Raymond B. Cattell

The scientific use of factor analysis in behavioral and life sciences

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Age differences in fluid and crystallized intelligence

Abstract The general purpose of this study was to describe differences in intellectual functioning associated with aging in adulthood. Estimates of broad factors identified as fluid intelligence, crystallized intelligence, general visualization, speediness, carefulness and fluency were obtained by combining scores on several tests found to define these factors in previous research. A sample of 297 subjects was divided into five age groupings: 14–17 year-olds, 18–20 year-olds, 21–28 year-olds, 29–39 year-olds and 40–61 year-olds. Analyses of variance and covariance were carried out on these factors and age groupings, using sex and education, as well as the factors themselves, as covariates. These analyses revealed that: (a) The mean level of fluid intelligence was systematically higher for younger adults (relative to older adults), (b) The mean level of crystallized intelligence was systematically higher for older adults (relative to younger adults), (c) The mean for the general visualization function was highest for the grouping of 21–28 year-olds and the means systematically dropped off on either side of the high value, (d) No systematic age trends were discernible for the general speediness, carefulness and fluency factors. These results provided support for the theory of fluid and crystallized intelligence.

The Meaning and Strategic Use of Factor Analysis

The general surveys of multivariate analysis methods in other chapters in this and the first edition give some idea of the relation of factor analysis to other methods in a mathematical sense. However, factor analysis differs also in a wide, experimental, strategic sense, from, for example, both multiple-correlation linear equations, and discriminant functions, in not arbitrarily choosing a criterion variable or criterion group, but in arriving at a reduced number of abstract variables and a weighting of observed variables according to structural indications in the data itself. It is thus a means of creating concepts, not merely of employing them or checking their fit to new data, though the new methods of Maxwell, Lawley, and Joreskog also fit it for hypothesis testing.

A Comprehensive Trial Of The Scree And Kg Criteria For Determining The Number Of Factors

In most well designed researches larger substantive factors show a break in size from those of a trivial lower degree of variance, which are due to error and other sources. The only short test for the number of such factors that has been repeatedly supported by plasmode results is the scree. The present experiment extends this empirical testing of the scree by taking 15 plasmodes, which vary in (1) number of variables, (2) of factors, (3) degree of obliquity, from orthogonal cases on, (4) presence of simple structure, (5) presence of error, extending to factoring random numbers, and (6) size of communality. The results support the scree and show it superior to the Kaiser-Guttman unity root criterion. Apart from the scree itself, a brief examination is made of the reliability of its use in the hands of trained and untrained judges. A second evaluation of the intrinsic validity of the scree is made by examining internal consistency of item and parcel factoring, of different sampling of variables and of change of population. The result again supports its capacity to locate the correct number of factors within narrow limits.

The Behavior Of Number-Of-Factors Rules With Simulated Data

issues related to the decision of the number of factors to retain in factor analysis are identified, and three widely-used decision rules -- the Kaiser-Guttman, scree, and likelihood ratio tests -- are isolated for empirical study. Using two differing structural models and incorporating a number of relevant independent variables (such as number of variables, ratio of number of factors to number of variables, variable communality levels, and factorial complexity), the authors simulated 144 population data sets and, then, from these, 288 sample data sets, each with a precisely known (or incorporated) number of factors. The Kaiser-Guttman and scree rules were applied to the population data in Part I of the study, and all three rules were applied to the sample data sets in Part II. Overall trends and interactive results, in terms of the independent variables examined, are discussed in detail, and methods are presented for assessing the quality of the number-of-factors indicated by a particular rule.

Confirmation and clarification of primary personality factors

In connection with a study bridging rating, questionnaire, and objective test factors, confirmation was sought with respect to the twelve personality factors previously found for young adult men. Variables were chosen to clarify and discriminate the nature of related factors. Ratings of and by 373 students were obtained, and the present study describes the separate factorization for the 133 men among them. Factorization yielded eleven factors, of which, on “blind” rotation for simple structure, 9 or 10 proved to be identical with those of the previous study. A new factorM is described.

“Parallel proportional profiles” and other principles for determining the choice of factors by rotation

The choosing of a set of factors likely to correspond to the real psychological unitary traits in a situation usually reduces to finding a satisfactory rotation in a Thurstone centroid analysis. Seven principles, three of which are new, are described whereby rotation may be determined and/or judged. It is argued that the most fundamental is the principle of “parallel proportional profiles” or “simultaneous simple structure.” A mathematical proof of the uniqueness of determination by this means is attempted and equations are suggested for discovering the unique position.

P-technique demonstrated in determining psychophysiological source traits in a normal individual

P-technique, a method employing intra-individual correlation, is tried out for the first time. As part of the general design it uses some variables the same as those in a coordinatedR-technique study and a second, parallelP-technique study with a clinical case. Definite factors are obtained among the psychological and physiological variables, which can be mutually matched. One is a fatigue factor, but the rest are general personality factors readily identifiable with those obtained in pastR-technique researches.

The Importance of Factor-Trueness and Validity, Versus Homogeneity and Orthogonality, in Test Scales1

EVALUATION of the fitness of tests, in terms of parameters of validity and reliability, is nowadays beginning to be seen in a, new light. Elsewhere (Cattell, in press) it has been suggested that the nomenclature, which has been stationery since the work of the APA Committee a decade ago (1954) is in need of revision. Most of the impulse for this restructuring has come from the extension of psychological measurement beyond the achievement and ability fields into personality and motivation investigation, where the limitations of the concepts previously innocently developed in the more restricted

Extracting the Correct Number of Factors in Factor Analysis

ingly potent role in psychology and the life sciences generally. Factor analysis is the king-post of multivariate analysis procedures, but its objectivity has been assailed on two issues: (a) the choice of communalities, affecting the number of factors extracted, and (b) the statistical significance and uniqueness of the simple structure rotational resolution. Both are involved in the proposed solution in the present article. Fortunately for the progress of psychological research, effective contribution to structural knowledge and concept formation has been possible through factor analysis despite its lacking an exact criterion of the completeness of extraction of factors from a given matrix. When a shrewd estimate of the number required to account for the correlations is made, the factors last taken out, whether they happen to exceed or still to fall short of the true number (if such exists), tends to be of such trivial variance that they affect the total extracted factor variance