Factor and discriminant analysis of the Bem Sex-Role Inventory

Several studies have recently recommended that items which fail to load substantially (< .40) on one of several primary factors characterizing the Bem Sex-Rote Inventory (BSRI) could be deleted without substantial loss of interpretability. This recommendation is questioned on the basis that the extent of interrelatedness of the items is an insufficient indicator of the contribution each item makes towards the classification (identifying sex-types by Bem's median split technique) efficiency of the inventory. Empirical support of this contention was provided by conducting several discriminant analyses (predicting sex-types) on a sample of 1117 BSRI protocols and excluding the various items suggested by the earlier research. These results were then compared with the results of a discriminant analysis using the 40 masculine and feminine items. The analyses using less. than all 40 items produced substantially poorer discrimination than when all 40 items were included. The results Suggest that decisions to exclude items on the basis of factor analysis may be inappropriate and risk serious loss of power in classifying individuals by sex-type.     

Robust canonical discriminant analysis

A method for robust canonical discriminant analysis via two robust objective loss functions is discussed. These functions are useful to reduce the influence of outliers in the data. Majorization is used at several stages of the minimization procedure to obtain a monotonically convergent algorithm. An advantage of the proposed method is that it allows for optimal scaling of the variables. In a simulation study it is shown that under the presence of outliers the robust functions outperform the ordinary least squares function, both when the underlying structure is linear in the variables as when it is nonlinear. Furthermore, the method is illustrated with empirical data.The research of the first author was supported by the Netherlands Organization of Scientific Research (NWO grant 560-267-029).     

Ideal point discriminant analysis

A new method of multiple discriminant analysis was developed that allows a mixture of continuous and discrete predictors. The method can be justified under a wide class of distributional assumptions on the predictor variables. The method can also handle three different sampling situations, conditional, joint and separate. In this method both subjects (cases or any other sampling units) and criterion groups are represented as points in a multidimensional euclidean space. The probability of a particular subject belonging to a particular criterion group is stated as a decreasing function of the distance between the corresponding points. A maximum likelihood estimation procedure was developed and implemented in the form of a FORTRAN program. Detailed analyses of two real data sets were reported to demonstrate various advantages of the proposed method. These advantages mostly derive from model evaluation capabilities based on the Akaike Information Criterion (AIC).The work reported in this paper has been supported by Grant A6394 from the Natural Sciences and Engineering Research Council of Canada and by a leave grant from the Social Sciences and Humanities Research Council of Canada to the first author. Portions of this study were conducted while the first author was at the Institute of Statistical Mathematics in Tokyo on leave from McGill University. He would like to express his gratitude to members of the Institute for their hospitality. Thanks are also due to T. Komazawa at the Institute for letting us use his data, to W. J. Krzanowski at the University of Reading for providing us with Armitage, McPherson, and Copas' data, and to Don Ramirez, Jim Ramsay and Stan Sclove for their helpful comments on an earlier draft of this paper.     

Qualitative analysis of experiences of members of a psychoeducational assertiveness group

This study describes qualitatively a psychoeducational assertiveness intervention for 20 women's perceptions of positive and negative experiences, undertaken to identify whether therapeutic mechanisms operating in group therapy as described by Yalom might be inferred. There were 14 90-min. weekly sessions organized around educational material. Two groups were conducted with 10 university women each (M= 20.9 yr., SD= 1.9). Qualitative analysis of the 20 interviews identified five of Yalom's therapeutic mechanisms, namely, self-understanding, universality, acceptance, catharsis, and self-disclosure. The positive experiences were group cohesiveness, self-understanding, self-disclosure, positive views about the self and learning, and cognitive benefits. Self-disclosing at the early stages of group development was the most frequently reported negative experience or difficulty in the group. Although participants stated they improved interpersonal communication skills, analysis suggested the cultural context was an important mediator of assertive behavior.     

The structure of honesty: Factor analysis of the reid report

The present study conducted principal component factor analyses of the Reid Report honesty test using two large (N=1281, N=3071) samples of applicants for employment. The results, which replicated across samples, strongly supported the existence of four major factors involved in the Reid Report measure of employee honesty. The Self-Punitiveness factor of the Reid Report contains items in which individuals indicate the extent to which they hold themselves to high standards of conduct. The Other-Punitiveness factor involves questions in which individuals indicate whether they are relatively harsh towards other people who commit crimes or act dishonestly. The Self-Projection factor of the Reid Report incorporates items in which individuals admit or deny that they have personal fantasies about dishonest behavior, such as taking company merchandise home with them. Finally, on the Other-Projection factor, respondents indicate the extent to which they see dishonest intentions or behaviors in others. Such results suggest a basis for more detailed assessments of a person's honesty than is provided merely by a single overall honesty score.This study was initiated while Dr. Ash was affiliated with Reid Psychological Systems, and was completed after he moved to London House, Inc. An earlier version of this study was presented by Dr. Ash at the Second Annual Conference of the Society of Industrial and Organizational Psychology, Atlanta, April, 1987. The authors are grateful for the cooperation of Reid Psychological Systems in providing the data used in the present study, and to David Arnold and Paul Brooks for their comments on an earlier draft.     

