shadow cast by the cap's bill falls away, he sees her big blue eyes the ones she'll pass on to their daughter. One look into those eyes and the war is over without a single shot fired; he belongs to her as surely as any young man ever belonged to any young woman. The rest, as they say around here, was just courtin. The old man had three children, but Lance was the only one he seemed to care about. (‘Daughter's crazier'n a shithouse mouse,' Bill said matter-of-factly. ‘In some laughin academy in California. Think I heard she caught her a cancer, too.') The fact that Lance had no interest in computers and software actually seemed to please his father. He had another son who was capable of running the business. In another way, however, Lance Devore's older half-brother wasn't capable at all: there would be no grandchildren from that one. ‘Rump-wrangler,' Bill said. ‘Understand there's a lot of that going around out there in California.' There was a fair amount of it going around on the TR, too, I imagined, but thought it not my place to offer sexual instruction to my caretaker. Lance Devore had been attending Reed College in Oregon, majoring in forestry the kind of guy who falls in love with green flannel pants, red suspenders, and the sight of condors at dawn. A Brothers Grimm woodcutter, in fact, once you got past the academic jargon. In the summer between his junior and senior years, his father had summoned him to the family compound in Palm Springs, and had presented him with a boxy lawyer's suitcase crammed with maps, aerial photos, and legal papers. These had little order that Lance could see, but I doubt that he cared. Imagine a comic-book collector given a crate crammed with rare old copies of Donald Duck. Imagine a movie collector given the rough cut of a never-released film starring Humphrey Bogart and Marilyn Monroe. Then imagine this avid young forester realizing that his father owned not just acres or square miles in the vast unincorporated forests of western Maine, but entire realms. Although Max Devore had left the TR in 1933, he'd kept a lively interest in the area where he'd grown up, subscribing to area newspapers and getting magazines such as Down East and the Maine Times. In the early eighties, he had begun to buy long columns of land just east of the Maine-New Hampshire border. God knew there had been plenty for sale; the paper companies which owned most of it had fallen into a recessionary pit, and many had become convinced that their New England holdings and operations would be the best place to begin retrenching. So this land, stolen from the Indians and clear-cut ruthlessly in the twenties and fifties, came into Max Devore's hands. He might have bought it just because it was there, a good bargain he could afford to take advantage of. He might have bought it as a way of demonstrating to himself that he had really survived his childhood; had, in point of fact, triumphed over it. Or he might have bought it as a toy for his beloved younger son. In the years when Devore was making his major land purchases in western Maine, Lance would have been just a kid . . . but old enough for a perceptive father to see where his interests were tending. Devore asked Lance to spend the summer of 1994 surveying purchases which were, for the most part, already ten years old. He wanted the boy to put the paperwork in order, but he wanted more than that he wanted Lance to make sense of it. It wasn't a land-use recommendation he was looking for, exactly, although I guess he would have listened if Lance had wanted to make one; he simply wanted a sense of what he had purchased. Would Lance take a summer in western Maine trying to find out what his sense of it was? At a salary of two or three thousand dollars a month? I imagine Lance's reply was a more polite version of Buddy Jellison's ‘Does a crow shit in the pine tops?' The kid arrived in June of 1994 and set up shop in a tent on the far side of Dark Score Lake. He was due back at Reed in late August. Instead, though, he decided to take a year's leave of absence. His father wasn't pleased. His father smelled what he called ‘girl trouble.' ‘Yeah, but it's a damned long sniff from California to Maine,' Bill Dean said, leaning against the driver's door of his truck with his sunburned arms folded. ‘He had someone a lot closer than Palm Springs doin his sniffin for him.' ‘What are you talking about?' I asked. †Bout talk. People do it for free, and most are willing to do even more if they're paid.' ‘People like Royce Merrill?' ‘Royce might be one,' he agreed, ‘but he wouldn't be the only one. Times around here don't go between bad and good; if you're a local, they mostly go between bad and worse. So when a guy like Max Devore sends a guy out with a supply of fifty- and hundred-dollar bills . . . ‘ ‘Was it someone local? A lawyer?' Not a lawyer; a real-estate broker named Richard Osgood (‘a greasy kind of fella' was Bill Dean's judgment of him) who denned and did business in Motton. Eventually Osgood had hired a lawyer from Castle Rock. The greasy fella's initial job, when the summer of '94 ended and Lance Devore remained on the TR, was to find out what the hell was going on and put a stop to it. ‘And then?' I asked. Bill glanced at his watch, glanced at the sky, then centered his gaze on me. He gave a funny little shrug, as if to say, ‘We're both men of the world, in a quiet and settled sort of way you don't need to ask a silly question like that.' ‘Then Lance Devore and Mattie Stanchfield got married in the Grace Baptist Church right up there on Highway 68. There were tales made the rounds about what Osgood might've done to keep it from comin off I heard he even tried to bribe Reverend Gooch into refusin to hitch em, but I think that's stupid, they just would have gone someplace else. ‘Sides, I don't see much sense in repeating what I don't know for sure.' Bill unfolded an arm and began to tick items off on the leathery fingers of his right hand. ‘They got married in the middle of September, 1994, I know that.' Out popped the thumb. ‘People looked around with some curiosity to see if the groom's father would put in an appearance, but he never did.' Out popped the forefinger. Added to the thumb, it made a pistol. ‘Mattie had a baby in April of '95, making the kiddie a dight premature . . . but not enough to matter. I seen it in the store with my own eyes when it wasn't a week old, and it was just the right size.' Out with the second finger. ‘I don't know that Lance Devore's old man absolutely refused to help em financially, but I do know they were living in that trailer down below Dickie's Garage, and that makes me think they were havin a pretty hard skate.' ‘Devore put on the choke-chain,' I said. ‘It's what a guy used to getting his own way would do . . . but if he loved the boy the way you seem to think, he might have come around.' ‘Maybe, maybe not.' He glanced at his watch again. ‘Let me finish up quick and get out of your sunshine . . . but you ought to hear one more little story, because it really shows how the land lies. ‘In July of last year, less'n a month before he died, Lance Devore shows up at the post-office counter in the Lakeview General. He's got a manila envelope he wants to send, but first he needs to show Carla DeCinces what's inside. She said he was all fluffed out, like daddies sometimes get over their kids when they're small.' I nodded, amused at the idea of skinny, stuttery Lance Devore all fluffed out. But I could see it in my mind's eye, and the image was also sort of sweet. ‘It was a studio pitcher they'd gotten taken over in the Rock. Showed the kid . . . what's her name? Kayla?' ‘Kyra.' ‘Ayuh, they call em anything these days, don't they? It showed Kyra sittin in a big leather chair, with a pair of joke spectacles on her little snub of a nose, lookin at one of the aerial photos of the woods over across the lake in TR-100 or TR-110 part of what the old man had picked up, anyway. Carla said the baby had a surprised look on her face, as if she hadn't suspected there could be so much woods in the whole world. Said it was awful cunnin, she did.' ‘Cunnin as a cat a-runnin,' I murmured. ‘And the envelope Registered, Express Mail was addressed to Maxwell Devore, in Palm Springs, California.' ‘Leading you to deduce that the old man either thawed enough to ask for a picture of his only grandchild, or that Lance Devore thought a picture might thaw him.' Bill nodded, looking as pleased as a parent whose child has managed a difficult sum. ‘Don't know if it did,' he said. ‘Wasn't enough time to tell, one way or the other. Lance had bought one of those little satellite dishes, like what you've got here. There was a bad storm the day he put it up hail, high wind, blowdowns along the lakeshore, lots of lightnin. That was along toward evening. Lance put his dish up in the afternoon, all done and safe, except around the time the storm commenced he remembered he'd left his socket wrench on the trailer roof. He went up to get it so it wouldn't get all wet n rusty ‘ ‘He was struck by lightning? Jesus, Bill!' ‘Lightnin struck, all right, but it hit across the way. You go past the place where Wasp Hill Road runs into 68 and you'll see the stump of the tree that stroke knocked over. Lance was comin down the ladder with his socket wrench when it hit. If you've never had a lightnin bolt tear right over your head, you don't know how scary it is it's like havin a drunk driver veer across into your lane, headed right for you, and then swing back onto his own side just in time. Close lightnin makes your hair stand up makes your damned prick stand up. It's apt to play the radio on your steel fillins, it makes your ears hum, and it makes the air taste roasted. Lance fell off the ladder. If he had time to think anything before he hit the ground, I bet he thought he was electrocuted. Poor boy. He loved the TR, but it wasn't lucky for him.' ‘Broke his neck?' ‘Ayuh. With all the thunder, Mattie never heard him fall or yell or anything. She looked out a minute or two later when it started to hail and he still wasn't in. And there he was, layin on the ground and lookin up into the friggin hail with his eyes open.' Bill looked at his watch one final time, then swung open the door to his truck. ‘The old man wouldn't come for their weddin, but he came for his son's funeral and he's been here ever since. He didn't want nawthin to do with the young woman ‘ ‘But he wants the kid,' I said. It was no more than what I already knew, but I felt a sinking in the pit of my stomach just the same. Don't talk about this, Mattie had asked me on the morning of the Fourth. It's not a good time for Ki and me. ‘How far along in the process has he gotten?' ‘On the third turn and headin into the home stretch, I sh'd say. There'll be a hearin in Castle County Superior Court, maybe later this month, maybe next. The judge could rule then to hand the girl over, or put it off until fall. I don't think it matters which, because the one thing that's never going to happen on God's green earth is a rulin in favor of the mother. One way or another, that little girl is going to grow up in California.