The Effect of Individual Differences in Factor Loadings on the Standard Factor Model (original) (raw)

2007, Multivariate Behavioral Research

It is shown that the population-covariance matrix of a heterogeneous factor model may be indistinguishable from that of a standard factor model and that the standard likelihood-ratio goodness-of-fit statistic has but little power in detecting loading heterogeneity. The relation between loading heterogeneity and factor score reliability is studied and it is recommended that non-normality of the test-score distributions be tested to use factor scores with more confidence. Substantive justifications for the model assumptions and model-based methods to test specific hypotheses about the loading distribution, are discussed. In applied psychology, factor analysis is often used to develop diagnostic instruments. To obtain a good measure of a construct of interest (Cronbach & Meehl, 1955), a calibration study is performed wherein a battery of tests is administered to a large sample of subjects. Under the standard assumptions of multivariate normality of factors and residuals, test statistics and parameter estimates are computed from the covariance matrix (Jöreskog, 1971; Lawley & Maxwell, 1971). If the model fits the data, the parameter estimates are used to compute new subjects' factor scores and their confidence intervals to determine their position on the construct (Mellenbergh, 1994, 1996). In this paper, it is shown that a well-fitting factor model thus obtained does not necessarily mean that the essential assumptions hold and that factor scores The authors would like to thank an anonymous reviewer, and the editor, Roger Millsap, for their helpful comments on previous drafts and Conor V. Dolan for help with some of the statistics and graphics.