Evaluation of factor analytic research procedures by means of simulated correlation matrices

In order to study the effectiveness of factor analytic methods, a procedure was developed for computing simulated correlation matrices which are more similar to real data correlation matrices than are those matrices computed from the factor analysis structural model. In the present investigation, three methods of factor extraction were studied as applied to 54 simulated correlation matrices which varied in proportion of variance derived from a major factor domain, number of factors in the major domain, and closeness of the simulation procedure to the factor analysis structural model. While the factor extraction methods differed little from one another in quality of results for matrices more dissimilar to the factor analytic model, major differences in quality of results were associated with fewer factors in the major domain, higher proportion of variance from the major domain, and closeness of the simulation procedure to the factor analysis structural model.

[1]  H. Hotelling Analysis of a complex of statistical variables into principal components. , 1933 .

[2]  T. L. Kelley Essential Traits of Mental Life , 2012, Nature.

[3]  Harry H. Harman,et al.  Comparison of two factorial analyses , 1938 .

[4]  H. Eysenck PRIMARY MENTAL ABILITIES , 1939 .

[5]  C. Spearman,et al.  Thurstone's work re-worked. , 1939 .

[6]  L. Thurstone Current issues in factor analysis. , 1940 .

[7]  D. Lawley VI.—The Estimation of Factor Loadings by the Method of Maximum Likelihood , 1940 .

[8]  L. Thurstone Primary mental abilities. , 1938, Science.

[9]  C. Burt FACTOR ANALYSIS AND CANONICAL CORRELATIONS , 1948 .

[10]  L. Tucker A METHOD FOR SYNTHESIS OF FACTOR ANALYSIS STUDIES , 1951 .

[11]  Louis Guttman,et al.  Image theory for the structure of quantitative variates , 1953 .

[12]  Wayne S. Zimmerman,et al.  A revised orthogonal rotational solution for Thurstone's original primary mental abilities test battery , 1953 .

[13]  L. Guttman Some necessary conditions for common-factor analysis , 1954 .

[14]  Calyampudi R. Rao Estimation and tests of significance in factor analysis , 1955 .

[15]  Louis Guttman,et al.  THE DETERMINACY OF FACTOR SCORE MATRICES WITH IMPLICATIONS FOR FIVE OTHER BASIC PROBLEMS OF COMMON‐FACTOR THEORY1 , 1955 .

[16]  R. Tryon,et al.  Reliability and behavior domain validity: reformulation and historical critique. , 1957, Psychological bulletin.

[17]  Robert C. Tryon,et al.  Communality of a variable: Formulation by cluster analysis , 1957 .

[18]  R. Tryon Cumulative Communality Cluster Analysis , 1958 .

[19]  Louis Guttman,et al.  To what extent can communalities reduce rank? , 1958 .

[20]  Henry F. Kaiser Varimax solution for primary mental abilities , 1960 .

[21]  H. Kaiser A NOTE ON GUTTMAN'S LOWER BOUND FOR THE NUMBER OF COMMON FACTORS1 , 1961 .

[22]  R. Cattell,et al.  A dynamic model of physical influences demonstrating the necessity of oblique simple structure. , 1962, Psychological bulletin.

[23]  Chester W. Harris,et al.  Some rao-guttman relationships , 1962 .

[24]  Henry F. Kaiser,et al.  Alpha factor analysis , 1965, Psychometrika.

[25]  J. Loevinger,et al.  PERSON AND POPULATION AS PSYCHOMETRIC CONCEPTS. , 1965, Psychological review.

[26]  P. Odell,et al.  A Numerical Procedure to Generate a Sample Covariance Matrix , 1966 .

[27]  N. Cliff,et al.  The study of sampling errors in factor analysis by means of artificial experiments. , 1967, Psychological bulletin.

[28]  R. Linn A monte carlo approach to the number of factors problem , 1968, Psychometrika.