For the confirmatory factor model a series of inequalities is given with respect to the mean square error (MSE) of three main factor score predictors. The eigenvalues of these MSE matrices are a monotonic function of the eigenvalues of the matrix gamma[subscript rho] = theta[superscript 1/2] lambda[subscript rho] 'psi[subscript rho] [superscript…

The assumptions of the model for factor analysis do not exclude a class of indeterminate covariances between factors and error variables (Grayson, 2003). The construction of all factors of the model for factor analysis is generalized to incorporate indeterminate factor-error covariances. A necessary and sufficient condition is given for…

Personality tests often consist of a set of dichotomous or Likert items. These response formats are known to be susceptible to an agreeing-response bias called acquiescence. The common assumption in balanced scales is that the sum of appropriately reversed responses should be reasonably free of acquiescence. However, inter-item correlation (or…

Discusses Guttman's index of indeterminacy in light of alternative solutions which are equally likely to be correct and alternative solutions for the factor which are not equally likely to be chosen. Offers index which measures a different aspect of the same indeterminacy problem. (ROF)

A summary and interpretation of the recent literature on the indeterminancy of factor scores is given in simple terms. A good index of factor score determinancy is the squared multiple correlation of the factor with the observed variables. (Author)

Scoring of response vectors to give maximum test-retest correlation is investigated. A general method is given for finding the best scores, deriving them for the normal factor model, and showing that for a standard model for binary response it is easy to approximate the best scores. (SLD)