Raymond Cattell Multivariate research
what is the multivariate research?
what is the multivariate research?
Rather than pursue a "univariate" research approach to psychology, studying the effect that a single variable (such as "dominance") might have on another variable (such as "decision-making"), Cattell pioneered the use of multivariate experimental psychology (the analysis of several variables simultaneously). He believed that behavioral dimensions were too complex and interactive to fully understand variables in isolation. The classical univariate approach required bringing the individual into an artificial laboratory situation and measuring the effect of one particular variable on another - also known as the "bivariate" approach, while the multivariate approach allowed psychologists to study the whole person and their unique combination of traits within a natural environmental context. Multivariate experimental research designs and multivariate statistical analyses allowed for the study of "real-life" situations (e.g., depression, divorce, loss) that could not be manipulated in an artificial laboratory environment.  Cattell applied multivariate research methods across several intrapersonal psychological domains: the trait constructs (both normal and abnormal) of personality, motivational or dynamic traits, emotional and mood states, as well as the diverse array of cognitive abilities. In each of these domains, he considered there must be a finite number of basic, unitary dimensions that could be identified empirically. He drew a comparison between these fundamental, underlying (source) traits and the basic dimensions of the physical world that were discovered and presented, for example, in the periodic table of chemical elements.  In 1960, Cattell organized and convened an international symposium to increase communication and cooperation among researchers who were using multivariate statistics to study human behavior. This resulted in the foundation of the Society of Multivariate Experimental Psychology (SMEP) and its flagship journal, Multivariate Behavioral Research. He brought many researchers from Europe, Asia, Africa, Australia, and South America to work in his lab at the University of Illinois. Many of his books involving multivariate experimental research were written in collaboration with notable colleagues. CANNOTANSWER
Rather than pursue a "univariate" research approach to psychology, studying the effect that a single variable (such as "dominance") might have on another variable (such as "decision-making"),
Raymond Bernard Cattell (20 March 1905 – 2 February 1998) was a British-American psychologist, known for his psychometric research into intrapersonal psychological structure. His work also explored the basic dimensions of personality and temperament, the range of cognitive abilities, the dynamic dimensions of motivation and emotion, the clinical dimensions of abnormal personality, patterns of group syntality and social behavior, applications of personality research to psychotherapy and learning theory, predictors of creativity and achievement, and many multivariate research methods including the refinement of factor analytic methods for exploring and measuring these domains. Cattell authored, co-authored, or edited almost 60 scholarly books, more than 500 research articles, and over 30 standardized psychometric tests, questionnaires, and rating scales. According to a widely cited ranking, Cattell was the 16th most eminent, 7th most cited in the scientific journal literature, and among the most productive psychologists of the 20th century. He was, however, a controversial figure, due in part to false accusations of his friendships with and intellectual respect for white supremacists and neo-Nazis.

Cattell was an early proponent of using factor analytic methods instead of what he called "subjective verbal theorizing" to explore empirically the basic dimensions of personality, motivation, and cognitive abilities. One of the results of Cattell's application of factor analysis was his discovery of 16 separate primary trait factors within the normal personality sphere (based on the trait lexicon). He called these factors "source traits". This theory of personality factors and the self-report instrument used to measure them are known respectively as the 16 personality factor model and the 16PF Questionnaire (16PF).

Cattell also undertook a series of empirical studies into the basic dimensions of other psychological domains: intelligence, motivation, career assessment and vocational interests. Cattell theorized the existence of fluid and crystallized intelligence to explain human cognitive ability, investigated changes in Gf and Gc over the lifespan, and constructed the Culture Fair Intelligence Test to minimize the bias of written language and cultural background in intelligence testing.

Innovations and accomplishments
Cattell's research was mainly in personality, abilities, motivations, and innovative multivariate research methods and statistical analysis (especially his many refinements to exploratory factor analytic methodology). In his personality research, he is best remembered for his factor-analytically derived 16-factor model of normal personality structure, arguing for this model over Eysenck's simpler higher-order 3-factor model, and constructing measures of these primary factors in the form of the 16PF Questionnaire (and its downward extensions: HSPQ, and CPQ, respectively). He was the first to propose a hierarchical, multi-level model of personality with the many basic primary factors at the first level and the fewer, broader, "second-order" factors at a higher stratum of personality organization. These "global trait" constructs are the precursors of the currently popular Big Five (FFM) model of personality. Cattell's research led to further advances, such as distinguishing between state and trait measures (e.g., state-trait anxiety), ranging on a continuum from immediate transitory emotional states, through longer-acting mood states, dynamic motivational traits, and also relatively enduring personality traits. Cattell also conducted empirical studies into developmental changes in personality trait constructs across the lifespan.

