Anti-ridge regression for communality estimation in factor analysis

An Exploratory Study of the Relationships between Reported Imagery and the Comprehension and Recall of a Story

The symmetric treatment of an asymmetric approach to factor analysis is shown to provide accurate communality estimates. In comparison with existing estimates including upper and lower bounds, the present approach is shown to be superior. In one example with known communalities, the present approach perfectly captures those communalities. In two empirical examples, it is shown to produce better communality estimates than any existing method.

The factor analysis model and Lazarsfeld's latent structure scheme for analyzing dichotomous attributes are derived to show how the latter model avoids three knotty problems in factor analysis: communality estimation, rotation, and curvilinearity. Then the latent structure model is generalized into latent profile analysis for the study of interrelations among quantitative measures. Four latent profile examples are presented and discussed in terms of their limitations and the problems of latent metric and dimensionality thereby raised. The possibility of treating higher order empirical relations in a manner paralleling their various uses in the latent structure model is indicated.

Female teachers indicated degree of agreement with 83 philosophy of education items. The 25 Jordanian Arab and Florida Americans were intercorrelated to disclose similarity of responding. The resulting intercorrelation matrix with communality estimates in the diagonal was factor analyzed. The Varimax rotated factor matrix revealed three type-factors; a major American factor, a major Arab, and a minor Arab factor. A profile of contrasting differences between the two major types is given. Only one of the 50 subjects could not be identified from loadings on the two major type-factors. National stereotypes may be useful and the view of Westerns and non-Westerns as “brothers” seems to have a better basis in humanism than in science.

Many persons ( 1, 2, 3, 4, 7, 10, 11, 13, 14, 15, 18) have applied factor analysis to the Wechsler? and the consensus of most of their results has led to the prevailing psychometric view that this battery measures just three common factors. However, discordant results have recently been reported by Cohen (6, 8), who obtained evidence in support of five common factors for a series of samples spanning a wide range of ages. Earlier, Davis (9 ) reported a factor analytic study of the WB-I together with other test variables, in which he found ten distinct factors each of which was correlated with at least one Wechsler subtest. In evaluating this situation it must be borne in mind that common factor analysis, using communality estimates in the diagonal of an 11 by 11 subtest intercorrelation matrix and assuming the validity of conventional factor analytic reasoning, cannot require more than seven factors under any conditions, and can provide a very good fit to the observed correlations with even fewer factors. It is therefore reasonable to suspect that the typical three-factor result may depend more on this limiting feature of the methodology rather than on any reality of the data. Cohen's results provide support for such a hypothesis, even his fivefactor results having been obtained from matrices that could require eight at most. (His WISC matrices were 12 by 12.) Davis' results also support such a hypothesis, but they are not fully convincing, both because other non-Wechsler

Some researchers have recently argued that a four-factor structure best represents the Self-Consciousness Scale. The present study provides evidence that a three-factor structure is superior to a four-factor structure in accounting for the variability among items. The three-factor version of the scale is shown to provide a closer approximation to simple structure than the four-factor model. The three-factor solution is also relatively invariant across communality estimates and rotations, whereas the composition of the four-factor solution is more affected by these factor parameters. Finally, confirmatory factor analysis shows that the four-factor solution does not provide a closer fit to the data than the three-factor solution. General issues regarding the role of factor analysis in theory development are addressed.

ABSTRACTOne purpose of communality estimation in factor analysis is to promote factorial invariance, i.e., to improve the chances of recovering demonstrably related factor structures from diverse sets of variables and samples of subjects. Recognition of this purpose may help to resolve ambiguities that have appeared in efforts to define unique communalities for isolated correlation matrices. The estimation of even approximate values for communality may be well worth the effort as a contribution to factorial invariance.A convenient, programable procedure is described that leads simultaneously to useful estimates of communality and of the number of factors. On the basis of actual data for two samples, properties of the communalities obtained by this procedure are compared with those obtained from a conventional principal axis analysis using diagonal entries of unity.The clinical scales of the MMPI, plus Si, are judged to provide reliable measurement on at least eight orthogonal dimensions, each well‐marked by a different scale. Stable differences exist in the item‐reliabilities of the ten scales studied. Neither of these consistencies in the data for the two samples was available from application of the conventional analysis.Tucker's procedure for examining factor congruence is found to be capable of yielding misleading results in the context of poor communality estimates.

A new method for correcting erroneous communality estimates is applicable to any completed orthogonal factor solution. It seeks, by direct correction of factor loadings, to make the residuals conform to the chance error criteria of zero mean and zero skewness for each row separately. Two numerical examples, with one and two factors, respectively, are presented. The method can be used as a short cut for Dwyer's extension in adding variables to a matrix. It can also be used as a short cut in cross-validation factor studies. Successful use on problems with many variables and numerous factors is claimed. Factors can be made oblique, after correction, if desired.

In South Africa, client satisfaction with the quality of health care has received minimal attention; probably due to the lack of locally developed and tested measures. Therefore, we developed and tested a 20-item attitude scale to determine satisfaction with Family Planning (FP) services. The objectives of this study were to: ascertain reliability of the scale and confirm, through factor analysis, that satisfaction with the FP service was based on interpersonal and organisational dimensions. The sample comprised 199 black adult interviewees (158 women and 41 men), who had previously used or were currently using contraception, from an informal settlement in Gauteng, South Africa. Three items were removed from the scale due to unacceptable communality estimates. The reliability coefficient of 0.76 for the 17-item scale was satisfactory. The principal components analysis, with orthogonal and oblique rotations, extracted two factors; accounting for 51.8% of the variance. The highest loadings on Factor I involved an interpersonal dimension (friendly, encouraging, competent, informative and communicative). Factor II tended to focus on the organisational elements of the system, such as different methods, choice of methods, service availability and length of waiting time. It was concluded that this scale was a reliable, easily administered and scored measure of satisfaction, with underlying interpersonal and organisational dimensions.