Intraorganizational and interorganizational job change: A discriminant analysis

Using March and Simon's (1958) participation model as a framework, this study employs the 1973–77 Quality of Employment Survey panel data to compare the determinants of intraorganizational and interorganizational job change. Two discriminant functions were significant, the first distinguishing between intraorganizational changers and stayers and the second between interorganizational changers and stayers. Moreover, the variables that distinguished between intraorganizational changers and stayers were either different from or opposite in influence to those distinguishing between interorganizational changers and stayers.     

Factor analysis and AIC

The information criterion AIC was introduced to extend the method of maximum likelihood to the multimodel situation. It was obtained by relating the successful experience of the order determination of an autoregressive model to the determination of the number of factors in the maximum likelihood factor analysis. The use of the AIC criterion in the factor analysis is particularly interesting when it is viewed as the choice of a Bayesian model. This observation shows that the area of application of AIC can be much wider than the conventional i.i.d. type models on which the original derivation of the criterion was based. The observation of the Bayesian structure of the factor analysis model leads us to the handling of the problem of improper solution by introducing a natural prior distribution of factor loadings.The author would like to express his thanks to Jim Ramsay, Yoshio Takane, Donald Ramirez and Hamparsum Bozdogan for helpful comments on the original version of the paper. Thanks are also due to Emiko Arahata for her help in computing.     

Metacontrast suppression and criterion content: A discriminant function analysis

Three test and three mask energies of a metacontrast display were varied orthogonally and randomly over trials. The stimulus onset asynchrony (SOA) separating them was varied over blocks of trials from 0 to 180 msec in 30-msec steps. Both the accuracy in judging the test and the coherence (consistency) of the judgments were U-shaped functions of SOA. Thus, metacontrast suppression is in part due to inadequate information. In addition, mask energy was found to correlate negatively with judgments of the test at short SO As but positively at longer SOAs. This indicates that part of the masking effect is due to inappropriate use of information. Certain similarities were noted between these findings and those obtained with judgments of frequency in the auditory-recognition masking paradigm. In general, the results indicate that subjects respond to different features of the stimulus situation as SOA varies.     

Analysis of contingency tables by ideal point discriminant analysis

Cross-classified data are frequently encountered in behavioral and social science research. The loglinear model and dual scaling (correspondence analysis) are two representative methods of analyzing such data. An alternative method, based on ideal point discriminant analysis (DA), is proposed for analysis of contingency tables, which in a certain sense encompasses the two existing methods. A variety of interesting structures can be imposed on rows and columns of the tables through manipulations of predictor variables and/or as direct constraints on model parameters. This, along with maximum likelihood estimation of the model parameters, allows interesting model comparisons. This is illustrated by the analysis of several data sets.Presented as the Presidential Address to the Psychometric Society's Annual and European Meetings, June, 1987. Preparation of this paper was supported by grant A6394 from the Natural Sciences and Engineering Research Council of Canada. Thanks are due to Chikio Hayashi of University of the Air in Japan for providing the ISM data, and to Jim Ramsay and Ivo Molenaar for their helpful comments on an earlier draft of this paper.     

Neuropsychological assessment of learning disabilities: a discriminant analysis

The neuropsychological test scores of 23 learning disabled children were compared with those of a matched population of normal children in the 9-1 to 13-1 age range. All children were administered the Wechsler Intelligence Scale for Children-Revised (WISC-R), a dichotic listening task involving both free and directed recall conditions, a handedness inventory, the Tactile Performance Test and the Category Test from the Halstead-Reitan Neuropsychological Test Battery. A multivariate analysis of variance resulted in a significant separation between groups (p less than .001) using these procedures. A stepwise discriminant function analysis revealed that both of the directed dichotic tasks contributed the most of all 13 measures to the significant group separation. In addition, other cognitive tasks found to discriminate normal from learning disabled children include general verbal processes, concept formation, and tactile memory. These findings suggest that the directed dichotic listening procedure and the WISC-R Verbal IQ measure are reasonably valuable clinical tools in the classification of learning disabilities.     

