If the factor loadings of a core set of variables (fitting the general factor model) are the same when analyzed alone, and when analyzed along with the rest of the variables in an infinite behavior domain, there is only one factor variable in the domain that is a possible factor variable of the core set. If the condition of consistency of factor…

Rubin and Thayer recently presented equations to implement maximum likelihood estimation in factor analysis via the EM algorithm. It is argued here that the advantages of using the EM algorithm remain to be demonstrated. (Author/JKS)

The paper is a critique of the traditional mode of interpreting factor analyses; it is not a criticism of factor analysis per se. Instead, the author proposes a statistical procedure based upon stepwise regression (SRP). The traditional mode focuses on the largest factor loadings (FL). A factor is both described and named by these heavily weighted…

A limitation of the principal components method is its scale dependence. This note shows that the method is scale invariant if the normalization is modified in an obvious way. Then the effect of a change in units is as transparent as in linear regression, and principal components can be used without apology. Most researchers who use multivariate…

A population data set was randomly generated from which a random sample was drawn. This sample was randomly divided into two data sets, one of which was used to generate parameter estimates, which were then used in the second data set for cross-validation purposes. The best variable subset models were compared between the two data sets on the…

Critics have occasionally asserted that the number of factors in the 16PF tests is too large. This study discusses factor-analytic methodology and reviews more than 50 studies in the field. It concludes that the number of important primaries encapsulated in the series is no fewer than the stated number. (Author/JAZ)

The general goal of this paper is to help researchers conduct appropriately designed goodness of fit studies for item response model applications. The specific purposes are to describe: (1) an up-to-date set of promising and useful methods for addressing a variety of goodness of fit questions; and (2) current research studies to advance this set…