In the cognitive abilities domain, Cattell researched a wide range of abilities, but is best known for the distinction between fluid and crystallized intelligence. He distinguished between the abstract, adaptive, biologically-influenced cognitive abilities that he called "fluid intelligence" and the applied, experience-based and learning-enhanced ability that he called "crystallized intelligence." Thus, for example, a mechanic who has worked on airplane engines for 30 years might have a huge amount of "crystallized" knowledge about the workings of these engines, while a new young engineer with more "fluid intelligence" might focus more on the theory of engine functioning, these two types of abilities might complement each other and work together toward achieving a goal.  As a foundation for this distinction, Cattell developed the investment-model of ability, arguing that crystallized ability emerged from the investment of fluid ability in a particular topic of knowledge. He contributed to cognitive epidemiology with his theory that crystallized knowledge, while more applied, could be maintained or even increase after fluid ability begins to decline with age, a concept used in the National Adult Reading Test (NART). Cattell constructed a number of ability tests, including the Comprehensive Ability Battery (CAB) that provides measures of 20 primary abilities, and the Culture Fair Intelligence Test (CFIT) which was designed to provide a completely non-verbal measure of intelligence like that now seen in the Raven's. The Culture Fair Intelligence Scales were intended to minimize the influence of cultural or educational background on the results of intelligence tests.

In regard to statistical methodology, in 1960 Cattell founded the Society of Multivariate Experimental Psychology (SMEP), and its journal Multivariate Behavioral Research, in order to bring together, encourage, and support scientists interested in multi-variate research. He was an early and frequent user of factor analysis (a statistical procedure for finding underlying factors in data). Cattell also developed new factor analytic techniques, for example, by inventing the scree test, which uses the curve of latent roots to judge the optimal number of factors to extract. He also developed a new factor analysis rotation procedure—the "Procrustes" or non-orthogonal rotation, designed to let the data itself determine the best location of factors, rather than requiring orthogonal factors. Additional contributions include the Coefficient of Profile Similarity (taking account of shape, scatter, and level of two score profiles); P-technique factor analysis based on repeated measurements of a single individual (sampling of variables, rather than sampling of persons); dR-technique factor analysis for elucidating change dimensions (including transitory emotional states, and longer-lasting mood states); the Taxonome program for ascertaining the number and contents of clusters in a data set; the Rotoplot program for attaining maximum simple structure factor pattern solutions. As well, he put forward the Dynamic Calculus for assessing interests and motivation, the Basic Data Relations Box (assessing dimensions of experimental designs), the group syntality construct ("personality" of a group), the triadic theory of cognitive abilities, the Ability Dimension Analysis Chart (ADAC), and Multiple Abstract Variance Analysis (MAVA), with "specification equations" to embody genetic and environmental variables and their interactions.

As Lee J. Cronbach at Stanford University stated:

Biography

England
Raymond Cattell was born on 20 March 1905 in Hill Top, West Bromwich, a small town in England near Birmingham where his father's family was involved in inventing new parts for engines, automobiles and other machines. Thus, his growing up years were a time when great technological and scientific ideas and advances were taking place and this greatly influenced his perspective on how a few people could actually make a difference in the world. He wrote: "1905 was a felicitous year in which to be born. The airplane was just a year old. The Curies and Rutherford in that year penetrated the heart of the atom and the mystery of its radiations, Alfred Binet launched the first intelligence test, and Einstein, the theory of relativity.

When Cattell was about five years old, his family moved to Torquay, Devon, in the south-west of England, where he grew up with strong interests in science and spent a lot of time sailing around the coastline. He was the first of his family (and the only one in his generation) to attend university: in 1921, he was awarded a scholarship to study chemistry at King's College, London, where he obtained a BSc (Hons) degree with 1st-class honors at age 19 years. While studying physics and chemistry at university he learned from influential people in many other fields, who visited or lived in London. He writes:

As he observed first-hand the terrible destruction and suffering after World War I, Cattell was increasingly attracted to the idea of applying the tools of science to the serious human problems that he saw around him. He stated that in the cultural upheaval after WWI, he felt that his laboratory table had begun to seem too small and the world's problems so vast. Thus, he decided to change his field of study and pursue a PhD in psychology at King's College, London, which he received in 1929. The title of his PhD dissertation was "The Subjective Character of Cognition and Pre-Sensational Development of Perception". His PhD advisor at King's College, London, was Francis Aveling, D.D., D.Sc., PhD, D.Litt., who was also President of the British Psychological Society from 1926 until 1929. In 1939, Cattell was honored for his outstanding contributions to psychological research with conferral of the prestigious higher doctorate D.Sc. from the University of London.

While working on his PhD, Cattell had accepted a position teaching and counseling in the Department of Education at Exeter University. He ultimately found this disappointing because there was limited opportunity to conduct research. Cattell did his graduate work with Charles Spearman, the English psychologist and statistician who is famous for his pioneering work on assessing intelligence, including the development of the idea of a general factor of intelligence termed g. During his three years at Exeter, Cattell courted and married Monica Rogers, whom he had known since his boyhood in Devon and they had a son together. She left him about four years later. Soon afterward he moved to Leicester where he organized one of England's first child guidance clinics. It was also in this time period that he finished his first book "Under Sail Through Red Devon," which described his many adventures sailing around the coastline and estuaries of South Devon and Dartmoor.

United States
In 1937, Cattell left England and moved to the United States when he was invited by Edward Thorndike to come to Columbia University. When the G. Stanley Hall professorship in psychology became available at Clark University in 1938, Cattell was recommended by Thorndike and was appointed to the position. However, he conducted little research there and was "continually depressed." Cattell was invited by Gordon Allport to join the Harvard University faculty in 1941. While at Harvard he began some of the research in personality that would become the foundation for much of his later scientific work.