Factor analysis and physical types

Physical measurements, obtained from several different age-groups and national groups, have been correlated and factorized. The largest of the investigations was based on 2,400 British airmen in the R.A.F., and the most recent included as many as 17 traits. The methods of factorization employed were those worked out in early investigations of mental and scholastic tests, and differed in minor respects from those more recently used by Thurstone in his re-analysis of some of our data. The factor patterns reveal a remarkable constancy from age to age and from one national group to another. The general factor accounts for about the same proportion of the variance as the general factor in cognitive tests. The largest of the bipolar factors classifies traits into longitudinal and transverse, thus in some measure confirming the traditional classification of body-types.     

Factor analysis and body types

A factorial analysis was made of a small battery of twelve anthropometric measurements. The correlations can be accounted for by four factors in a simple structure. This small battery has been used by the author for teaching purposes. Several of these factors seem to be meaningful, but their acceptance must depend on more comprehensive studies of body measurements with a larger number of measurements.     

Factor analysis and personality theory

This article deals with the factor analytic approach to personality. More specifically, it deals with problems in factor analyses of personality questionnaires which contribute to factorial confusion. It is stated that in fact the factorial results make better sense than is usually admitted. The apparent disparity of results can be accounted for by technical defects in the chosen factor analytic method. Furthermore, it is shown that another source of disagreement lies in the interpretation of what are essentially the same factors.     

Factor analysis and scale revision

This article reviews methodological issues that arise in the application of exploratory factor analysis (EFA) to scale revision and refinement. The authors begin by discussing how the appropriate use of EFA in scale revision is influenced by both the hierarchical nature of psychological constructs and the motivations underlying the revision. Then they specifically address (a) important issues that arise prior to data collection (e.g., selecting an appropriate sample), (b) technical aspects of factor analysis (e.g., determining the number of factors to retain), and (c) procedures used to evaluate the outcome of the scale revision (e.g., determining whether the new measure functions equivalently for different populations).     

Aggression in African-American boys: a discriminant analysis.

The main purposes of this study were to determine whether familial variables found to be related to the development of aggressive behavior in Caucasian boys may also be related to similar aggressive patterns in inner-city African-American boys and to assess the relative importance of these variables for classifying the subject population into aggressive and nonaggressive groups. Discriminant analyses were performed using 83 African-American boys, with a mean age of 13.9 years, who were classified as institutionalized aggressive, noninstitutionalized aggressive, and noninstitutionalized nonaggressive subjects. Although the same father and mother variables were used in the analyses, the father variables were not related to group membership. Furthermore, the results showed that both groups of aggressive boys reported more aggression within as well as outside their family home settings than their nonaggressive counterparts. Socioeconomic-related factors such as employment status of parent(s), size of family, and number of parents in the household were not useful predictors of aggressive and nonaggressive group membership.     

A comparison of linear and mixture models for discriminant analysis under nonnormality

Methods for discriminant analysis were compared with respect to classification accuracy under nonnormality through Monte Carlo simulation. The methods compared were linear discriminant analyses based both on raw scores and on ranks; linear logistic discrimination; and mixture discriminant analysis. Linear discriminant analysis and linear logistic discrimination were suboptimal in a number of scenarios with skewed predictors. Linear discriminant analysis based on ranks yielded the highest rates of classification accuracy in only a limited number of situations and did not produce a practically important advantage over competing methods. Mixture discriminant analysis, with a relatively small number of components in each group, attained relatively high rates of classification accuracy and was most useful for conditions in which skewed predictors had relatively small values of kurtosis.     

Values of British political extremists and potential extremists: A discriminant analysis

Studied the value systems of political extremists and potential extremists, comparing them with the value systems of centrist activists and supporters. Samples of political activists from the Labour, Conservative, Communist and National Front parties were obtained, as well as samples of non-active supporters. The non-active supporters were defined as Potential Extremists, if they supported a centrist party as first choice, but either Communist or National Front as second choice. All subjects completed the Rokeach Value Survey. Discriminant analysis showed that the four groups of activists could be clearly distinguished on the bask of their values. However the values of the Potential Extremists did not especially resemble the values of actual National Front or Communist activists. There were value differences between the Potential Extremists and the centrist supporters; nevertheless these two groups tended to be distinguished by very different values from those which distinguished between the activists. The appeal of value symbols for different types of political involvement was discussed.