† Put that way, it gave me a very nasty little chill. Bill slid behind the wheel of his truck. ‘Stay out of it, Mike,' he said. ‘Stay away from Mattie Devore and her daughter. And if you get called to court on account of seem the two of em on Saturday, smile a lot and say as little as you can.' ‘Max Devore's charging that she's unfit to raise the child.' ‘Ayuh.' ‘Bill, I saw the child, and she's fine.' He grinned again, but this time there was no amusement in it. †Magine she is. But that's not the point. Stay clear of their business, old boy. It's my job to tell you that; with Jo gone, I guess I'm the only caretaker you got.' He slammed the door of his Ram, started the engine, reached for the gearshift, then dropped his hand again as something else occurred to him. ‘If you get a chance, you ought to look for the owls.' ‘What owls?' ‘There's a couple of plastic owls around here someplace. They might be in y'basement or out in Jo's studio. They come in by mail-order the fall before she passed on.' ‘The fall of 1993?' ‘Ayuh.' ‘That can't be right.' We hadn't used Sara in the fall of 1993. †Tis, though. I was down here puttin on the storm doors when Jo showed up. We had us a natter, and then the UPS truck come. I lugged the box into the entry and had a coffee I was still drinkin it then while she took the owls out of the carton and showed em off to me. Gorry, but they looked real! She left not ten minutes after. It was like she'd come down to do that errand special, although why anyone'd drive all the way from Derry to take delivery of a couple of plastic owls I don't know.' ‘When in the fall was it, Bill? Do you remember?' ‘Second week of November,' he said promptly. ‘Me n the wife went up to Lewiston later that afternoon, to ‘Vette's sister's. It was her birthday. On our way back we stopped at the Castle Rock Agway so ‘Vette could get her Thanksgiving turkey.' He looked at me curiously. ‘You really didn't know about them owls?' ‘No.' ‘That's a touch peculiar, wouldn't you say?' ‘Maybe she told me and I forgot,' I said. ‘I guess it doesn't matter much now in any case.' Yet it seemed to matter. It was a small thing, but it seemed to matter. ‘Why would Jo want a couple of plastic owls to begin with?' ‘To keep the crows from shittin up the woodwork, like they're doing out on your deck. Crows see those plastic owls, they veer off.' I burst out laughing in spite of my puzzlement . . . or perhaps because of it. ‘Yeah? That really works?' ‘Ayuh, long's you move em every now and then so the crows don't get suspicious. Crows are just about the smartest birds going, you know. You look for those owls, save yourself a lot of mess.' ‘I will,' I said. Plastic owls to scare the crows away it was exactly the sort of knowledge Jo would come by (she was like a crow herself in that way, picking up glittery pieces of information that happened to catch her interest) and act upon without bothering to tell me. All at once I was lonely for her again missing her like hell. ‘Good. Some day when I've got more time, we'll walk the place all the way around. Woods too, if you want. I think you'll be satisfied.' ‘I'm sure I will. Where's Devore staying?' The bushy eyebrows went up. ‘Warrington's. Him and you's practically neighbors. I thought you must know.' I remembered the woman I'd seen black bathing-suit and black shorts somehow combining to give her an exotic cocktail-party look and nodded. ‘I met his wife.' Bill laughed heartily enough at that to feel in need of his handkerchief. He fished it off the dashboard (a blue paisley thing the size of a football pennant) and wiped his eyes. ‘What's so funny?' I asked. ‘Skinny woman? White hair? Face sort of like a kid's Halloween mask?' It was my turn to laugh. ‘That's her.' ‘She ain't his wife, she's his whatdoyoucallit, personal assistant. Rogette Whitmore is her name.' He pronounced it ro-GET, with a hard G. ‘Devore's wives're all dead. The last one twenty years.' ‘What kind of name is Rogette? French?' ‘California,' he said, and shrugged as if that one word explained everything. ‘There's people in town scared of her.' ‘Is that so?' ‘Ayuh.' Bill hesitated, then added with one of those smiles we put on when we want others to know that we know we're saying something silly: ‘Brenda Meserve says she's a witch.' ‘And the two of them have been staying at Warrington's almost a year?' ‘Ayuh. The Whitmore woman comes n goes, but mostly she's been here. Thinkin in town is that they'll stay until the custody case is finished off, then all go back to California on Devore's private jet. Leave Osgood to sell Warrington's, and ‘ ‘Sell it? What do you mean, sell it?' ‘I thought you must know,' Bill said, dropping his gearshift into drive. ‘When old Hugh Emerson told Devore they closed the lodge after Thanksgiving, Devore told him he had no intention of moving. Said he was comfortable right where he was and meant to stay put.' ‘He bought the place.' I had been by turns surprised, amused, and angered over the last twenty minutes, but never exactly dumbfounded. Now I was. ‘He bought Warrington's Lodge so he wouldn't have to move to Lookout Rock Hotel over in Castle View, or rent a house.' ‘Ayuh, so he did. Nine buildins, includin the main lodge and The Sunset Bar; twelve acres of woods, a six-hole golf course, and five hundred feet of shorefront on The Street. Plus a two-lane bowlin alley and a softball field. Four and a quarter million. His friend Osgood did the deal and Devore paid with a personal check. I wonder how he found room for all those zeros. See you, Mike.' With that he backed up the driveway, leaving me to stand on the stoop, looking after him with my mouth open. Plastic owls. Bill had told me roughly two dozen interesting things in between peeks at his watch, but the one which stayed on top of the pile was the fact (and I did accept it as a fact; he had been too positive for me not to) that Jo had come down here to take delivery on a couple of plastic goddam owls. Had she told me? She might have. I didn't remember her doing so, and it seemed to me that I would have, but Jo used to claim that when I got in the zone it was no good to tell me anything; stuff went in one ear and out the other. Sometimes she'd pin little notes errands to run, calls to make to my shirt, as if I were a first-grader. But wouldn't I recall if she'd said ‘I'm going down to Sara, hon, UPS is delivering something I want to receive personally, interested in keeping a lady company?' Hell wouldn't I have gone? I always liked an excuse to go to the TR. Except I'd been working on that screenplay . . . and maybe pushing it a little . . . notes pinned to the sleeve of my shirt . . . If you go out when you're finished, we need milk and orange juice . . . I inspected what little was left of Jo's vegetable garden with the July sun beating down on my neck and thought about owls, the plastic god-dam owls. Suppose Jo had told me she was coming down here to Sara Laughs? Suppose I had declined almost without hearing the offer because I was in the writing zone? Even if you granted those things, there was another question: why had she felt the need to come down here personally when she could have just called someone and asked them to meet the delivery truck? Kenny Auster would have been happy to do it, ditto Mrs. M. And Bill Dean, our caretaker, had actually been here. This led to other questions one was why she hadn't just had UPS deliver the damned things to Derry and finally I decided I couldn't live without actually seeing a bona fide plastic owl for myself. Maybe, I thought, going back to the house, I'd put one on the roof of my Chew when it was parked in the driveway. Forestall future bombing runs. I paused in the entry, struck by a sudden idea, and called Ward Hankins, the guy in Waterville who handles my taxes and my few non-writing-related business affairs. ‘Mike,' he said heartily. ‘How's the lake?' ‘The lake's cool and the weather's hot, just the way we like it,' I said. ‘Ward, you keep all the records we send you for five years, don't you? Just in case IRS decides to give us some grief?' ‘Five is accepted practice,' he said, ‘but I hold your stuff for seven in the eyes of the tax boys, you're a mighty fat pigeon.' Better a fat pigeon than a plastic owl, I thought but didn't say. What I said was ‘That includes desk calendars, right? Mine and. Jo's, up until she died?' ‘You bet. Since neither of you kept diaries, it was the best way to cross-reference receipts and claimed expenses with ‘ ‘Could you find Jo's desk calendar for 1993 and see what she had going in the second week of November?' ‘Td be happy to. What in particular are you looking for?' For a moment I saw myself sitting at my kitchen table in Derry on my first night as a widower, holding up a box with the words Norco Home Pregnancy Test printed on the side. Exactly what was I looking for at this late date? Considering that I had loved the lady and she was almost four years in her grave, what was I looking for? Besides trouble, that was? ‘I'm looking for two plastic owls,' I said. Ward probably thought I was talking to him, but I'm not sure I was. ‘I know that sounds weird, but it's what I'm doing. Can you call me back?' ‘Within the hour.' ‘Good man,' I said, and hung up. Now for the actual owls themselves. Where was the most likely spot to store two such interesting artifacts? My eyes went to the cellar door. Elementary, my dear Watson. The cellar stairs were dark and mildly dank. As I stood on the landing groping for the lightswitch, the door banged shut behind me with such force that I cried out in surprise. There was no breeze, no draft, the day was perfectly still, but the door banged shut just the same. Or was sucked shut. I stood in the dark at the top of the stairs, feeling for the lightswitch, smelling that oozy smell that even good concrete foundations get after awhile if there is no proper airing-out. It was cold, much colder than it had been on the other side of the door. I wasn't alone and I knew it. I was afraid, I'd be a liar to say I wasn't . . . but I was also fascinated. Something was with me. Something was in here with me. I dropped my hand away from the wall where the switch was and just stood with my arms at my sides. Some time passed. I don't know how much. My heart was beating furiously in my chest; I could feel it in my temples. It was cold. ‘Hello?' I asked. Nothing in response. I could hear the faint, irregular drip of water as condensation fell from one of the pipes down below, I could hear my own breathing, and faintly far away, in another world where the sun was out I could hear the triumphant caw of a crow. Perhaps it had just dropped a load on the hood of my car. I really need an owl, I thought. In fact, I don't know how I ever got along without one. ‘Hello?' I asked again. ‘Can you talk?' Nothing. I wet my lips. I should have felt silly, perhaps, standing there in the dark and calling to the ghosts. But I didn't. Not a bit. The damp had been replaced by a coldness I could feel, and I had company. Oh, yes. ‘Can you tap, then? If you can shut the door, you must be able to tap.' I stood there and listened to the soft, isolated drips from the pipes. There was nothing else. I was reaching out for the lightswitch again when there was a soft thud from not far below me. The cellar of Sara Laughs is high, and the upper three feet of the concrete the part which lies against the ground's frost-belt had been insulated with big silver-backed panels of Insu-Gard. The sound that I heard was, I am quite sure, a fist striking against one of these. Just a fist hitting a square of insulation, but every gut and muscle of my body seemed to come unwound. My hair stood up. My eyesockets seemed to be expanding and my eyeballs contracting, as if my head were trying to turn into a skull. Every inch of my skin broke out in gooseflesh. Something was in here with me. Very likely something dead. I could no longer have turned on the light if I'd wanted to. I no longer had the strength to raise my arm. I tried to talk, and at last, in a husky whisper I hardly recognized, I said: ‘Are you really there?' Thud. ‘Who are you?' I could still do no better than that husky whisper, the voice of a man giving last instructions to his family as he lies on his deathbed. This time there was nothing from below. I tried to think, and what came to my struggling mind was Tony Curtis as Harry Houdini in some old movie. According to the film, Houdini had been the Diogenes of the Ouija board circuit, a guy who spent