John L. Horn

A rationale and test for the number of factors in factor analysis

It is suggested that if Guttmans latent-root-one lower bound estimate for the rank of a correlation matrix is accepted as a psychometric upper bound, following the proofs and arguments of Kaiser and Dickman, then the rank for a sample matrix should be estimated by subtracting out the component in the latent roots which can be attributed to sampling error, and least-squares “capitalization” on this error, in the calculation of the correlations and the roots. A procedure based on the generation of random variables is given for estimating the component which needs to be subtracted.

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 Theory of Fluid and Crystallized Intelligence in Relation to Concepts of Cognitive Psychology and Aging in Adulthood

The principal purpose of this chapter is to lay out some of the major results and conclusions of a series of studies conducted by this investigator and his coworkers (principally Donaldson, Engstrom, and Mason) over the last few years. To comprehend these results and conclusions it is necessary to have some appreciation of the theory and assumptions on which the research has been based. These ideas are not major themes in the research and theory of mainstream cognitive developmental psychology. It is probably worthwhile, therefore, to sketch at the outset some features of the research that is to be reviewed.

CHAPTER 16 – Organization of Data on Life-Span Development of Human Abilities

Data pertaining to the development of intellectual abilities in childhood and adulthood are reviewed within the framework of a general theory in which the cohesion-producing influences associated with acculturation and neurophysiology are emphasized and contrasted. First, it is noted that a striking amount of interrelationship has been found among abilities which, on the face of it, could be quite different–and when abilities are measured at quite different points in development (excluding only the first two years of life wherein the measured abilities bear little resemblance to, and are not predictive of, intellectual abilities measured in later childhood and thereafter). This broad cohesiveness is seen to represent a fact of interdependence of acculturational and neurophysiological influences–the fact that, to some extent, one determines and is determined by the other. It is noted, next, that interwoven within this broad pattern of interdependence are subpatterns of varying degrees of generality. Some of these are seen to result from relatively focused kinds of training, as this derives from selective exposures, fairly specific kinds of motivations and similar factors. Quite broad patterns are found, however, and the evidence suggests that these represent more pervasive influences in development, such as those of acculturation, as such, and those associated with neurophysiological structure, maturation and damage. Indeed, accumulations of these pervasive influences throughout development appear to produce two broad patterns of the abilities which are identified as indicating intelligence. These patterns are said to indicate two intelligences, symbolized as Gf and Gc. In later childhood and adulthood the predictive and construct validities for these two become quite distinct. The abilities of Gc tend to increase–or at least not noticably decrease–with age in adulthood, but the abilities of Gf tend to decrease consistently and to a noteworthy extent throughout most of adulthood. Evidence indicating the neurophysiological and experiential factors associated with these changes is outlined.

On Subjectivity in Factor Analysis

ROTATION to simple structure in factor analysis was devised by Thurstone (1935) as a means for solving the indeterminacy problem. I n the usual factor analysis based upon a matrix of intercorrelations there is an infinite number of factor solutions, each involving the same number of factors and each allowing reproduction of the correlation matrix with the same degree of accuracy. A simple structure solution is one of the infinite number of possible solutions, but one which, for the various reasons Thurstone gave, might be expected to be more interpretable, more replicatable and, in general, more useful in scientific Tvork than any other solution (at least for some kinds of substantive problems). Thurstone viewed rotation, then, as a means of making factor analysis a more useful research tool. The various solutions obtainable by use of standard procedures for calculating factors represent different criteria of rotation, as Thurstone (1947) himself demonstrated. The principal axes solution, for example, is a rotation to a set of factors such that the first accounts for the maximum possible linear covariation among the variables; the second accounts for the maximum possible of such covariation after that accounted for by the first factor has been removed, etc. In a traditional bi-factor solution the first factor is rotated in much the same way as in the principal axis solution, but subsequent factors are rotated in a way to obtain large loadings for a small number of variables and near-zero loadings for the remaining variables. I n a Tryon cluster analysis all factors are rotated in this latter manner. I n any other so-called “direct” Eohltion there is, similarly, an implicit rotational criterion.

An Empirical Comparison of Methods for Estimating Factor Scores

came readily available-the computation of factor scores was a task of such Herculean proportions that an investigator could hardly be blamed for not planning his study to include these procedures. But this is no longer true. Computers reduce the task to easily managed proportions. Present indications are that factor analysis will continue to be a popular research tool. It may very well become more popular. Psychometricians working with the method have known for some time

Human abilities revealed through auditory tests.

