The effect of individual differences in factor loadings on the standard factor model

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.