During World War II, Cattell served as a civilian consultant to the U.S. government researching and developing tests for selecting officers in the armed forces. Cattell returned to teaching at Harvard and married Alberta Karen Schuettler, a PhD student in mathematics at Radcliffe College. Over the years, she worked with Cattell on many aspects of his research, writing, and test development. They had three daughters and a son. They divorced in 1980.

Herbert Woodrow, professor of psychology at the University of Illinois at Urbana-Champaign, was searching for someone with a background in multivariate methods to establish a research laboratory. Cattell was invited to assume this position in 1945. With this newly created research professorship in psychology, he was able to obtain sufficient grant support for two PhD associates, four graduate research assistants, and clerical assistance.

One reason that Cattell moved to the University of Illinois was because the first electronic computer built and owned entirely by a US educational institution "Illinois Automatic Computer" was being developed there, which made it possible for him to complete large-scale factor analyses. Cattell founded the Laboratory of Personality Assessment and Group Behavior. In 1949, he and his wife founded the Institute for Personality and Ability Testing (IPAT). Karen Cattell served as director of IPAT until 1993. Cattell remained in the Illinois research professorship until he reached the university's mandatory retirement age in 1973.  A few years after he retired from the University of Illinois he built a home in Boulder, Colorado, where he wrote and published the results of a variety of research projects that had been left unfinished in Illinois.

In 1977, Cattell moved to Hawaii, largely because of his love of the ocean and sailing.  He continued his career as a part-time professor and adviser at the University of Hawaii. He also served as adjunct faculty of the Hawaii School of Professional Psychology. After settling in Hawaii he married Heather Birkett, a clinical psychologist, who later carried out extensive research using the 16PF and other tests. During the last two decades of his life in Hawaii, Cattell continued to publish a variety of scientific articles, as well as books on motivation, the scientific use of factor analysis, two volumes of personality and learning theory, the inheritance of personality, and co-edited a book on functional psychological testing, as well as a complete revision of his highly renowned Handbook of Multivariate Experimental Psychology.

Cattell and Heather Birkett Cattell lived on a lagoon in the southeast corner of Oahu where he kept a small sailing boat. Around 1990, he had to give up his sailing career because of navigational challenges resulting from old age. He died at home in Honolulu on 2 February 1998, at age 92 years. He is buried in the Valley of the Temples on a hillside overlooking the sea. His will provided for his remaining funds to build a school for underprivileged children in Cambodia. He was an agnostic.

Scientific orientation
When Cattell began his career in psychology in the 1920s, he felt that the domain of personality was dominated by speculative ideas that were largely intuitive with little/no empirical research basis. Cattell accepted E.L. Thorndike's empiricist viewpoint that "If something actually did exist, it existed in some amount and hence could be measured.".

Cattell found that constructs used by early psychological theorists tended to be somewhat subjective and poorly defined. For example, after examining over 400 published papers on the topic of "anxiety" in 1965, Cattell stated: "The studies showed so many fundamentally different meanings used for anxiety and different ways of measuring it, that the studies could not even be integrated." Early personality theorists tended to provide little objective evidence or research bases for their theories.  Cattell wanted psychology to become more like other sciences, whereby a theory could be tested in an objective way that could be understood and replicated by others. In Cattell's words:

"Psychology appeared to be a jungle of confusing, conflicting, and arbitrary concepts.  These pre-scientific theories doubtless contained insights which still surpass in refinement those depended upon by psychiatrists or psychologists today.  But who knows, among the many brilliant ideas offered, which are the true ones?  Some will claim that the statements of one theorist are correct, but others will favour the views of another.  Then there is no objective way of sorting out the truth except through scientific research."

Emeritus Professor Arthur B. Sweney, an expert in psychometric test construction, summed up Cattell's methodology:

"[Cattell] was without exception the one man who made the most major strides in systematizing the field of behavioral science from all of its diverse facets into a real science based on empirical, replicable and universal principles. Seldom has psychology had such a determined, systematic explorer dedicated not only to the basic search for scientific knowledge but also to the need to apply science for the benefit of all." 

Also, according to Sheehy (2004, p. 62),

"Cattell made fundamental contributions to our understanding of ability and the structure of personality."

In 1994, Cattell was one of 52 signatories of "Mainstream Science on Intelligence," an editorial written by Linda Gottfredson and published in the Wall Street Journal. In the letter the signers, some of whom were intelligence researchers, defended the publication of the book The Bell Curve. There was sharp pushback on the letter, with a number of signers (not Cattell) having received funding from white supremacist organizations.

His works can be categorized or defined as part of cognitive psychology, due to his nature to measure every psychological aspect especially personality aspect.

Multivariate research
Rather than pursue a "univariate" research approach to psychology, studying the effect that a single variable (such as "dominance") might have on another variable (such as "decision-making"), Cattell pioneered the use of multivariate experimental psychology (the analysis of several variables simultaneously). He believed that behavioral dimensions were too complex and interactive to fully understand variables in isolation. The classical univariate approach required bringing the individual into an artificial laboratory situation and measuring the effect of one particular variable on another also known as the "bivariate" approach, while the multivariate approach allowed psychologists to study the whole person and their unique combination of traits within a natural environmental context. Multivariate experimental research designs and multivariate statistical analyses allowed for the study of "real-life" situations (e.g., depression, divorce, loss) that could not be manipulated in an artificial laboratory environment.

