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…

Some mathematical aspects of minimum trace factor analysis (MTFA) are discussed. The uniqueness of an optimal point of MTFA is proved, and necessary and sufficient conditions for any particular point to be optimal are given. The connection between MTFA and classical minimum rank factor analysis is discussed. (Author/JKS)

Using higher order factor models, this article illustrates latent curve analysis for the purpose of modeling longitudinal change directly in a latent construct. Provides examples with simultaneous estimation of covariance and mean structures for a single-group and two-group structure. (SLD)

As psychologists increasingly employ more elaborate and comprehensive data collection schemes, sophisticated analytic techniques will play an ever more important role in understanding behavioral data. This paper outlines one such promising technique, Tucker's three-mode factor analysis, which enables the researcher to explore new taxonomic…

The Akaike Information Criterion (AIC) was introduced to extend the method of maximum likelihood to the multimodel situation. Use of the AIC in factor analysis is interesting when it is viewed as the choice of a Bayesian model; thus, wider applications of AIC are possible. (Author/GDC)

Equivalence of marginal likelihood of the two-parameter normal ogive model in item response theory and factor analysis of dichotomized variables was formally proved. Ordered and unordered categorical data and paired comparisons data were discussed, and a taxonomy of data for the models was suggested. (Author/GDC)

In defense of retaining the "latent trait theory" term, instead of replacing it with "item response theory" as some recent research would have it, the following objectives are outlined: (1) investigation of theory and method for estimating the operating characteristics of discrete item responses using a minimum number of…

Multi-indicator growth models were formulated as special three-level hierarchical generalized linear models to analyze growth of a trait latent variable measured by ordinal items. Items are nested within a time-point, and time-points are nested within subject. These models are special because they include factor analytic structure. This model can…

Several methods of assessing test item bias are described, and the concept of fair use of tests is examined. A test item is biased if individuals of equal ability have different probabilities of attaining the item correct. The following seven general procedures used to examine test items for bias are summarized and discussed: (1) analysis of…

Procedures for simultaneous confirmatory factor analysis in several populations are useful in a variety of problems. This is demonstrated with examples involving missing data, comparison of part correlations between groups, testing the equality of regression weights between groups with multiple indicators of each variable, and the formulation of…

In this paper we explore the consequences of particular stage linkage structures for the evolution of a population. We first argue the importance of mixed-sex pairs of subjects discussed a legal case, each pair seated first five feet of examples the implications of various stage connections for poulation movements. In discussing dynamic models,…