his spare time just looking for an honest medium. He'd attended one s? ¦ance where the dead communicated by ‘Tap once for yes, twice for no,' I said. ‘Can you do that?' Thud. It was on the stairs below me . . . but not too far below. Five steps down, six or seven at most. Not quite close enough to touch if I should reach out and wave my hand in the black basement air . . . a thing I could imagine, but not actually imagine doing. ‘Are you . . . ‘ My voice trailed off. There was simply no strength in my diaphragm. Chilly air lay on my chest like a flatiron. I gathered all my will and tried again. ‘Are you Jo?' Thud. That soft fist on the insulation. A pause, and then: Thud-thud. Yes and no. Then, with no idea why I was asking such an inane question: ‘Are the owls down here?' Thud-thud. ‘Do you know where they are?' Thud. ‘Should I look for them?' Thud! Very hard. Why did she want them? I could ask, but the thing on the stairs had no way to an Hot fingers touched my eyes and I almost screamed before realizing it was sweat. I raised my hands in the dark and wiped the heels of them up my face to the hairline. They skidded as if on oil. Cold or not, I was all but bathing in my own sweat. ‘Are you Lance Devore?' Thud-thud, at once. ‘Is it safe for me at Sara? Am I safe?' Thud. A pause. And I knew it was a pause, that the thing on the stairs wasn't finished. Then: Thud-thud. Yes, I was safe. No, I wasn't safe. I had regained marginal control of my arm. I reached out, felt along the wall, and found the lightswitch. I settled my fingers on it. Now the sweat on my face felt as if it were turning to ice. ‘Are you the person who cries in the night?' I asked. Thud-thud from below me, and between the two thuds, I flicked the switch. The cellar globes came on. So did a brilliant hanging bulb at least a hundred and twenty-five watts over the landing. There was no time for anyone to hide, let alone get away, and no one there to try, either. Also, Mrs. Meserve admirable in so many ways had neglected to sweep the cellar stairs. When I went down to where I estimated the thudding sounds had been coming from, I left tracks in the light dust. But mine were the only ones. I blew out breath in front of me and could see it. So it had been cold, still was cold . . . but it was warming up fast. I blew out another breath and could see just a hint of fog. A third exhale and there was nothing. I ran my palm over one of the insulated squares. Smooth. I pushed a finger at it, and although I didn't push with any real force, my finger left a dimple in the silvery surface. Easy as pie. If someone had been thumping a fist down here, this stuff should be pitted, the thin silver skin perhaps even broken to reveal the pink fill underneath. But all the squares were smooth. ‘Are you still there?' I asked. No response, and yet I had a sense that my visitor was still there. Somewhere. ‘I hope I didn't offend you by turning on the light,' I said, and now I did feel slightly odd, standing on my cellar stairs and talking out loud, sermonizing to the spiders. ‘I wanted to see you if I could.' I had no idea if that was true or not. Suddenly so suddenly I almost lost my balance and tumbled down the stairs I whirled around, convinced the shroud-creature was behind me, that it had been the thing knocking, it, no polite M. R. James ghost but a horror from around the rim of the universe. There was nothing. I turned around again, took two or three deep, steadying breaths, and then went the rest of the way down the cellar stairs. Beneath them was a perfectly serviceable canoe, complete with paddle. In the corner was the gas stove we'd replaced after buying the place; also the claw-foot tub Jo had wanted (over my objections) to turn into a planter. I found a trunk filled with vaguely recalled table-linen, a box of mildewy cassette tapes (groups like the Delfonics, Funkadelic, and. 38 Special), several cartons of old dishes. There was a life down here, but ultimately not a very interesting one. Unlike the life I'd sensed in Jo's studio, this one hadn't been cut short but evolved out of, shed like old skin, and that was all right. Was, in fact, the natural order of things. There was a photo album on a shelf of knickknacks and I took it down, both curious and wary. No bombshells this time, however; nearly all the pix were landscape shots of Sara Laughs as it had been when we bought it. I found a picture of Jo in bellbottoms, though (her hair parted in the middle and white lipstick on her mouth), and one of Michael Noonan wearing a flowered shirt and muttonchop sideburns that made me cringe (the bachelor Mike in the photo was a Barry White kind of guy I didn't want to recognize and yet did). I found Jo's old broken treadmill, a rake I'd want if I was still around here come fall, a snowblower I'd want even more if I was around come winter, and several cans of paint. What I didn't find was any plastic owls. My insulation-thumping friend had been right. Upstairs the telephone started ringing. I hurried to answer it, going out through the cellar door and then reaching back in to flick off the lightswitch. This amused me and at the same time seemed like perfectly normal behavior . . . just as being careful not to step on sidewalk cracks had seemed like perfectly normal behavior to me when I was a kid. And even if it wasn't normal, what did it matter? I'd only been back at Sara for three days, but already I'd postulated Noonan's First Law of Eccentricity: when you're on your own, strange behavior really doesn't seem strange at all. I snagged the cordless. ‘Hello?' ‘Hi, Mike. It's Ward.' ‘That was quick.' ‘The file-room's just a short walk down the hall,' he said. ‘Easy as pie. There's only one thing on Jo's calendar for the second week of November in 1993. It says ‘S-Ks of Maine, Freep, 11 A.M.' That's on Tuesday the sixteenth. Does it help?' ‘Yes,' I said. ‘Thank you, Ward. It helps a lot.' I broke the connection and put the phone back in its cradle. Yes, it helped. S-Ks of Maine was Soup Kitchens of Maine. Jo had been on their board of directors from 1992 until her death. Freep was Freeport. It must have been a board meeting. They had probably discussed plans for feeding the homeless on Thanksgiving . . . and then Jo had driven the seventy or so miles to the TR in order to take delivery of two plastic owls. It didn't answer all the questions, but aren't there always questions in the wake of a loved one's death? And no statute of limitations on when they come up. The UFO voice spoke up then. While you're right here by the phone, it said, why not call Bonnie Amudson? Say hi, see how she's doing? Jo had been on four different boards during the nineties, all of them doing charitable work. Her friend Bonnie had persuaded her onto the Soup Kitchens board when a seat fell vacant. They had gone to a lot of the meetings together. Not the one in November of 1993, presumably, and Bonnie could hardly be expected to remember that one particular meeting almost five years later . . . but if she'd saved her old minutes-of-the-meeting sheets . . . Exactly what the fuck was I thinking of? Calling Bonnie, making nice, then asking her to check her December 1993 minutes? Was I going to ask her if the attendance report had my wife absent from the November meeting? Was I going to ask if maybe Jo had seemed different that last year of her life? And when Bonnie asked me why I wanted to know, what would I say? Give me that, Jo had snarled in my dream of her. In the dream she hadn't looked like Jo at all, she'd looked like some other woman, maybe like the one in the Book of Proverbs, the strange woman whose lips were as honey but whose heart was full of gall and wormwood. A strange woman with fingers as cold as twigs after a frost. Give me that, it's my dust-catcher. I went to the cellar door and touched the knob. I turned it . . . then let it go. I didn't want to look down there into the dark, didn't want to risk the chance that something might start thumping again. It was better to leave that door shut. What I wanted was something cold to drink. I went into the kitchen, reached for the fridge door, then stopped. The magnets were back in a circle again, but this time four letters and one number had been pulled into the center and lined up there. They spelled a single lower-case word: hello There was something here. Even back in broad daylight I had no doubt of that. I'd asked if it was safe for me to be here and had received a mixed message . . . but that didn't matter. If I left Sara now, there was nowhere to go. I had a key to the house in Derry, but matters had to be resolved here. I knew that, too. ‘Hello,' I said, and opened the fridge to get a soda. ‘Whoever or whatever you are, hello.'

Cluster Analysis

Chapter 9 Cluster Analysis Learning Objectives After reading this chapter you should understand: – The basic concepts of cluster analysis. – How basic cluster algorithms work. – How to compute simple clustering results manually. – The different types of clustering procedures. – The SPSS clustering outputs. Keywords Agglomerative and divisive clustering A Chebychev distance A City-block distance A Clustering variables A Dendrogram A Distance matrix A Euclidean distance A Hierarchical and partitioning methods A Icicle diagram A k-means A Matching coef? cients A Pro? ing clusters A Two-step clustering Are there any market segments where Web-enabled mobile telephony is taking off in different ways? To answer this question, Okazaki (2006) applies a twostep cluster analysis by identifying segments of Internet adopters in Japan. The ? ndings suggest that there are four clusters exhibiting distinct attitudes towards Web-enabled mobile telephony adoption. In terestingly, freelance, and highly educated professionals had the most negative perception of mobile Internet adoption, whereas clerical of? ce workers had the most positive perception.Furthermore, housewives and company executives also exhibited a positive attitude toward mobile Internet usage. Marketing managers can now use these results to better target speci? c customer segments via mobile Internet services. Introduction Grouping similar customers and products is a fundamental marketing activity. It is used, prominently, in market segmentation. As companies cannot connect with all their customers, they have to divide markets into groups of consumers, customers, or clients (called segments) with similar needs and wants.Firms can then target each of these segments by positioning themselves in a unique segment (such as Ferrari in the high-end sports car market). While market researchers often form E. Mooi and M. Sarstedt, A Concise Guide to Market Research, DOI 10. 1007/978-3-642-1 2541-6_9, # Springer-Verlag Berlin Heidelberg 2011 237 238 9 Cluster Analysis market segments based on practical grounds, industry practice and wisdom, cluster analysis allows segments to be formed that are based on data that are less dependent on subjectivity.The segmentation of customers is a standard application of cluster analysis, but it can also be used in different, sometimes rather exotic, contexts such as evaluating typical supermarket shopping paths (Larson et al. 2005) or deriving employers’ branding strategies (Moroko and Uncles 2009). Understanding Cluster Analysis Cluster analysis is a convenient method for identifying homogenous groups of objects called clusters. Objects (or cases, observations) in a speci? c cluster share many characteristics, but are very dissimilar to objects not belonging to that cluster.Let’s try to gain a basic understanding of the cluster analysis procedure by looking at a simple example. Imagine that you are interested in segment ing your customer base in order to better target them through, for example, pricing strategies. The ? rst step is to decide on the characteristics that you will use to segment your customers. In other words, you have to decide which clustering variables will be included in the analysis. For example, you may want to segment a market based on customers’ price consciousness (x) and brand loyalty (y).These two variables can be measured on a 7-point scale with higher values denoting a higher degree of price consciousness and brand loyalty. The values of seven respondents are shown in Table 9. 