Cattell applied multivariate research methods across several intrapersonal psychological domains: the trait constructs (both normal and abnormal) of personality, motivational or dynamic traits, emotional and mood states, as well as the diverse array of cognitive abilities. In each of these domains, he considered there must be a finite number of basic, unitary dimensions that could be identified empirically.  He drew a comparison between these fundamental, underlying (source) traits and the basic dimensions of the physical world that were discovered and presented, for example, in the periodic table of chemical elements.

In 1960, Cattell organized and convened an international symposium to increase communication and cooperation among researchers who were using multivariate statistics to study human behavior.  This resulted in the foundation of the Society of Multivariate Experimental Psychology (SMEP) and its flagship journal, Multivariate Behavioral Research. He brought many researchers from Europe, Asia, Africa, Australia, and South America to work in his lab at the University of Illinois. Many of his books involving multivariate experimental research were written in collaboration with notable colleagues.

Factor analysis
Cattell noted that in the hard sciences such as chemistry, physics, astronomy, as well as in medical science, unsubstantiated theories were historically widespread until new instruments were developed to improve scientific observation and measurement. In the 1920s, Cattell worked with Charles Spearman who was developing the new statistical technique of factor analysis in his effort to understand the basic dimensions and structure of human abilities.  Factor analysis became a powerful tool to help uncover the basic dimensions underlying a confusing array of surface variables within a particular domain.

Factor analysis was built upon the earlier development of the correlation coefficient, which provides a numerical estimate of the degree to which variables are "co-related".  For example, if "frequency of exercise" and "blood pressure level" were measured on a large group of people, then intercorrelating these two variables would provide a quantitative estimate of the degree to which "exercise" and "blood pressure" are directly related to each other. Factor analysis performs complex calculations on the correlation coefficients among the variables within a particular domain (such as cognitive ability or personality trait constructs) to determine the basic, unitary factors underlying the particular domain.

While working at the University of London with Spearman exploring the number and nature of human abilities, Cattell postulated that factor analysis could be applied to other areas beyond the domain of abilities.  In particular, Cattell was interested in exploring the basic taxonomic dimensions and structure of human personality. He believed that if exploratory factor analysis were applied to a wide range of measures of interpersonal functioning, the basic dimensions within the domain of social behavior could be identified.  Thus, factor analysis could be used to discover the fundamental dimensions underlying the large number of surface behaviors, thereby facilitating more effective research.

As noted above, Cattell made many important innovative contributions to factor analytic methodology, including the Scree Test to estimate the optimal number of factors to extract, the "Procrustes" oblique rotation strategy, the Coefficient of Profile Similarity, P-technique factor analysis, dR-technique factor analysis, the Taxonome program, as well the Rotoplot program for attaining maximum simple structure solutions. In addition, many eminent researchers received their grounding in factor analytic methodology under the guidance of Cattell, including Richard Gorsuch, an authority on exploratory factor analytic methods.

Personality theory
In order to apply factor analysis to personality, Cattell believed it was necessary to sample the widest possible range of variables.  He specified three kinds of data for comprehensive sampling, to capture the full range of personality dimensions:
 Life data (or L-data), which involves collecting data from the individual's natural, everyday life behaviors, measuring their characteristic behavior patterns in the real world.  This could range from number of traffic accidents or number of parties attended each month, to grade point average in school or number of illnesses or divorces.
 Experimental data (or T-data) which involves reactions to standardized experimental situations created in a lab where a subject's behavior can be objectively observed and measured.
 Questionnaire data (or Q-data), which involves responses based on introspection by the individual about their own behavior and feelings.  He found that this kind of direct questioning often measured subtle internal states and viewpoints that might be hard to see or measure in external behavior.

In order for a personality dimension to be called "fundamental and unitary," Cattell believed that it needed to be found in factor analyses of data from all three of these measurement domains. Thus, Cattell constructed measures of a wide range of personality traits in each medium (L-data; Q-data; T-data).  He then conducted a programmatic series of factor analyses on the data derived from each of the three measurement media in order to elucidate the dimensionality of human personality structure.

With the help of many colleagues, Cattell's factor-analytic studies continued over several decades, eventually finding at least 16 primary trait factors underlying human personality (comprising 15 personality dimensions and one cognitive ability dimension: Factor B in the 16PF).  He decided to name these traits with letters (A, B, C, D, E...) in order to avoid misnaming these newly discovered dimensions, or inviting confusion with existing vocabulary and concepts.  Factor-analytic studies conducted by many researchers in diverse cultures around the world have provided substantial support for the validity of these 16 trait dimensions.