Established findings from studies of visual, musical, and speech perception abilities were used to guide the construction of auditory ability tests. Fortyfour measures based on these tests were obtained from a sample of 241 adult males. Correlation and factorial analyses were used to indicate structural interrelationships and relationships with education, musical experience, general intelligence, .and age. The results indicated separate capacities for Auditory Verbal Comprehension, Auditory Immediate Memory, Temporal Tracking, Auditory Cognition of Relationships, Discrimination Among Sound Patterns, Speech Perception Under Distraction/Distortion, and Maintaining and Judging Rhythm.

A contemporary method for developmental‐genetic analyses of age changes in intellectual abilities

The purpose of this article is to describe a methodology for the evaluation of biometric genetic hypotheses in the context of a developmental model of growth and change. Linear structural equation models are described for longitudinal and twin data, including aspects of subject attrition and practice effects. These models are applied to 2 variables measured at several points in time in the New York Twin Study (Jarvik, Kallman, & Falek, 1962; Kallman, Feingold, & Bondy, 1951). The patterns of psychometric and biometric changes are different for the 2 intellectual variables. Substantive results are discussed in relation to gf/gc theory (Cattell, 1971; Horn, 1988), and some methodological limitations are emphasized.

Auditory and visual factors of intelligence

Abstract In a sample of 241 convicts, most of whom were between 20 and 35 years of age, a sample of 18 primary mental abilities was factored to explore the idea that in performances that are believed to indicate human intelligence there are organizations among visual and auditory functions that operate independently from the relation-perceiving and correlate-educing functions of fluid and crystallized intelligence. Objectively rotated results suggest that, indeed, reliable overlapping (common-factor) functions of Auditory Acuity (Ac), Auditory Organization (Ga), Visual Organization (Gv), Acculturational Eduction (Gc) and Fluid Eduction (Gf) represent separate components of individual differences in performances on intellectual tasks broadly conceived.

Concepts of intellect in relation to learning and adult development

Abstract This article is a summary and integration of results from studies of the organization and development of human abilities. Several kinds of results are interpreted as converging toward support of theories stipulating a hierarchy of intellectual functions. Near the top of this hierarchy, most related to intelligence as this is usually conceived, are the two broad sets of abilities known as fluid intelligence (Gf) and crystallized intelligence (Gc). The major focus of the review is on the decline of Gf through the “vital years of adulthood,” from 20 to 60 years of age. Major conclusions are: 1. Sensory detector functions, near the bottom of the hierarchy of intellectual capacities, decline with development through the vital years, but this kind of decline is not responsible for aging decline of the major features of fluid intelligence: keenness of sensory function is not of the sine qua non of mature expressions of human intelligence. 2. Memory abilities are somewhat higher in the hierarchy of intellectual functions, and thus are more strongly related to intelligence, than are sensory detectors. With increase in time interval over which retention is required, there is increase in the relationship of memory to Gf and to decline of Gf over the vital years. Accompanying this increase is an increase in the extent to which memory is dependent upon adequacy of organization at the stage of encoding. This, in turn, reflects the adequacy of eduction of relations and correlates, which is an essential feature of Gf. 3. To the extent that very short-term memory is implicated in fluid intelligence, and the decline of this, it is intimately related to either a capacity or inclination to maintain close attention under conditions of high demand for attention. 4. The speed with which one obtains correct answers to difficult problems is not closely related to the number of correct answers obtained when all subjects attempt all items in fluid intelligence tests, but clerical/perpetual speed, as indicated in tasks of quickly finding a particular symbol among others or tasks of making same/different judgments, is related to aging decline of Gf. As with short-term memory, this form of intellectual speediness appears to be closely related to capacities (or inclinations) for maintaining attention, dividing attention, and holding things in mind while doing other things. 5. Crystallized intelligence probably increases over the vital years. This reflects dynamic restructuring of knowledge systems. It appears that there is not only an aging increase in knowledge but also an increase in the accessibility of information, a result being that humans become more creative (in one sense) as age increases through the vital years. 6. Results from multivariate cross-sectional studies of intelligence are seen to be consistent with comparable results obtained with other kinds of research strategies.