1 and the scatter plot in Fig. 9. 1. The objective of cluster analysis is to identify groups of objects (in this case, customers) that are very similar with regard to their price consciousness and brand loyalty and assign them into clusters. After having decided on the clustering variables (brand loyalty and price consciousness), we need to decide on the clustering procedure to form our group s of objects.This step is crucial for the analysis, as different procedures require different decisions prior to analysis. There is an abundance of different approaches and little guidance on which one to use in practice. We are going to discuss the most popular approaches in market research, as they can be easily computed using SPSS. These approaches are: hierarchical methods, partitioning methods (more precisely, k-means), and two-step clustering, which is largely a combination of the ? rst two methods.Each of these procedures follows a different approach to grouping the most similar objects into a cluster and to determining each object’s cluster membership. In other words, whereas an object in a certain cluster should be as similar as possible to all the other objects in the Table 9. 1 Data Customer x y A 3 7 B 6 7 C 5 6 D 3 5 E 6 5 F 4 3 G 1 2 Understanding Cluster Analysis 7 6 A C D E B 239 Brand loyalty (y) 5 4 3 2 1 0 0 1 2 G F 3 4 5 6 7 Price consciousness (x) Fig. 9. 1 Scatter plot same cluster, it should likewise be as distinct as possible from objects in different clusters. But how do we measure similarity?Some approaches – most notably hierarchical methods – require us to specify how similar or different objects are in order to identify different clusters. Most software packages calculate a measure of (dis)similarity by estimating the distance between pairs of objects. Objects with smaller distances between one another are more similar, whereas objects with larger distances are more dissimilar. An important problem in the application of cluster analysis is the decision regarding how many clusters should be derived from the data. This question is explored in the next step of the analysis.Sometimes, however, we already know the number of segments that have to be derived from the data. For example, if we were asked to ascertain what characteristics distinguish frequent shoppers from infrequent ones, we need to ? nd two different c lusters. However, we do not usually know the exact number of clusters and then we face a trade-off. On the one hand, you want as few clusters as possible to make them easy to understand and actionable. On the other hand, having many clusters allows you to identify more segments and more subtle differences between segments.In an extreme case, you can address each individual separately (called one-to-one marketing) to meet consumers’ varying needs in the best possible way. Examples of such a micro-marketing strategy are Puma’s Mongolian Shoe BBQ (www. mongolianshoebbq. puma. com) and Nike ID (http://nikeid. nike. com), in which customers can fully customize a pair of shoes in a hands-on, tactile, and interactive shoe-making experience. On the other hand, the costs associated with such a strategy may be prohibitively high in many 240 9 Cluster Analysis Decide on the clustering variables Decide on the clustering procedureHierarchical methods Select a measure of similarity or dissimilarity Partitioning methods Two-step clustering Select a measure of similarity or dissimilarity Choose a clustering algorithm Decide on the number of clusters Validate and interpret the cluster solution Fig. 9. 2 Steps in a cluster analysis business contexts. Thus, we have to ensure that the segments are large enough to make the targeted marketing programs pro? table. Consequently, we have to cope with a certain degree of within-cluster heterogeneity, which makes targeted marketing programs less effective.In the ? nal step, we need to interpret the solution by de? ning and labeling the obtained clusters. This can be done by examining the clustering variables’ mean values or by identifying explanatory variables to pro? le the clusters. Ultimately, managers should be able to identify customers in each segment on the basis of easily measurable variables. This ? nal step also requires us to assess the clustering solution’s stability and validity. Figure 9. 2 illu strates the steps associated with a cluster analysis; we will discuss these in more detail in the following sections.Conducting a Cluster Analysis Decide on the Clustering Variables At the beginning of the clustering process, we have to select appropriate variables for clustering. Even though this choice is of utmost importance, it is rarely treated as such and, instead, a mixture of intuition and data availability guide most analyses in marketing practice. However, faulty assumptions may lead to improper market Conducting a Cluster Analysis 241 segments and, consequently, to de? cient marketing strategies. Thus, great care should be taken when selecting the clustering variables. There are several types of clustering variables and these can be classi? d into general (independent of products, services or circumstances) and speci? c (related to both the customer and the product, service and/or particular circumstance), on the one hand, and observable (i. e. , measured directly) and un observable (i. e. , inferred) on the other. Table 9. 2 provides several types and examples of clustering variables. Table 9. 2 Types and examples of clustering variables General Observable (directly Cultural, geographic, demographic, measurable) socio-economic Unobservable Psychographics, values, personality, (inferred) lifestyle Adapted from Wedel and Kamakura (2000)Speci? c User status, usage frequency, store and brand loyalty Bene? ts, perceptions, attitudes, intentions, preferences The types of variables used for cluster analysis provide different segments and, thereby, in? uence segment-targeting strategies. Over the last decades, attention has shifted from more traditional general clustering variables towards product-speci? c unobservable variables. The latter generally provide better guidance for decisions on marketing instruments’ effective speci? cation. It is generally acknowledged that segments identi? ed by means of speci? unobservable variables are usually more h omogenous and their consumers respond consistently to marketing actions (see Wedel and Kamakura 2000). However, consumers in these segments are also frequently hard to identify from variables that are easily measured, such as demographics. Conversely, segments determined by means of generally observable variables usually stand out due to their identi? ability but often lack a unique response structure. 1 Consequently, researchers often combine different variables (e. g. , multiple lifestyle characteristics combined with demographic variables), bene? ing from each ones strengths. In some cases, the choice of clustering variables is apparent from the nature of the task at hand. For example, a managerial problem regarding corporate communications will have a fairly well de? ned set of clustering variables, including contenders such as awareness, attitudes, perceptions, and media habits. However, this is not always the case and researchers have to choose from a set of candidate variable s. Whichever clustering variables are chosen, it is important to select those that provide a clear-cut differentiation between the segments regarding a speci? c managerial objective. More precisely, criterion validity is of special interest; that is, the extent to which the â€Å"independent† clustering variables are associated with 1 2 See Wedel and Kamakura (2000). Tonks (2009) provides a discussion of segment design and the choice of clustering variables in consumer markets. 242 9 Cluster Analysis one or more â€Å"dependent† variables not included in the analysis. Given this relationship, there should be signi? cant differences between the â€Å"dependent† variable(s) across the clusters. These associations may or may not be causal, but it is essential that the clustering variables distinguish the â€Å"dependent† variable(s) signi? antly. Criterion variables usually relate to some aspect of behavior, such as purchase intention or usage frequency. Gen erally, you should avoid using an abundance of clustering variables, as this increases the odds that the variables are no longer dissimilar. If there is a high degree of collinearity between the variables, they are not suf? ciently unique to identify distinct market segments. If highly correlated variables are used for cluster analysis, speci? c aspects covered by these variables will be overrepresented in the clustering solution.In this regard, absolute correlations above 0. 90 are always problematic. For example, if we were to add another variable called brand preference to our analysis, it would virtually cover the same aspect as brand loyalty. Thus, the concept of being attached to a brand would be overrepresented in the analysis because the clustering procedure does not differentiate between the clustering variables in a conceptual sense. Researchers frequently handle this issue by applying cluster analysis to the observations’ factor scores derived from a previously car ried out factor analysis.However, according to Dolnicar and Grâ‚ ¬n u (2009), this factor-cluster segmentation approach can lead to several problems: 1. The data are pre-processed and the clusters are identi? ed on the basis of transformed values, not on the original information, which leads to different results. 2. In factor analysis, the factor solution does not explain a certain amount of variance; thus, information is discarded before segments have been identi? ed or constructed. 3. Eliminating variables with low loadings on all the extracted factors means that, potentially, the most important pieces of information for the identi? ation of niche segments are discarded, making it impossible to ever identify such groups. 4. The interpretations of clusters based on the original variables become questionable given that the segments have been constructed using factor scores. Several studies have shown that the factor-cluster segmentation signi? cantly reduces the success of segmen t recovery. 