Wilson H. Guertin

Research with the Wechsler Intelligence Scales for Adults: 1965–1970

Research of the past 5 years with the adult Wechsler scales is critically reviewed. Most investigators used the Wechsler Adult Intelligence Scale. Topical coverage includes: comparative validity; short forms; special populations and applications; refinements and critiques; personality correlates; investigations of diagnostic value; special diagnostic groups; and scatter, patterns, and diagnosis. The 260 articles reviewed show that there is no diminution in the number of researches in the area. While the quality of the research has improved, too many investigators repeat the errors contained in earlier studies, despite the periodic publication of these critical reviews.

The Superiority of Factor Scores as Predictors.

Common factor scores were compared to unfactored data-level variables as predictors in terms of the correlation of a criterion with the predicted value in multiple regression equations applied to replication (cross-validation) samples. Data were generated by computer to provide populations with three different degrees of common variance inherent in their predictor variable intercorrelation matrices. Two replication populations differing from the original by specified amounts in their intercorrelation matrices were created for each common variance level. Results indicated that shrinkage was less for factor scores than for data-level variables for all combinations of common variance and difference of replication population. Moreover, the actual correlation describing accuracy of prediction was higher for factor scores than for data-level variables at the extreme conditions of common variance and difference of replication population.

Distortion as a Function of the Number of Factors Rotated under Varying Levels of Common Variance and Error.

This study examined the effects of under and overrotation on common factor loading stability under three levels of common variance and three levels of error. Four representative factor matrices were selected. In each case, the factor matrix was adjusted to account for 30%, 45%, and 60% of common variance. Each of the adjusted matrices was postmultiplied by its transpose and the intercorrelation matrix obtained was factor analyzed to obtain the criterion matrix. Using Fishers z transformations, randomly-generated error based on 100, 200, and 500 subjects was added to the similarly transformed intercorrelation matrix. Each error-laden matrix of zs was then transformed back to r s and factor analyzed. Ten replications were completed for each experimental condition. Several rotations were tried below, equal to, and above the correct number of factors for each problem matrix chosen. Root-mean-square (RMS) mean values were obtained between the first few factors of each criterion matrix and the corresponding factors from the successive rotations. The RMS mean deviation values were plotted against the number of factors rotated and a multifactor repeated measures ANOVA performed. The number of factors rotated, the interaction of rotations with common variance, and the interaction of rotations with error were found significant at the .01 level in all four problems. The interaction of rotations with common variance and error was found significant at the .01 level for Problems Three and Four only. Although these findings must be considered within the logistical limitations imposed upon this study, it appears, nevertheless, that matrices which account for large amounts of common variance are less susceptible to the vagaries of overrotation. Hence, these matrices tend to have stable factor loadings. Furthermore, common-factor space is clearly distorted in the case of underrotation.

Correlates of Life Satisfaction for Old Libyans Compared with the Judgments of Libyan Youth.

Two hundred fifteen Libyans—106 young male and female undergraduate students and 109 aged male and female relatives—responded to a questionnaire designed to measure correlates of life satisfaction in old age. It was predicted that current cultural and social changes associated with the industrialization of Libya would result in significant differences in responses between young and old men and women. The young Libyan men rated close ties with their children, social relationships with individuals outside the family, and having basic physical needs met as more important than did the old Libyan men who considered social prestige, living with their spouse, and independence as more important for satisfaction in old age. The young Libyan women also considered social relationships outside the family and having basic physical needs met in old age as more important than did their older counterparts. Health and adequate living conditions were rated more highly by the young Libyan women than by the old. All participants rated social prestige equally high, but old women rated it higher than any other aspect except belief in God and self-understanding. Findings and implications for services to Libyas elderly are discussed.

RELATING MULTIDIMENSIONAL SETS OF VARIABLES: CANONICAL CORRELATION OR FACTOR ANALYSIS?

Several prominent multivariate psychological methodologists recommend the use of canonical correlation to relate multidimensional sets of variables. This method along with separate factor analyses of the sets is considered in relation to the questions they may be able to answer on a specific research problem. Alternate analyses of data from the social sciences illustrate the value of common factor analysis compared with canonical analysis as a method for relating the underlying constructs across sets of variables.

Typing Ships with Transpose Factor Analysis.

ally with people as rows and test variables as columns, the intercorrelations are computed between all possible pairs of columns. Stephenson (1936) and Burt (1937) both are credited with recognizing the possibility of transposing the data matrix before intercorrelating columns and factor analyzing. When the transposed rows become columns, the intercorrelation of columns is an intercorrelation of people. Factor analysis of the intercorrelations of test variables explicates clusters of these variables in test-space. When the correlation is between people the analysis is of people-space instead of test-space. Therefore, we can say that the transpose factor analysis explicates clusters of these persons in people-space. With superficial classification the correspondence between per-

Test Item Dependence of Several Oblique Factor Solutions

SEVERAL studies have focused on factor loading stability in an effort to define the sampling distribution of rotated factor loadings. Pennell (1968) provides a concise summary of Eome published work in this area (JSroskog, 1963; Cliff and Hamburger, 1967; Cliff and Pennell, 1967; and Bailey, 1969). The sampling error of rotated factor loadings appears t o be a function of certain parameters of the factoring problem, notably N and test item communality. However, one of the constraints which must be imposed on generalizing from the results of all these studies relates to the mathematical methods used to determine the factor loadings, eg., the rotational scheme used by the researcher to make factor analysis a more useful tool to him. Standard machine procedures use any number of algorithms representing different criteria to arrive a t useful solutions. These automatic methods, especially those which attempt to approximate in mathematical terms the simple structure criteria formulated by Thurstone (1947), have not been shown innocent of contributing to the deviant behavior of loadings. Kaiser (1958) demonstrated the stability of varimax factor loadings in a convincing empirical manner using actual test data. \Vhen the particular test items included in the battery were varied, the size of the computed factor loadings remained surprisingly similar. But common factor structure often dictates the use of

A Computer Program to Relate Factors Across Separately Factor Analyzed Variable Domains

A computer program written in FORTRAN IV is presented which will cross-correlate least squares estimated factor scores across separately factor analyzed variable domains without the tedious necessity of actually calculating the factor scores. Canonical correlations, associated redundancy statistics, and tests of independence for the reduced domains are also output. Documentation is provided.

SORTO: Factor Analyzing Q Sorts of Kelly's Personal Construct Productions

Summary A procedure for evaluating personality is described. Conventional and transposed factor analyses are made from Q sort data describing the important people in the subjects life in terms of his own constructs (a la Kelly) as variables. The scoring procedure produces construct-factors and people-factors. Sorts from a subject illustrate the method. Cross-cultural applications are possible since the translation of personal constructs is not essential. Simulation of relationships to others, SORTO, combines Kellys (1955) personal constructs with Stephensons (1953) Q sort procedure. A large amount of personal data is factor analyzed by the computer to reveal the main idiosyncratic features of a subjects perceptions of his relationships to others. Maximum output from the analysis occurs when the nature of personal constructs employed is supplied as input to the analysis.

Do the Different Methods of Factor Analysis Still Give Almost Identical Results

The question is examined 30 yr. after Wolfle summarized the field to see if newer methods of factor analysis have changed the picture substantially. An eight-variable two-factor physical body measurement problem is solved with a variety of methods and different estimates of communality. All give very similar results after the factor matrix is rotated to the varimax criterion. Even the image covariance analysis and principal components solutions portray the same structure as found by more conventional common-factor procedures.