Andrew L. Comrey

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).

Distortions in a Commonly Used Factor Analytic Procedure.

A currently popular procedure in empirical factor analytic studies is to use unities in the main diagonal as communality estimates, extract all factors with eigenvalues of 1.0 or higher, and rotate these factors by varimax. This procedure and others are applied to several previously published correlation matrices and some artificial matrices. This procedure results in the retention of too many factors, unrealistic elevation of the amount of common factor variance analyzed, and distortions in the conclusions drawn from the factor analytic investigation. Ways of avoiding these difficulties, are discussed.

The Minimum Residual Method of Factor Analysis

Thus, al is a function of the remaining factor loadings, excluding itself, and the correlations which variable i has with the other variables. If an initial estimated factor vector A is assumed, estimates of the 4 values may be obtained by the use of Equations [ 2 ] . This can give rise to a n interative process in which the newly estimated A vector can in turn be substituted in Equations [2] to obtain still another estimate. A n iterative process is of value only if (1) i t converges to an acceptable solution, and ( 2 ) convergence occurs rapidly enough to make the computations reasonable. In extensive applications of this method to date, no difficulry has been encountered i n obtaining satisfactory convergence until after the normal number of factors has been extracted. Convergence does not take place in the typical manner, however. If we substitute an initial trial vector, obtain an iterated vector, substitute the iterated vector to obtain a second iterated vector, and so on, convergence appears to take place about two saddle

A Factor Analysis of Items On the MMPI Paranoia Scale

FACTOR analyses have already been reported (i, 2, 3, ~) for items from the Hypochondriasis, Depression, Hysteria, and Psychopathic Deviate scales of the Minnesota Multiphasic Personality Inventory (5). Important factors isolated in these analyses have been entitled Poor Physical Health (i, 2, 3), Neuroticism (2, 3, 4), Cynicism (2, 3), Shyness (3, 4), Euphoria (2, 4), and Paranoia (4). Other factors not strongly or repeatedly identified have occurred which may be of considerable importance. Workable scales based on MMPI items have been suggested for the first two factors mentioned. These scales were called &dquo;Health Concern&dquo; and &dquo;Neu-

A Factor Analysis of Items on the Mmpi Hypochondriasis Scale1

PROBABLY no test in the personality field has enjoyed such great popularity and wide use as the Minnesota Multiphasic Personality Inventory (3). This wide usage suggests that the test has many desirable features, and most psychologists would probably agree that i t does. Certain weaknesses also exist in the MMPI, however. It is well established that the abnormal scales overlap to a considerable degree in many instances. Wheeler, Little, and Lehner, for example, report a correlation of .86 between the Sc and Pt scales, .77 between the Sc and F scales, and .73 between the Hs and each of the D and Hy scales (7). An examination of the intercorrelations among items on the abnormal scales leads one to question how the existing grouping can be justified. Factor analyses of MMPI scales have been published from time to time, but valuable as these studies are, they do not help greatly in the problem of determining the factor content of the items themselves. In view of the marked overlapping variance between scales and the apparent lack of homogeneity within scales, i t appears desirable to know something about the factorial content of the items themselves. Such knowledge should be helpful in regrouping present items and in suggesting areas where additional items might be developed. It is one thing to say that factor analyses of items within

A factor analysis of items on the MMPI hysteria scale.

PREVIOUS papers (I, 2) have reported results of factor analyses of items on the Hypochondriasis and Depression scales of the Minnesota Multiphasic Personality Inventory (3). The most prominent factor in the Hs scale analysis was called “Poor Physical Health.” On the Depression scale, the main factor was described as “Neuroticism.” From the first of these factors a scale of 17 items was proposed, with the title “Health Concern.” From the Neuroticism factor on the D scale, a second scale was suggested. It contains 26 items and was entitled “Neuroticism.” Continuing with the series of analyses of items on the principal abnormal scales of the MMPI, the present article is concerned with items from the Hysteria (Hy) scale. The procedure will be outlined here but certain details presented in the initial article of the series (I) will not be repeated. The factor analysis variables included the 60 MMPI H y scale items plus three additional dichotomized variables, Age, Sex, and Hospitalization. Of the 360 cases in the sample, 77 per cent were 25 years of age or more, 51 per cent were male, and 47 per cent were Los Angeles Veterans’ Administration Hospital patients of random psychiatric diagnosis. The hospital cases were about equally divided among men and women. A majority of the normal cases were education students

A Factor Analysis of Items On the MMPI Psychopathic Deviate Scale

most important factor in the Hs scale, Poor Physical Health, was used to suggest items for a new scale entitled &dquo;Health Concern.&dquo; The most important new factor in the D scale analysis was called &dquo;Neuroticism&dquo; and a scale based on this factor was suggested. Both these factors were again isolated in the Hy scale analysis along with two other factors judged to be of sufficient clarity and importance to warrant scale construction. These two factors were called &dquo;Shyness&dquo; and &dquo;Cynicism.&dquo; For neither of these two factors were sufficient items present on the Hy scale to provide an adequate scale. The current analysis, continuing the series of analyses for the important abnormal MMPI scales, is devoted to the 50 items from the Psychopathic Deviate (Pd) scale plus three additional dichotomized variables, Age, Sex, and Hospitalization. Although

A Factor Analysis of Items on the MMPI Hypomania Scale

OTHER articles in this series ( 1, 2, 3, 4, 5, 6, 7) have reported the results of factor analyses of items in the Hypochondriasis, Depression, Hysteria, Psychopathic Deviate, Paranoia, Psychasthenia, and Schizophrenia scales of the Minnesota Multiphasic Personality Inventory (8). Over thirty different factors have been found in the scales analyzed although relatively few were well defined. All the MMPI scales have proved to be highly complex factorially and many of the factors have appeared on two or more scales. The most prominently represented factor, called &dquo;Neuroticism,&dquo; has been identified in the Depression, Hysteria, Psychopathic Deviate, Paranoia, and Psychasthenia scales. These findings suggest that items from the MMPI should be regrouped into more homogeneous and independent scales wherever possible. Drawing from the pool of items analyzed

Tandem criteria for analytic rotation in factor analysis

Two related orthogonal analytic rotation criteria for factor analysis are proposed. Criterion I is based upon the principle that variables which appear on the same factor should be correlated. Criterion II is based upon the principle that variables which are uncorrelated should not appear on the same factor. The recommended procedure is to rotate first by criterion I, eliminate the minor factors, and then rerotate the remaining major factors by criterion II. An example is presented in which this procedure produced a rotational solution very close to expectations whereas a varimax solution exhibited certain distortions. A computer program is provided.

A Factor Analysis of Items on the MMPI Schizophrenia Scale

SEVERAL previous articles in this series ( 1, 2, 3, 4, 5, 6) have reported factor analyses of the items on the Hypochondriasis, Depression, Hysteria, Psychopathic Deviate, Paranoia, and Psychasthenia scales of the Minneso a Multiphasic Personality Inventory (7). Findings generally have shown these scales to be highly complex factorially and greatly overlapping in factor content. As a result of the factor analyses carried out, it has been possible to suggest some revised scales which have greater unity of content. For certain of these scales, e.g., Neuroticism, Health Concern, and Paranoia, there probably are enough items in the