3 Consequently, you should rather reduce the number of items in the questionnaire’s pre-testing phase, retaining a reasonable number of relevant, non-redundant questions that you believe differentiate the segments well.However, if you have your doubts about the data structure, factorclustering segmentation may still be a better option than discarding items that may conceptually be necessary. Furthermore, we should keep the sample size in mind. First and foremost, this relates to issues of managerial relevance as segments’ sizes need to be substantial to ensure that targeted marketing programs are pro? table. From a statistical perspective, every additional variable requires an over-proportional increase in 3 See the studies by Arabie and Hubert (1994), Sheppard (1996), or Dolnicar and Grâ‚ ¬n (2009). uConducting a Cluster Analysis 243 observations to ensure valid results. Unfortunately, there is no generally accepted rule of thumb regarding minimum sampl e sizes or the relationship between the objects and the number of clustering variables used. In a related methodological context, Formann (1984) recommends a sample size of at least 2m, where m equals the number of clustering variables. This can only provide rough guidance; nevertheless, we should pay attention to the relationship between the objects and clustering variables. It does not, for example, appear logical to cluster ten objects using ten variables.Keep in mind that no matter how many variables are used and no matter how small the sample size, cluster analysis will always render a result! Ultimately, the choice of clustering variables always depends on contextual in? uences such as data availability or resources to acquire additional data. Marketing researchers often overlook the fact that the choice of clustering variables is closely connected to data quality. Only those variables that ensure that high quality data can be used should be included in the analysis. This is v ery important if a segmentation solution has to be managerially useful.Furthermore, data are of high quality if the questions asked have a strong theoretical basis, are not contaminated by respondent fatigue or response styles, are recent, and thus re? ect the current market situation (Dolnicar and Lazarevski 2009). Lastly, the requirements of other managerial functions within the organization often play a major role. Sales and distribution may as well have a major in? uence on the design of market segments. Consequently, we have to be aware that subjectivity and common sense agreement will (and should) always impact the choice of clustering variables.Decide on the Clustering Procedure By choosing a speci? c clustering procedure, we determine how clusters are to be formed. This always involves optimizing some kind of criterion, such as minimizing the within-cluster variance (i. e. , the clustering variables’ overall variance of objects in a speci? c cluster), or maximizing th e distance between the objects or clusters. The procedure could also address the question of how to determine the (dis)similarity between objects in a newly formed cluster and the remaining objects in the dataset.There are many different clustering procedures and also many ways of classifying these (e. g. , overlapping versus non-overlapping, unimodal versus multimodal, exhaustive versus non-exhaustive). 4 A practical distinction is the differentiation between hierarchical and partitioning methods (most notably the k-means procedure), which we are going to discuss in the next sections. We also introduce two-step clustering, which combines the principles of hierarchical and partitioning methods and which has recently gained increasing attention from market research practice.See Wedel and Kamakura (2000), Dolnicar (2003), and Kaufman and Rousseeuw (2005) for a review of clustering techniques. 4 244 9 Cluster Analysis Hierarchical Methods Hierarchical clustering procedures are characte rized by the tree-like structure established in the course of the analysis. Most hierarchical techniques fall into a category called agglomerative clustering. In this category, clusters are consecutively formed from objects. Initially, this type of procedure starts with each object representing an individual cluster.These clusters are then sequentially merged according to their similarity. First, the two most similar clusters (i. e. , those with the smallest distance between them) are merged to form a new cluster at the bottom of the hierarchy. In the next step, another pair of clusters is merged and linked to a higher level of the hierarchy, and so on. This allows a hierarchy of clusters to be established from the bottom up. In Fig. 9. 3 (left-hand side), we show how agglomerative clustering assigns additional objects to clusters as the cluster size increases. Step 5 Step 1 A, B, C, D, EAgglomerative clustering Step 4 Step 2 Divisive clustering A, B C, D, E Step 3 Step 3 A, B C, D E Step 2 Step 4 A, B C D E Step 1 Step 5 A B C D E Fig. 9. 3 Agglomerative and divisive clustering A cluster hierarchy can also be generated top-down. In this divisive clustering, all objects are initially merged into a single cluster, which is then gradually split up. Figure 9. 3 illustrates this concept (right-hand side). As we can see, in both agglomerative and divisive clustering, a cluster on a higher level of the hierarchy always encompasses all clusters from a lower level.This means that if an object is assigned to a certain cluster, there is no possibility of reassigning this object to another cluster. This is an important distinction between these types of clustering and partitioning methods such as k-means, which we will explore in the next section. Divisive procedures are quite rarely used in market research. We therefore concentrate on the agglomerative clustering procedures. There are various types Conducting a Cluster Analysis 245 of agglomerative procedures. However, before we discuss these, we need to de? ne how similarities or dissimilarities are measured between pairs of objects.Select a Measure of Similarity or Dissimilarity There are various measures to express (dis)similarity between pairs of objects. A straightforward way to assess two objects’ proximity is by drawing a straight line between them. For example, when we look at the scatter plot in Fig. 9. 1, we can easily see that the length of the line connecting observations B and C is much shorter than the line connecting B and G. This type of distance is also referred to as Euclidean distance (or straight-line distance) and is the most commonly used type when it comes to analyzing ratio or interval-scaled data. In our example, we have ordinal data, but market researchers usually treat ordinal data as metric data to calculate distance metrics by assuming that the scale steps are equidistant (very much like in factor analysis, which we discussed in Chap. 8). To use a hierarchical c lustering procedure, we need to express these distances mathematically. By taking the data in Table 9. 1 into consideration, we can easily compute the Euclidean distance between customer B and customer C (generally referred to as d(B,C)) with regard to the two variables x and y by using the following formula: q Euclidean ? B; C? ? ? xB A xC ? 2 ? ?yB A yC ? 2 The Euclidean distance is the square root of the sum of the squared differences in the variables’ values. Using the data from Table 9. 1, we obtain the following: q p dEuclidean ? B; C? ? ? 6 A 5? 2 ? ?7 A 6? 2 ? 2 ? 1:414 This distance corresponds to the length of the line that connects objects B and C. In this case, we only used two variables but we can easily add more under the root sign in the formula. However, each additional variable will add a dimension to our research problem (e. . , with six clustering variables, we have to deal with six dimensions), making it impossible to represent the solution graphically. Si milarly, we can compute the distance between customer B and G, which yields the following: q p dEuclidean ? B; G? ? ? 6 A 1? 2 ? ?7 A 2? 2 ? 50 ? 7:071 Likewise, we can compute the distance between all other pairs of objects. All these distances are usually expressed by means of a distance matrix. In this distance matrix, the non-diagonal elements express the distances between pairs of objects 5Note that researchers also often use the squared Euclidean distance. 246 9 Cluster Analysis and zeros on the diagonal (the distance from each object to itself is, of course, 0). In our example, the distance matrix is an 8 A 8 table with the lines and rows representing the objects (i. e. , customers) under consideration (see Table 9. 3). As the distance between objects B and C (in this case 1. 414 units) is the same as between C and B, the distance matrix is symmetrical. Furthermore, since the distance between an object and itself is zero, one need only look at either the lower or upper non-di agonal elements.Table 9. 3 Euclidean distance matrix Objects A B A 0 B 3 0 C 2. 236 1. 414 D 2 3. 606 E 3. 606 2 F 4. 123 4. 472 G 5. 385 7. 071 C D E F G 0 2. 236 1. 414 3. 162 5. 657 0 3 2. 236 3. 606 0 2. 828 5. 831 0 3. 162 0 There are also alternative distance measures: The city-block distance uses the sum of the variables’ absolute differences. This is often called the Manhattan metric as it is akin to the walking distance between two points in a city like New York’s Manhattan district, where the distance equals the number of blocks in the directions North-South and East-West.Using the city-block distance to compute the distance between customers B and C (or C and B) yields the following: dCityAblock ? B; C? ? jxB A xC j ? jyB A yC j ? j6 A 5j ? j7 A 6j ? 2 The resulting distance matrix is in Table 9. 4. Table 9. 4 City-block distance matrix Objects A B A 0 B 3 0 C 3 2 D 2 5 E 5 2 F 5 6 G 7 10 C D E F G 0 3 2 4 8 0 3 3 5 0 4 8 0 4 0 Lastly, when working with metr ic (or ordinal) data, researchers frequently use the Chebychev distance, which is the maximum of the absolute difference in the clustering variables’ values. In respect of customers B and C, this result is: dChebychec ? B; C? max? jxB A xC j; jyB A yC j? ? max? j6 A 5j; j7 A 6j? ? 1 Figure 9. 4 illustrates the interrelation between these three distance measures regarding two objects, C and G, from our example. Conducting a Cluster Analysis 247 C Brand loyalty (y) Euclidean distance City-block distance G Chebychev distance Price consciousness (x) Fig. 9. 4 Distance measures There are other distance measures such as the Angular, Canberra or Mahalanobis distance. In many situations, the latter is desirable as it compensates for collinearity between the clustering variables. However, it is (unfortunately) not menu-accessible in SPSS.In many analysis tasks, the variables under consideration are measured on different scales or levels. This would be the case if we extended our set o f clustering variables by adding another ordinal variable representing the customers’ income measured by means of, for example, 15 categories. Since the absolute variation of the income variable would be much greater than the variation of the remaining two variables (remember, that x and y are measured on 7-point scales), this would clearly distort our analysis results. We can resolve this problem by standardizing the data prior to the analysis.Different standardization methods are available, such as the simple z standardization, which rescales each variable to have a mean of 0 and a standard deviation of 1 (see Chap. 5). In most situations, however, standardization by range (e. g. , to a range of 0 to 1 or A1 to 1) performs better. 6 We recommend standardizing the data in general, even though this procedure can reduce or in? ate the variables’ in? uence on the clustering solution. 6 See Milligan and Cooper (1988). 248 9 Cluster Analysis Another way of (implicitly) sta ndardizing the data is by using the correlation between the objects instead of distance measures.For example, suppose a respondent rated price consciousness 2 and brand loyalty 3. Now suppose a second respondent indicated 5 and 6, whereas a third rated these variables 3 and 3. Euclidean, city-block, and Chebychev distances would indicate that the ? rst respondent is more similar to the third than to the second. Nevertheless, one could convincingly argue that the ? rst respondent’s ratings are more similar to the second’s, as both rate brand loyalty higher than price consciousness. This can be accounted for by computing the correlation between two vectors of values as a measure of similarity (i. . , high correlation coef? cients indicate a high degree of similarity). Consequently, similarity is no longer de? ned by means of the difference between the answer categories but by means of the similarity of the answering pro? les. Using correlation is also a way of standardiz ing the data implicitly. Whether you use correlation or one of the distance measures depends on whether you think the relative magnitude of the variables within an object (which favors correlation) matters more than the relative magnitude of each variable across objects (which favors distance).However, it is generally recommended that one uses correlations when applying clustering procedures that are susceptible to outliers, such as complete linkage, average linkage or centroid (see next section). Whereas the distance measures presented thus far can be used for metrically and – in general – ordinally scaled data, applying them to nominal or binary data is meaningless. In this type of analysis, you should rather select a similarity measure expressing the degree to which variables’ values share the same category. These socalled matching coef? ients can take different forms but rely on the same allocation scheme shown in Table 9. 