In order to measure these trait constructs across different age ranges, Cattell constructed (Q-data) instruments that included the Sixteen Personality Factor Questionnaire (16PF) for adults, the High School Personality Questionnaire (HSPQ) now named the Adolescent Personality Questionnaire (APQ), and the Children's Personality Questionnaire (CPQ). Cattell also constructed the (T-data) Objective Analytic Battery (OAB) that provided measures of the 10 largest personality trait factors extracted factor analytically, as well as objective (T-data) measures of dynamic trait constructs such as the Motivation Analysis Test (MAT), the School Motivation Analysis Test (SMAT), and the Children's Motivation Analysis Test (CMAT). In order to measure trait constructs within the abnormal personality sphere, Cattell constructed the Clinical Analysis Questionnaire (CAQ) Part 1 of the CAQ measures the 16PF factors, While Part 2 measures an additional 12 abnormal (psychopathological) personality trait dimensions. The CAQ was later re-badged as the PsychEval Personality Questionnaire (PEPQ). Also within the broadly conceptualized personality domain, Cattell constructed measures of mood states and transitory emotional states, including the Eight State Questionnaire (8SQ) In addition, Cattell was at the forefront in constructing the Central Trait-State Kit.

From the very beginning of his academic career, Cattell reasoned that, as in other scientific domains like intelligence, there might be an additional, higher level of organization within personality which would provide a structure for the many primary traits.  When he factor analyzed the intercorrelations of the 16 primary trait measures themselves, he found no fewer than five "second-order" or "global factors", now commonly known as the Big Five. These second-stratum or "global traits" are conceptualized as broad, overarching domains of behavior, which provide meaning and structure for the primary traits.  For example, the "global trait" Extraversion has emerged from factor-analytic results comprising the five primary trait factors that are interpersonal in focus.

Thus, "global" Extraversion is fundamentally defined by the primary traits that are grouped together factor analytically, and, moving in the opposite direction, the second-order Extraversion factor gives conceptual meaning and structure to these primary traits, identifying their focus and function in human personality.  These two levels of personality structure can provide an integrated understanding of the whole person, with the "global traits" giving an overview of the individual's functioning in a broad-brush way, and the more-specific primary trait scores providing an in-depth, detailed picture of the individual's unique trait combinations (Cattell's "Depth Psychometry" p. 71).

Research into the 16PF personality factors has shown these constructs to be useful in understanding and predicting a wide range of real life behaviors. Thus, the 16 primary trait measures plus the five major second-stratum factors have been used in educational settings to study and predict achievement motivation, learning or cognitive style, creativity, and compatible career choices; in work or employment settings to predict leadership style, interpersonal skills, creativity, conscientiousness, stress-management, and accident-proneness; in medical settings to predict heart attack proneness, pain management variables, likely compliance with medical instructions, or recovery pattern from burns or organ transplants; in clinical settings to predict self-esteem, interpersonal needs, frustration tolerance, and openness to change; and, in research settings to predict a wide range of behavioral proclivities such as aggression, conformity, and authoritarianism.

Cattell's programmatic multivariate research which extended from the 1940s through the 70's resulted in several books that have been widely recognized as identifying fundamental taxonomic dimensions of human personality and motivation and their organizing principles:
 The Description and Measurement of Personality (1946)
 An Introduction to Personality Study (1949)
 Personality: A Systematic, Theoretical, and Factual Study (1950)
 Factor Analysis (1952)
 Personality and Motivation Structure and Measurement (1957)
 The Meaning and Measurement of Neuroticism and Anxiety (1961)
 Personality Factors in Objective Test Devices (1965)
 The Scientific Analysis of Personality (1965)
 Handbook of Multivariate Experimental Psychology (1966)
 Objective Personality and Motivation Tests (1967)
 Handbook for the Sixteen Personality Questionnaire (16PF) (1970)
 Personality and Mood by Questionnaire (1973)
 Motivation and Dynamic Structure (1975)
 Handbook of Modern Personality Theory (1977)
 The Scientific Analysis of Personality and Motivation (1977)
 Personality Theory in Action: Handbook for the O-A Test Kit (1978)
 The Scientific use of Factor Analysis in Behavioral and Life Sciences (1978)
 Personality and Learning Theory: Vols. 1 & 2 (1979)
 Structured Personality-Learning Theory (1983)
 Human Motivation and the Dynamic Calculus (1985)
 Psychotherapy by Structured Learning Theory (1987)
 Handbook of Multivariate Experimental Psychology (1988)

The books listed above document a programmatic series of empirical research studies based on quantitative personality data derived from objective tests (T-data), from self-report questionnaires (Q-data), and from observer ratings (L-data). They present a theory of personality development over the human life span, including effects on the individual's behavior from family, social, cultural, biological, and genetic influences, as well as influences from the domains of motivation and ability.

As Hans Eysenck at the Institute of Psychiatry, London remarked:"Cattell has been one of the most prolific writers in psychology since Wilhelm Wundt....According to the Citation Index, he is one of the ten most cited psychologists, and this is true with regard to not only citations in social science journals but also those in science journals generally. Of the two hundred and fifty most cited scientists, only three psychologists made the grade, namely, Sigmund Freud in the first place, then the reviewer [H.J. Eysenck], and then Cattell. Thus there is no question that Cattell has made a tremendous impression on psychology and science in general."