After a brief history of asymmetric approaches in factor analysis and related fields, there is derived a new asymmetric procedure that avoids communality estimation and other difficulties. This new solution splits a test battery 1 into sub‐batteries x and y, each of which spans the same factor space as does a test battery 2. This permits finding the unknown transformation that converts any factorization of the between‐battery correlations R12 into an orthogonal factor matrix reproducing both R12 and Rxy, the between‐sub‐battery correlations.

The inter-battery method of factor analysis was devised to provide information relevant to the stability of factors over different selections of tests. Two batteries of tests, postulated to depend on the same common factors, but not parallel tests, are given to one sample of individuals. Factors are determined from the correlation of the tests in one battery with the tests in the other battery. These factors are only those that are common to the two batteries. No communality estimates are required. A statistical test is provided for judging the minimum number of factors involved. Rotation of axes is carried out independently for the two batteries. A final step provides the correlation between factors determined by scores on the tests in the two batteries. The correlations between corresponding factors are taken as factor reliability coefficients.

University of MinnesotaThis study was undertaken to identify independent interest dimensions thatwere equivalent across different subject samples, as a first step toward mappingthe vocational interest domain. The responses to 347 female form items and357 male form items from the Strong Vocational Interest Blank (SVIB) wereobtained, using the appropriate form for the following five single-sex samples:women in general (n = 1,000), men in general (n = 1,000), female occupational(n — 2,500), male occupational (n — 3,600), and male rehabilitation client(n — 1,874). Separately for each sample the SVIB items were intercorrelated,and the correlation matrices were factored by a principal axes technique, usingthe highest off-diagonal correlations as communality estimates with rotation toa varimax criterion. Factors between same-sex samples were compared usingTucker's coefficient of congruence. The analyses resulted in 11-13 factors, de-pending on the sample, of which 9 and 8 were judged to be equivalent acrossthe two female and three male samples, respectively.The Strong Vocational Interest Blank(SVIB; Strong, 1943), initially published in1927, has been one of the most successful andwidely used instruments in vocational coun-seling practice and research. Much of what isreliably known about vocational interests isbased on research with the SVIB (Campbell,1971; Crites, 1969; Barley & Hagenah,1955; Strong, 1943; Tyler, 1965). The sev-enth edition of Mental Measurements Year-

Purpose: The overall purposes of this article are to report the development of a survey instrument, Scientific Misconduct Questionnaire-Revised (SMQ-R) that elicits the perceptions of research coordinators managing clinical trials about the various aspects of scientific misconduct and to present the psychometric analyses for the SMQ-R. Methods: A panel of five researchers and research coordinators reviewed the original SMQ (Rankin and Esteeves, 1997) and suggested an additional 42 items based on the review of the literature and their own experiences in research. The SMQ-Revised (SMQ-R) consists of 68 closed-choice items in six sections and one section with 12 open-ended questions. The SMQ-R was sent to 5302 persons who were members of the Association for Clinical Research Professionals (ACRP) or subscribers to Research Practitioner, published by the Center for Clinical Research Practice (CCRP). Findings: Internal consistency of subscales was assessed with Cronbach's alpha and ranged from .83 to .84. Confirmatory factor analysis was used to test construct validity of the instrument subscales. The factor structure was assessed with the principal factors method, using the squared multiple correlations as initial communality estimates followed by varimax (orthogonal) or biquartimax (oblique) rotations. Analyses revealed five distinct factors among three subscales. Construct validity for the SMQ-R was also assessed by testing hypothesized relationships using the known groups approach. Conclusion: The current effort demonstrated the usefulness of the SMQ-R in obtaining information from a national sample of experienced research coordinators about their perceptions of the prevalence of different types of scientific misconduct and of factors that influence the occurrence of misconduct. The psychometric evaluation of the SMQ-R suggests good internal consistency for most subscales and suggests adequate construct validity of the instrument as a whole. The analyses also suggest that further refinement of the instrument for future studies is warranted.

On the assumption that a partitioning can be found such that three mutually exclusive test vector configurations span the same factor space, a procedure is derived whereby symmetric parts of the correlation matrix are estimated from functions of asymmetric parts treated symmetrically. This yields an explicit matrix formula for communality estimation which generalizes earlier work by Albert. Conventional factoring methods, with all their computational and fitting advantages, can be applied once the symmetric portions of the correlation matrix have been estimated. Extension to four subgroups of test vectors allows for a matrix generalization of the old tetrad difference criterion to the multiple-factor case.

ABSTRACTThe primary purpose of this study was to determine student traits that faculty associate with desirability, separate and apart from those reflected by the traditional academic achievement indices.Ratings of students on 80 variables, including a student desirability variable, were obtained, together with high school and college grade averages and SAT scores. The resulting 84 × 84 correlation matrix was factored by the diagonal method, using precise communality estimates from a separate factor analysis. In this case, the procedure permits partialling out the variance in desirability and the other variables which is attributable to academic performance, and definition of residual desirability in terms of relationship of the residual of the other variables to desirability apart from academic performance. The diagonal factoring method was also used to examine the content, including academic performance, of general desirability, and to define desirability separate and apart from SAT and academic performance.Ratings of intellectual ability and values, motivation, and creativity, as well as actual grade point average, were found to be related to general desirability ratings. Desirability apart from grades, however, appears to consist of such traits as likableness, ethicality, open‐mindedness, altruism, maturity, and self‐insight, although ratings of intellectual ability and values have components related to grades and to desirability apart from grades. Ability as measured by the SAT, though reasonably related to performance, appears to have negative relationship to desirability apart from grades.