5. Table 9. 5 Allocation scheme for matching coef? cients Number of variables with category 1 a c Object 1 Number of variables with category 2 b d Object 2 Number of variables with category 1 Number of variables with category 2 Based on the allocation scheme in Table 9. 5, we can compute different matching coef? cients, such as the simple matching coef? cient (SM): SM ? a? d a? b? c? d This coef? cient is useful when both positive and negative values carry an equal degree of information.For example, gender is a symmetrical attribute because the number of males and females provides an equal degree of information. Conducting a Cluster Analysis 249 Let’s take a look at an example by assuming that we have a dataset with three binary variables: gender (male ? 1, female ? 2), customer (customer ? 1, noncustomer ? 2), and disposable income (low ? 1, high ? 2). The ? rst object is a male non-customer with a high disposable income, whereas the second object is a female non-customer with a high disposable income. Accord ing to the scheme in Table 9. , a ? b ? 0, c ? 1 and d ? 2, with the simple matching coef? cient taking a value of 0. 667. Two other types of matching coef? cients, which do not equate the joint absence of a characteristic with similarity and may, therefore, be of more value in segmentation studies, are the Jaccard (JC) and the Russel and Rao (RR) coef? cients. They are de? ned as follows: a JC ? a? b? c a RR ? a? b? c? d These matching coef? cients are – just like the distance measures – used to determine a cluster solution. There are many other matching coef? ients such as Yule’s Q, Kulczynski or Ochiai, but since most applications of cluster analysis rely on metric or ordinal data, we will not discuss these in greater detail. 7 For nominal variables with more than two categories, you should always convert the categorical variable into a set of binary variables in order to use matching coef? cients. When you have ordinal data, you should always use distance me asures such as Euclidean distance. Even though using matching coef? cients would be feasible and – from a strictly statistical standpoint – even more appropriate, you would disregard variable information in the sequence of the categories.In the end, a respondent who indicates that he or she is very loyal to a brand is going to be closer to someone who is somewhat loyal than a respondent who is not loyal at all. Furthermore, distance measures best represent the concept of proximity, which is fundamental to cluster analysis. Most datasets contain variables that are measured on multiple scales. For example, a market research questionnaire may ask about the respondent’s income, product ratings, and last brand purchased. Thus, we have to consider variables measured on a ratio, ordinal, and nominal scale. How can we simultaneously incorporate these variables into one analysis?Unfortunately, this problem cannot be easily resolved and, in fact, many market researchers s imply ignore the scale level. Instead, they use one of the distance measures discussed in the context of metric (and ordinal) data. Even though this approach may slightly change the results when compared to those using matching coef? cients, it should not be rejected. Cluster analysis is mostly an exploratory technique whose results provide a rough guidance for managerial decisions. Despite this, there are several procedures that allow a simultaneous integration of these variables into one analysis. 7See Wedel and Kamakura (2000) for more information on alternative matching coef? cients. 250 9 Cluster Analysis First, we could compute distinct distance matrices for each group of variables; that is, one distance matrix based on, for example, ordinally scaled variables and another based on nominal variables. Afterwards, we can simply compute the weighted arithmetic mean of the distances and use this average distance matrix as the input for the cluster analysis. However, the weights hav e to be determined a priori and improper weights may result in a biased treatment of different variable types.Furthermore, the computation and handling of distance matrices are not trivial. Using the SPSS syntax, one has to manually add the MATRIX subcommand, which exports the initial distance matrix into a new data ? le. Go to the 8 Web Appendix (! Chap. 5) to learn how to modify the SPSS syntax accordingly. Second, we could dichotomize all variables and apply the matching coef? cients discussed above. In the case of metric variables, this would involve specifying categories (e. g. , low, medium, and high income) and converting these into sets of binary variables. In most cases, however, the speci? ation of categories would be rather arbitrary and, as mentioned earlier, this procedure could lead to a severe loss of information. In the light of these issues, you should avoid combining metric and nominal variables in a single cluster analysis, but if this is not feasible, the two-ste p clustering procedure provides a valuable alternative, which we will discuss later. Lastly, the choice of the (dis)similarity measure is not extremely critical to recovering the underlying cluster structure. In this regard, the choice of the clustering algorithm is far more important.We therefore deal with this aspect in the following section. Select a Clustering Algorithm After having chosen the distance or similarity measure, we need to decide which clustering algorithm to apply. There are several agglomerative procedures and they can be distinguished by the way they de? ne the distance from a newly formed cluster to a certain object, or to other clusters in the solution. The most popular agglomerative clustering procedures include the following: l l l l Single linkage (nearest neighbor): The distance between two clusters corresponds to the shortest distance between any two members in the two clusters.Complete linkage (furthest neighbor): The oppositional approach to single linka ge assumes that the distance between two clusters is based on the longest distance between any two members in the two clusters. Average linkage: The distance between two clusters is de? ned as the average distance between all pairs of the two clusters’ members. Centroid: In this approach, the geometric center (centroid) of each cluster is computed ? rst. The distance between the two clusters equals the distance between the two centroids. Figures 9. 5–9. 8 illustrate these linkage procedures for two randomly framed clusters.Conducting a Cluster Analysis Fig. 9. 5 Single linkage 251 Fig. 9. 6 Complete linkage Fig. 9. 7 Average linkage Fig. 9. 8 Centroid 252 9 Cluster Analysis Each of these linkage algorithms can yield totally different results when used on the same dataset, as each has its speci? c properties. As the single linkage algorithm is based on minimum distances, it tends to form one large cluster with the other clusters containing only one or few objects each. We can make use of this â€Å"chaining effect† to detect outliers, as these will be merged with the remaining objects – usually at very large distances – in the last steps of the analysis.Generally, single linkage is considered the most versatile algorithm. Conversely, the complete linkage method is strongly affected by outliers, as it is based on maximum distances. Clusters produced by this method are likely to be rather compact and tightly clustered. The average linkage and centroid algorithms tend to produce clusters with rather low within-cluster variance and similar sizes. However, both procedures are affected by outliers, though not as much as complete linkage. Another commonly used approach in hierarchical clustering is Ward’s method. This approach does not combine the two most similar objects successively.Instead, those objects whose merger increases the overall within-cluster variance to the smallest possible degree, are combined. If you expect s omewhat equally sized clusters and the dataset does not include outliers, you should always use Ward’s method. To better understand how a clustering algorithm works, let’s manually examine some of the single linkage procedure’s calculation steps. We start off by looking at the initial (Euclidean) distance matrix in Table 9. 3. In the very ? rst step, the two objects exhibiting the smallest distance in the matrix are merged.Note that we always merge those objects with the smallest distance, regardless of the clustering procedure (e. g. , single or complete linkage). As we can see, this happens to two pairs of objects, namely B and C (d(B, C) ? 1. 414), as well as C and E (d(C, E) ? 1. 414). In the next step, we will see that it does not make any difference whether we ? rst merge the one or the other, so let’s proceed by forming a new cluster, using objects B and C. Having made this decision, we then form a new distance matrix by considering the single link age decision rule as discussed above.According to this rule, the distance from, for example, object A to the newly formed cluster is the minimum of d(A, B) and d(A, C). As d(A, C) is smaller than d(A, B), the distance from A to the newly formed cluster is equal to d(A, C); that is, 2. 236. We also compute the distances from cluster [B,C] (clusters are indicated by means of squared brackets) to all other objects (i. e. D, E, F, G) and simply copy the remaining distances – such as d(E, F) – that the previous clustering has not affected. This yields the distance matrix shown in Table 9. 6.Continuing the clustering procedure, we simply repeat the last step by merging the objects in the new distance matrix that exhibit the smallest distance (in this case, the newly formed cluster [B, C] and object E) and calculate the distance from this cluster to all other objects. The result of this step is described in Table 9. 7. Try to calculate the remaining steps yourself and compare your solution with the distance matrices in the following Tables 9. 8–9. 10. Conducting a Cluster Analysis Table 9. 6 Distance matrix after ? rst clustering step (single linkage) Objects A B, C D E F G A 0 B, C 2. 36 0 D 2 2. 236 0 E 3. 606 1. 414 3 0 F 4. 123 3. 162 2. 236 2. 828 0 G 5. 385 5. 657 3. 606 5. 831 3. 162 0 253 Table 9. 7 Distance matrix after second clustering step (single linkage) Objects A B, C, E D F G A 0 B, C, E 2. 236 0 D 2 2. 236 0 F 4. 123 2. 828 2. 236 0 G 5. 385 5. 657 3. 606 3. 162 0 Table 9. 8 Distance matrix after third clustering step (single linkage) Objects A, D B, C, E F G A, D 0 B, C, E 2. 236 0 F 2. 236 2. 828 0 G 3. 606 5. 657 3. 162 0 Table 9. 9 Distance matrix after fourth clustering step (single linkage) Objects A, B, C, D, E F G A, B, C, D, E 0 F 2. 236 0 G 3. 06 3. 162 0 Table 9. 10 Distance matrix after ? fth clustering step (single linkage) Objects A, B, C, D, E, F G A, B, C, D, E, F 0 G 3. 162 0 By following the single linkage proce dure, the last steps involve the merger of cluster [A,B,C,D,E,F] and object G at a distance of 3. 