Views on race and eugenics
William H. Tucker and Barry Mehler have criticized Cattell based on his writings about evolution and political systems. They argue that throughout his life Cattell adhered to a mixture of eugenics and a new religion of his devising which he eventually named Beyondism and proposed as "a new morality from science". Tucker also notes that Cattell thanked the prominent neo-Nazi and white supremacist ideologues Roger Pearson, Wilmot Robertson, and Revilo P. Oliver in the preface to his Beyondism, and that a Beyondist newsletter with which Cattell was involved favorably reviewed Robertson's book The Ethnostate.

Cattell claimed that a diversity of cultural groups was necessary to allow that evolution. Cattell speculated about natural selection based on both the separation of groups and also the restriction of "external" assistance to "failing" groups from "successful" ones. This included advocating for "educational and voluntary birth control measures"—i.e., by separating groups and limiting excessive growth of failing groups. John Gillis, biographer of Cattell has argued that, although some of Cattell's views are controversial, Tucker and Mehler have exaggerated and misrepresented his views by taking quotes out of context, and by referring back to outdated writings. Magrietha Lotz (2008, p. 136) also says he was taken out of context by his critics. Lotz says "the views he developed in the 1930s were common among his contemporaries when beliefs in racial differences were widely held, and should not be distorted by judgment according to today's standards. General scientific observations should not be read as personal moral statements." 

In 1997, Cattell was chosen by the American Psychological Association (APA) for its "Gold Medal Award for Lifetime Achievement in the Science of Psychology." Before the medal was presented, Mehler launched a publicity campaign against Cattell through his nonprofit foundation ISAR, accusing Cattell of being sympathetic to racist and fascist ideas. Mehler claimed that "it is unconscionable to honor this man whose work helps to dignify the most destructive political ideas of the twentieth century". A blue-ribbon committee was convened by the APA to investigate the legitimacy of the charges. Before the committee reached a decision, Cattell issued an open letter to the committee saying "I believe in equal opportunity for all individuals, and I abhor racism and discrimination based on race.  Any other belief would be antithetical to my life's work" and saying that "it is unfortunate that the APA announcement ... has brought misguided critics' statements a great deal of publicity." Cattell refused the award, withdrawing his name from consideration, and the committee was disbanded. Cattell died months later at the age of 92.

In 1984, Cattell said that: "The only reasonable thing is to be noncommittal on the race question – that's not the central issue, and it would be a great mistake to be sidetracked into all the emotional upsets that go on in discussions of racial differences. We should be quite careful to dissociate eugenics from it – eugenics' real concern should be with individual differences." Richard L. Gorsuch (1997) wrote (in a letter to the American Psychological Foundation, para. 4) that: "The charge of racism is 180 degrees off track. [Cattell] was the first one to challenge the racial bias in tests and to attempt to reduce that problem."

Selected publications
Raymond Cattell's papers and books are the 7th most highly referenced in peer-reviewed psychology journals over the past century. His 25 most cited publications are:

Cattell, R. B. (1943). The description of personality: Basic traits resolved into clusters. Journal of Abnormal and Social Psychology, 38, 476–506. (1725 citations)
Cattell, R. B. (1943). The measurement of adult intelligence. Psychological Bulletin, 40, 153–193. (982 citations)
Cattell, R. B. (1946). Description and Measurement of Personality.  New York: World Book. (2100 citations)
Cattell, R. B. (1947). Confirmation and clarification of primary personality factors. Psychometrika, 12, 197–220. (666 citations)
Cattell, R. B. (1950). Personality: A Systematic Theoretical and Factual Study. New York: McGraw Hill. (1636 citations)
Cattell, R. B. (1952). Factor Analysis: An Introduction and Manual for the Psychologist and Social Scientist. Oxford, UK: Harper. (362 citations)
Cattell, R. B. (1957). Personality and Motivation Structure and Measurement. New York: World Book. (3042 citations)**
Cattell, R. B. (1963). Theory of fluid and crystallized intelligence: A critical experiment. Journal of Educational Psychology, 54, 1–22. (3906 citations)
Cattell, R. B. & Scheier, I. H. (1961). The Meaning and Measurement of Neuroticism and Anxiety. New York: Ronald Press. (1154 citations)
Cattell, R. B. (1965). Factor analysis: An introduction to essentials I: The purpose and underlying models. Biometrics, 21, 190–215. (728 citations)
Horn, J. L. & Cattell, R. B. (1966). Refinement and test of the theory of fluid and crystallized intelligence. Journal of Educational Psychology, 57, 253–270. (2449 citations)
Cattell, R. B. (1966). The Scree Test for the number of factors. Multivariate Behavioral Research, 1(2), 245–276. (16489 citations)
Horn, J. L. & Cattell, R. B. (1967). Age difference in fluid and crystallized intelligence. Acta Psychologica, 26, 107–129. (1268 citations)
Cattell, R. B. & Scheier, I. H. (1967). Handbook for the IPAT Anxiety Scale Questionnaire. Champaign IL: IPAT. (631 citations)
Cattell, R. B. & Butcher, H. J. (1968). The Prediction of Achievement and Creativity. Oxford, UK: Bobbs-Merrill. (630 citations)
Cattell, R. B. et al. (1970). Handbook for the 16 Personality Factor Questionnaire (16PF) in Clinical Educational Industrial and Research Psychology. Champaign, IL: IPAT. (3486 citations)
Cattell, R. B., Eber, H. W., & Tatsuoka, M. M.  (1970). Handbook for the Sixteen Personality Factor Questionnaire (16 PF). Champaign IL: IPAT. (3048 citations)
Cattell, R. B. (1971). Abilities: Their Structure, Growth, and Action. Boston, MA: Houghton Mifflin. (4601 citations)
Cattell, R. B. (1973). Personality and Mood by Questionnaire.  San Francisco, CA: Jossey-Bass. (1106 citations)
Cattell, R. B. & Vogelmann, S. (1977). A comprehensive trial of the scree and KG criteria for determining the number of factors. Multivariate Behavioral Research, 12, 289–335. (697 citations)
Cattell, R. B. & Kline, P. (1977). The Scientific Analysis of Personality and Motivation. New York: Academic. (2340 citations)
Cattell, R. B. (1978). The Scientific Use of Factor Analysis in Behavioral and Life Sciences. New York: plenum. (3579 citations)
Cattell, R. B. (1987). Intelligence: Its Structure, Growth, and Action. Amsterdam: Elsevier. (1744 citations)
Nesselroade, J. R. & Cattell, R. B. (1988). Handbook of Multivariate Experimental Psychology (Rev. 2nd ed.) New York: Plenum. (1682 citations)
Cattell, R. B. (1988). The meaning and strategic use of factor analysis. In Handbook of Multivariate Experimental Psychology. New York: Plenum. (1065 citations)