162. Do you get the same results? As you can see, conducting a basic cluster analysis manually is not that hard at all – not if there are only a few objects in the dataset. A common way to visualize the cluster analysis’s progress is by drawing a dendrogram, which displays the distance level at which there was a ombination of objects and clusters (Fig. 9. 9). We read the dendrogram from left to right to see at which distance objects have been combined. For example, according to our calculations above, objects B, C, and E are combined at a distance level of 1. 414. 254 B C E A D F G 9 Cluster Analysis 0 1 2 Distance 3 Fig. 9. 9 Dendrogram Decide on the Number of Clusters An important question we haven’t yet addressed is how to decide on the number of clusters to retain from the data. Unfortunately, hierarchical methods provide only very limited guidance for making th is decision.The only meaningful indicator relates to the distances at which the objects are combined. Similar to factor analysis’s scree plot, we can seek a solution in which an additional combination of clusters or objects would occur at a greatly increased distance. This raises the issue of what a great distance is, of course. One potential way to solve this problem is to plot the number of clusters on the x-axis (starting with the one-cluster solution at the very left) against the distance at which objects or clusters are combined on the y-axis.Using this plot, we then search for the distinctive break (elbow). SPSS does not produce this plot automatically – you have to use the distances provided by SPSS to draw a line chart by using a common spreadsheet program such as Microsoft Excel. Alternatively, we can make use of the dendrogram which essentially carries the same information. SPSS provides a dendrogram; however, this differs slightly from the one presented in F ig. 9. 9. Speci? cally, SPSS rescales the distances to a range of 0–25; that is, the last merging step to a one-cluster solution takes place at a (rescaled) distance of 25.The rescaling often lengthens the merging steps, thus making breaks occurring at a greatly increased distance level more obvious. Despite this, this distance-based decision rule does not work very well in all cases. It is often dif? cult to identify where the break actually occurs. This is also the case in our example above. By looking at the dendrogram, we could justify a two-cluster solution ([A,B,C,D,E,F] and [G]), as well as a ? ve-cluster solution ([B,C,E], [A], [D], [F], [G]). Conducting a Cluster Analysis 255 Research has suggested several other procedures for determining the number of clusters in a dataset.Most notably, the variance ratio criterion (VRC) by Calinski and Harabasz (1974) has proven to work well in many situations. 8 For a solution with n objects and k segments, the criterion is given by: VRCk ? ?SSB =? k A 1 =? SSW =? n A k ; where SSB is the sum of the squares between the segments and SSW is the sum of the squares within the segments. The criterion should seem familiar, as this is nothing but the F-value of a one-way ANOVA, with k representing the factor levels. Consequently, the VRC can easily be computed using SPSS, even though it is not readily available in the clustering procedures’ outputs.To ? nally determine the appropriate number of segments, we compute ok for each segment solution as follows: ok ? ?VRCk? 1 A VRCk ? A ? VRCk A VRCkA1 ? : In the next step, we choose the number of segments k that minimizes the value in ok. Owing to the term VRCkA1, the minimum number of clusters that can be selected is three, which is a clear disadvantage of the criterion, thus limiting its application in practice. Overall, the data can often only provide rough guidance regarding the number of clusters you should select; consequently, you should rather revert to pr actical considerations.Occasionally, you might have a priori knowledge, or a theory on which you can base your choice. However, ? rst and foremost, you should ensure that your results are interpretable and meaningful. Not only must the number of clusters be small enough to ensure manageability, but each segment should also be large enough to warrant strategic attention. Partitioning Methods: k-means Another important group of clustering procedures are partitioning methods. As with hierarchical clustering, there is a wide array of different algorithms; of these, the k-means procedure is the most important one for market research. The k-means algorithm follows an entirely different concept than the hierarchical methods discussed before. This algorithm is not based on distance measures such as Euclidean distance or city-block distance, but uses the within-cluster variation as a Milligan and Cooper (1985) compare various criteria. Note that the k-means algorithm is one of the simplest n on-hierarchical clustering methods. Several extensions, such as k-medoids (Kaufman and Rousseeuw 2005) have been proposed to handle problematic aspects of the procedure. More advanced methods include ? ite mixture models (McLachlan and Peel 2000), neural networks (Bishop 2006), and self-organizing maps (Kohonen 1982). Andrews and Currim (2003) discuss the validity of some of these approaches. 9 8 256 9 Cluster Analysis measure to form homogenous clusters. Speci? cally, the procedure aims at segmenting the data in such a way that the within-cluster variation is minimized. Consequently, we do not need to decide on a distance measure in the ? rst step of the analysis. The clustering process starts by randomly assigning objects to a number of clusters. 0 The objects are then successively reassigned to other clusters to minimize the within-cluster variation, which is basically the (squared) distance from each observation to the center of the associated cluster. If the reallocation of an object to another cluster decreases the within-cluster variation, this object is reassigned to that cluster. With the hierarchical methods, an object remains in a cluster once it is assigned to it, but with k-means, cluster af? liations can change in the course of the clustering process. Consequently, k-means does not build a hierarchy as described before (Fig. . 3), which is why the approach is also frequently labeled as non-hierarchical. For a better understanding of the approach, let’s take a look at how it works in practice. Figs. 9. 10–9. 13 illustrate the k-means clustering process. Prior to analysis, we have to decide on the number of clusters. Our client could, for example, tell us how many segments are needed, or we may know from previous research what to look for. Based on this information, the algorithm randomly selects a center for each cluster (step 1). In our example, two cluster centers are randomly initiated, which CC1 (? st cluster) and CC2 (second clu ster) in Fig. 9. 10 A CC1 C B D E Brand loyalty (y) CC2 F G Price consciousness (x) Fig. 9. 10 k-means procedure (step 1) 10 Note this holds for the algorithms original design. SPSS does not choose centers randomly. Conducting a Cluster Analysis A CC1 C B 257 D E Brand loyalty (y) CC2 F G Price consciousness (x) Fig. 9. 11 k-means procedure (step 2) A CC1 CC1? C B Brand loyalty (y) D E CC2 CC2? F G Price consciousness (x) Fig. 9. 12 k-means procedure (step 3) 258 A CC1? 9 Cluster Analysis B C Brand loyalty (y) D E CC2? F G Price consciousness (x) Fig. 9. 13 k-means procedure (step 4) epresent. 11 After this (step 2), Euclidean distances are computed from the cluster centers to every single object. Each object is then assigned to the cluster center with the shortest distance to it. In our example (Fig. 9. 11), objects A, B, and C are assigned to the ? rst cluster, whereas objects D, E, F, and G are assigned to the second. We now have our initial partitioning of the objects into two c lusters. Based on this initial partition, each cluster’s geometric center (i. e. , its centroid) is computed (third step). This is done by computing the mean values of the objects contained in the cluster (e. . , A, B, C in the ? rst cluster) regarding each of the variables (price consciousness and brand loyalty). As we can see in Fig. 9. 12, both clusters’ centers now shift into new positions (CC1’ for the ? rst and CC2’ for the second cluster). In the fourth step, the distances from each object to the newly located cluster centers are computed and objects are again assigned to a certain cluster on the basis of their minimum distance to other cluster centers (CC1’ and CC2’). Since the cluster centers’ position changed with respect to the initial situation in the ? st step, this could lead to a different cluster solution. This is also true of our example, as object E is now – unlike in the initial partition – closer to t he ? rst cluster center (CC1’) than to the second (CC2’). Consequently, this object is now assigned to the ? rst cluster (Fig. 9. 13). The k-means procedure now repeats the third step and re-computes the cluster centers of the newly formed clusters, and so on. In other 11 Conversely, SPSS always sets one observation as the cluster center instead of picking some random point in the dataset. Conducting a Cluster Analysis 59 words, steps 3 and 4 are repeated until a predetermined number of iterations are reached, or convergence is achieved (i. e. , there is no change in the cluster af? liations). Generally, k-means is superior to hierarchical methods as it is less affected by outliers and the presence of irrelevant clustering variables. Furthermore, k-means can be applied to very large datasets, as the procedure is less computationally demanding than hierarchical methods. In fact, we suggest de? nitely using k-means for sample sizes above 500, especially if many clusterin g variables are used.From a strictly statistical viewpoint, k-means should only be used on interval or ratioscaled data as the procedure relies on Euclidean distances. However, the procedure is routinely used on ordinal data as well, even though there might be some distortions. One problem associated with the application of k-means relates to the fact that the researcher has to pre-specify the number of clusters to retain from the data. This makes k-means less attractive to some and still hinders its routine application in practice. However, the VRC discussed above can likewise be used for k-means clustering an application of this index can be found in the 8 Web Appendix ! Chap. 9). Another workaround that many market researchers routinely use is to apply a hierarchical procedure to determine the number of clusters and k-means afterwards. 12 This also enables the user to ? nd starting values for the initial cluster centers to handle a second problem, which relates to the procedureâ €™s sensitivity to the initial classi? cation (we will follow this approach in the example application). Two-Step Clustering We have already discussed the issue of analyzing mixed variables measured on different scale levels in this chapter.The two-step cluster analysis developed by Chiu et al. (2001) has been speci? cally designed to handle this problem. Like k-means, the procedure can also effectively cope with very large datasets. The name two-step clustering is already an indication that the algorithm is based on a two-stage approach: In the ? rst stage, the algorithm undertakes a procedure that is very similar to the k-means algorithm. Based on these results, the two-step procedure conducts a modi? ed hierarchical agglomerative clustering procedure that combines the objects sequentially to form homogenous clusters.This is done by building a so-called cluster feature tree whose â€Å"leaves† represent distinct objects in the dataset. The procedure can handle categoric al and continuous variables simultaneously and offers the user the ? exibility to specify the cluster numbers as well as the maximum number of clusters, or to allow the technique to automatically choose the number of clusters on the basis of statistical evaluation criteria. Likewise, the procedure guides the decision of how many clusters to retain from the data by calculating measures-of-? t such as Akaike’s Information Criterion (AIC) or Bayes 2 See Punji and Stewart (1983) for additional information on this sequential approach. 