Comprehensive list of Cattell's books

See also
16PF Questionnaire and factors
Big Five Personality Traits
Cattell–Horn–Carroll (CHC) theory
Culture Fair Intelligence Test
Factor Analysis
Fluid and Crystallized Intelligence
Trait Theory

References

External links

Prof. John Gillis's Website about Raymond B. Cattell
A Memorial to Raymond Bernard Cattell
Human Intelligence: Raymond B. Cattell
Cattell Legacy at IPAT
Cattell Biography
The Cattell Award
Biography Raymond Cattell
Biography Raymond Cattell
Biography Raymond Bernard Cattell
Personality Trait Theory
Personality Factors
  A Concise Beyondist Catechism
Interview With Raymond B. Cattell from The Eugenics Bulletin, Spring-Summer 1984.
Raymond B. Cattell and The Fourth Inquisition
Beyondism: Raymond B. Cattell and the New Eugenics

1905 births
1998 deaths
People educated at Torquay Boys' Grammar School
Alumni of King's College London
American atheists
American psychologists
British psychologists
Columbia University faculty
Clark University faculty
Harvard University faculty
University of Illinois faculty
University of Hawaiʻi faculty
Intelligence researchers
Personality trait theorists
Emotion psychologists
20th-century psychologists
American eugenicists
The Society of Multivariate Experimental Psychology (SMEP) is a small academic organization of research psychologists who have interests in multivariate statistical models for advancing psychological knowledge. It publishes a journal, Multivariate Behavioral Research.

History
SMEP was founded in 1960 by Raymond Cattell and others as an organization of scientific researchers interested in applying complex multivariate quantitative methods to substantive problems in psychology.  The two main functions of the society are to hold an annual meeting of scientific or quantitative psychology specialists and to publish a journal, Multivariate Behavioral Research.  The first meeting of the Society was held in Chicago in the fall of 1961.  Beginning in 1993, the meeting has been held annually.

Membership
The new members of SMEP are elected by existing members, and membership is considered to be honorific. To promote interaction among participants in the annual meeting, the membership is limited to 65 active members under the age of 65, as well as to emeritus members (active members aged 65 and older who attend the annual meeting regularly).  The Bylaws of SMEP stipulate that there should be twice the number of nominees for membership as available slots.

Presidents 
The president of SMEP is elected by the membership and the list of former presidents is below.

 2021: Niels Waller
 2020: David P. MacKinnon
 2019: Peter Molenaar
 2018: Debbi Bandalos
 2017: David Kaplan
 2016: Ken Bollen
 2015: Alan Nicewander 
 2014: William Shadish
 2013: Steven M. Boker
 2012: Scott M. Hofer
 2011: Scott E. Maxwell
 2010: Lisa L. Harlow
 2009: Patrick E. Shrout
 2008: Wayne F. Velicer
 2007: Stephen G. West
 2006: Leona S. Aiken
 2005: James H. Steiger
 2004: Joseph Lee Rodgers
 2003: David Rindskopf
 2002: Roderick McDonald
 2001: Roger Millsap
 2000: Robert C. MacCallum
 1999: John R. Nesselroade
 1998: Michael W. Browne
 1997: Susan Embretson
 1996: Keith F. Widaman
 1995: Linda M. Collins
 1994: Robert Cudeck
 1993: Patricia R. Cohen
 1992: John J. McArdle
 1991: Stanley A. Mulaik
 1990: Herbert W. Eber
 1989: John C. Loehlin
 1988: William M. Meredith
 1987: Andrew L. Comrey
 1986: A. Ralph Hakstian
 1985: Henry F. Kaiser
 1984: William Revelle
 1983: Norman Cliff
 1982: J. Douglas Carroll
 1981: Jack Block
 1980: Jerry Wiggins
 1979: Peter M. Bentler
 1978: John M. Digman
 1977: Goldine C. Gleser
 1976: John L. Horn
 1975: Douglas N. Jackson
 1974: Lewis R. Goldberg
 1973: Harry H. Harman
 1972: Desmond S. Cartwright
 1971: Warren T. Norman
 1970: Maurice Lorr
 1969: Jacob Cohen
 1968: Donald W. Fiske
 1967: Robert C. Tryon, succeeded by Merrill Roff
 1966: Chester W. Harris
 1965: Benjamin Fruchter
 1964: John W. French
 1963: Charles F. Wrigley
 1962: Saul B. Sells
 1961: Raymond B. Cattell
 1960: Raymond B. Cattell