260 9 Cluster Analysis Information Criterion (BIC). Furthermore, the procedure indicates each variable’s importance for the construction of a speci? c cluster. These desirable features make the somewhat less popular two-step clustering a viable alternative to the traditional methods. You can ? nd a more detailed discussion of the two-step clustering procedure in the 8 Web Appendix (! Chap. 9), but we will also apply this method in the subseque nt example.Validate and Interpret the Cluster Solution Before interpreting the cluster solution, we have to assess the solution’s stability and validity. Stability is evaluated by using different clustering procedures on the same data and testing whether these yield the same results. In hierarchical clustering, you can likewise use different distance measures. However, please note that it is common for results to change even when your solution is adequate. How much variation you should allow before questioning the stability of your solution is a matter of taste.Another common approach is to split the dataset into two halves and to thereafter analyze the two subsets separately using the same parameter settings. You then compare the two solutions’ cluster centroids. If these do not differ signi? cantly, you can presume that the overall solution has a high degree of stability. When using hierarchical clustering, it is also worthwhile changing the order of the objects in y our dataset and re-running the analysis to check the results’ stability. The results should not, of course, depend on the order of the dataset. If they do, you should try to ascertain if any obvious outliers may in? ence the results of the change in order. Assessing the solution’s reliability is closely related to the above, as reliability refers to the degree to which the solution is stable over time. If segments quickly change their composition, or its members their behavior, targeting strategies are likely not to succeed. Therefore, a certain degree of stability is necessary to ensure that marketing strategies can be implemented and produce adequate results. This can be evaluated by critically revisiting and replicating the clustering results at a later point in time. To validate the clustering solution, we need to assess its criterion validity.In research, we could focus on criterion variables that have a theoretically based relationship with the clustering variabl es, but were not included in the analysis. In market research, criterion variables usually relate to managerial outcomes such as the sales per person, or satisfaction. If these criterion variables differ signi? cantly, we can conclude that the clusters are distinct groups with criterion validity. To judge validity, you should also assess face validity and, if possible, expert validity. While we primarily consider criterion validity when choosing clustering variables, as well as in this ? al step of the analysis procedure, the assessment of face validity is a process rather than a single event. The key to successful segmentation is to critically revisit the results of different cluster analysis set-ups (e. g. , by using Conducting a Cluster Analysis 261 different algorithms on the same data) in terms of managerial relevance. This underlines the exploratory character of the method. The following criteria will help you make an evaluation choice for a clustering solution (Dibb 1999; Ton ks 2009; Kotler and Keller 2009). l l l l l l l l l l Substantial: The segments are large and pro? able enough to serve. Accessible: The segments can be effectively reached and served, which requires them to be characterized by means of observable variables. Differentiable: The segments can be distinguished conceptually and respond differently to different marketing-mix elements and programs. Actionable: Effective programs can be formulated to attract and serve the segments. Stable: Only segments that are stable over time can provide the necessary grounds for a successful marketing strategy. Parsimonious: To be managerially meaningful, only a small set of substantial clusters should be identi? ed.Familiar: To ensure management acceptance, the segments composition should be comprehensible. Relevant: Segments should be relevant in respect of the company’s competencies and objectives. Compactness: Segments exhibit a high degree of within-segment homogeneity and between-segment h eterogeneity. Compatibility: Segmentation results meet other managerial functions’ requirements. The ? nal step of any cluster analysis is the interpretation of the clusters. Interpreting clusters always involves examining the cluster centroids, which are the clustering variables’ average values of all objects in a certain cluster.This step is of the utmost importance, as the analysis sheds light on whether the segments are conceptually distinguishable. Only if certain clusters exhibit signi? cantly different means in these variables are they distinguishable – from a data perspective, at least. This can easily be ascertained by comparing the clusters with independent t-tests samples or ANOVA (see Chap. 6). By using this information, we can also try to come up with a meaningful name or label for each cluster; that is, one which adequately re? ects the objects in the cluster.This is usually a very challenging task. Furthermore, clustering variables are frequently unobservable, which poses another problem. How can we decide to which segment a new object should be assigned if its unobservable characteristics, such as personality traits, personal values or lifestyles, are unknown? We could obviously try to survey these attributes and make a decision based on the clustering variables. However, this will not be feasible in most situations and researchers therefore try to identify observable variables that best mirror the partition of the objects.If it is possible to identify, for example, demographic variables leading to a very similar partition as that obtained through the segmentation, then it is easy to assign a new object to a certain segment on the basis of these demographic 262 9 Cluster Analysis characteristics. These variables can then also be used to characterize speci? c segments, an action commonly called pro? ling. For example, imagine that we used a set of items to assess the respondents’ values and learned that a certain segm ent comprises respondents who appreciate self-ful? lment, enjoyment of life, and a sense of accomplishment, whereas this is not the case in another segment. If we were able to identify explanatory variables such as gender or age, which adequately distinguish these segments, then we could partition a new person based on the modalities of these observable variables whose traits may still be unknown. Table 9. 11 summarizes the steps involved in a hierarchical and k-means clustering. While companies often develop their own market segments, they frequently use standardized segments, which are based on established buying trends, habits, and customers’ needs and have been speci? ally designed for use by many products in mature markets. One of the most popular approaches is the PRIZM lifestyle segmentation system developed by Claritas Inc. , a leading market research company. PRIZM de? nes every US household in terms of 66 demographically and behaviorally distinct segments to help ma rketers discern those consumers’ likes, dislikes, lifestyles, and purchase behaviors. Visit the Claritas website and ? ip through the various segment pro? les. By entering a 5-digit US ZIP code, you can also ? nd a speci? c neighborhood’s top ? ve lifestyle groups.One example of a segment is â€Å"Gray Power,† containing middle-class, homeowning suburbanites who are aging in place rather than moving to retirement communities. Gray Power re? ects this trend, a segment of older, midscale singles and couples who live in quiet comfort. http://www. claritas. com/MyBestSegments/Default. jsp We also introduce steps related to two-step clustering which we will further introduce in the subsequent example. Conducting a Cluster Analysis 263 Table 9. 11 Steps involved in carrying out a factor analysis in SPSS Theory Action Research problem Identi? ation of homogenous groups of objects in a population Select clustering variables that should be Select relevant variables that potentially exhibit used to form segments high degrees of criterion validity with regard to a speci? c managerial objective. Requirements Suf? cient sample size Make sure that the relationship between objects and clustering variables is reasonable (rough guideline: number of observations should be at least 2m, where m is the number of clustering variables). Ensure that the sample size is large enough to guarantee substantial segments. Low levels of collinearity among the variables ?Analyze ? Correlate ? Bivariate Eliminate or replace highly correlated variables (correlation coef? cients > 0. 90). Speci? cation Choose the clustering procedure If there is a limited number of objects in your dataset or you do not know the number of clusters: ? Analyze ? Classify ? Hierarchical Cluster If there are many observations (> 500) in your dataset and you have a priori knowledge regarding the number of clusters: ? Analyze ? Classify ? K-Means Cluster If there are many observations in your datas et and the clustering variables are measured on different scale levels: ? Analyze ? Classify ?Two-Step Cluster Select a measure of similarity or dissimilarity Hierarchical methods: (only hierarchical and two-step clustering) ? Analyze ? Classify ? Hierarchical Cluster ? Method ? Measure Depending on the scale level, select the measure; convert variables with multiple categories into a set of binary variables and use matching coef? cients; standardize variables if necessary (on a range of 0 to 1 or A1 to 1). Two-step clustering: ? Analyze ? Classify ? Two-Step Cluster ? Distance Measure Use Euclidean distances when all variables are continuous; for mixed variables, use log-likelihood. ? Analyze ? Classify ?Hierarchical Cluster ? Choose clustering algorithm Method ? Cluster Method (only hierarchical clustering) Use Ward’s method if equally sized clusters are expected and no outliers are present. Preferably use single linkage, also to detect outliers. Decide on the number of clu sters Hierarchical clustering: Examine the dendrogram: ? Analyze ? Classify ? Hierarchical Cluster ? Plots ? Dendrogram (continued) 264 Table 9. 11 (continued) Theory 9 Cluster Analysis Action Draw a scree plot (e. g. , using Microsoft Excel) based on the coef? cients in the agglomeration schedule. Compute the VRC using the ANOVA procedure: ? Analyze ?Compare Means ? One-Way ANOVA Move the cluster membership variable in the Factor box and the clustering variables in the Dependent List box. Compute VRC for each segment solution and compare values. k-means: Run a hierarchical cluster analysis and decide on the number of segments based on a dendrogram or scree plot; use this information to run k-means with k clusters. Compute the VRC using the ANOVA procedure: ? Analyze ? Classify ? K-Means Cluster ? Options ? ANOVA table; Compute VRC for each segment solution and compare values. Two-step clustering: Specify the maximum number of clusters: ? Analyze ? Classify ? Two-Step Cluster ?Numbe r of Clusters Run separate analyses using AIC and, alternatively, BIC as clustering criterion: ? Analyze ? Classify ? Two-Step Cluster ? Clustering Criterion Examine the auto-clustering output. Re-run the analysis using different clustering procedures, algorithms or distance measures. Split the datasets into two halves and compute the clustering variables’ centroids; compare ce