Annual meeting
The annual meeting spans two and one half days and consists exclusively of presentations by members in a single session.  The program is arranged to allow ample discussion of each presentation. Since 2003, a half-day graduate student pre-conference has been held in conjunction with the annual meeting. PhD students sponsored by SMEP members present their research to those attending the annual meeting.   In addition, the Society awards an annual Saul Sells Award and Raymond B. Cattell Award for new investigators.  The meeting also elects a new president.

Journal
The SMEP journal, Multivariate Behavioral Research (MBR), publishes research articles on multivariate methodology and its use in psychological research. The 2021 Editor of MBR is Jeffrey Harring, and the journal is published by Taylor & Francis Group.

SMEP and Taylor & Francis also cooperate in the publication of a series of books on applications of multivariate quantitative methods to important substantive research issues. The book series is edited by Lisa Harlow.

The Society uses revenue from the journal to fund programs that promote learning of statistical methods in psychology and education, with a special emphasis on increasing the number of persons from under-represented groups in quantitative psychology.

References

External links
 The Society of Multivariate Experimental Psychology
 Current Issue of Multivariate Behavioral Research

Psychology organizations based in the United States
Statistical societies
Organizations established in 1960 In statistics, the multivariate t-distribution (or multivariate Student distribution) is a multivariate probability distribution. It is a generalization to random vectors of the Student's t-distribution, which is a distribution applicable to univariate random variables. While the case of a random matrix could be treated within this structure, the matrix t-distribution is distinct and makes particular use of the matrix structure.

Definition
One common method of construction of a multivariate t-distribution, for the case of  dimensions, is based on the observation that if  and  are independent and distributed as  and  (i.e. multivariate normal and chi-squared distributions) respectively, the matrix  is a p × p matrix, and , then  has the density

and is said to be distributed as a multivariate t-distribution with parameters . Note that  is not the covariance matrix since the covariance is given by  (for ).

The constructive definition of a multivariate t-distribution simultaneously serves as a sampling algorithm:
 Generate  and , independently.
 Compute .
This formulation gives rise to the hierarchical representation of a multivariate t-distribution as a scale-mixture of normals:  where  indicates a gamma distribution with density proportional to , and  conditionally follows .

In the special case , the distribution is a multivariate Cauchy distribution.

Derivation

There are in fact many candidates for the multivariate generalization of Student's t-distribution. An extensive survey of the field has been given by Kotz and Nadarajah (2004). The essential issue is to define a probability density function of several variables that is the appropriate generalization of the formula for the univariate case. In one dimension (), with  and , we have the probability density function

and one approach is to write down a corresponding function of several variables. This is the basic idea of elliptical distribution theory, where one writes down a corresponding function of  variables  that replaces  by a quadratic function of all the . It is clear that this only makes sense when all the marginal distributions have the same degrees of freedom . With , one has a simple choice of multivariate density function

which is the standard but not the only choice.

An important special case is the standard bivariate t-distribution, p = 2:

Note that .

Now, if  is the identity matrix, the density is

The difficulty with the standard representation is revealed by this formula, which does not factorize into the product of the marginal one-dimensional distributions. When  is diagonal the standard representation can be shown to have zero correlation but the marginal distributions do not agree with statistical independence.

Cumulative distribution function 
The definition of the cumulative distribution function (cdf) in one dimension can be extended to multiple dimensions by defining the following probability (here  is a real vector):

There is no simple formula for , but it can be approximated numerically via Monte Carlo integration.

Copulas based on the multivariate t
The use of such distributions is enjoying renewed interest due to applications in mathematical finance, especially through the use of the Student's t copula.

Related concepts

In univariate statistics, the Student's t-test makes use of Student's t-distribution. Hotelling's T-squared distribution is a distribution that arises in multivariate statistics. The matrix t-distribution is a distribution for random variables arranged in a matrix structure.

See also 
 Multivariate normal distribution, which is a special case of the multivariate Student's t-distribution when .
 Chi distribution, the pdf of the scaling factor in the construction the Student's t-distribution and also the 2-norm (or Euclidean norm) of a multivariate normally distributed vector (centered at zero).
Rayleigh distribution#Student's t, random vector length of multivariate t-distribution
 Mahalanobis distance

References

Literature

External links
Copula Methods vs Canonical Multivariate Distributions: the multivariate Student T distribution with general degrees of freedom
Multivariate Student's t distribution

Continuous distributions
Multivariate continuous distributions