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)

The extent to which one can reduce the rank of a symmetric matrix by only changing its diagonal entries is discussed. Extension of this work to minimum trace factor analysis is presented. (Author/JKS)

A multivariate reduced-rank growth curve model is proposed that extends the univariate reduced rank growth curve model to the multivariate case, in which several response variables are measured over multiple time points. The proposed model allows us to investigate the relationships among a number of response variables in a more parsimonious way…

Results of empirical comparisons of an inferential model of order analysis with factor analytic models were reported for two sets of data. On the prestructured data set both order and factor analytic models returned its dimensions of length, width and height, but on the random data set the factor analytic models indicated the presence of…

Multidimensional scaling (MDS) a highly reliable measurement technique, often requires an overwhelming task of the subject in the data collection procedure. This investigation was designed to determine the loss of precision in solution associated with five degrees of systematic reduction in the data collection task. Data were simulated via Monte…

A rigorous definition for a factor analysis model and a complete solution of the factor score indeterminacy problem are presented in this technical paper. The meaning and application of these results are discussed. (Author/JKS)

The use of the 2 x 2 matrix in qualitative data analysis and theory generation is discussed, embracing the perspective that the objective of qualitative research in general and the analysis of qualitative data in particular is the development of theory. A 2 x 2 matrix is considered to be a tabular representation of the relationship of two…

Interpretations regarding the effects of exogenous and endogenous variables on endogenous variables in linear structural equation systems depend upon the convergence of a matrix power series. The test for convergence developed by Joreskog and Sorbom is shown to be only sufficient, not necessary and sufficient. (Author/JKS)

Restricted multidimensional scaling models, allowing constraints on parameters, are extended to the case of asymmetric data. Examples of several models are provided, using journal citation data. Possible extensions of the models are considered. (Author/JKS)

Solutions for the indeterminate common factor of a group of variables satisfying the single common factor model are not unique. This paper examines a number of thereoms concerning that problem and draws conclusions from them for factor analysis in general. (Author/JKS)

Computer generated data representative of 16 Auto Regressive Integrated Moving Averages (ARIMA) models were used to compare the results of interrupted time-series analysis using: (1) the known model identification, (2) an assumed (l,0,0) model, and (3) an assumed (3,0,0) model as an approximation to the General Transformation approach. (Author/BW)

The general transformation approach to time series analysis is extended to the analysis of multiple unit data by the development of a patterned transformation matrix. The procedure includes alternatives for special cases and requires only minor revisions in existing computer software. (SLD)

This paper presents two extensions of the full-rank multivariate linear model that are particularly useful in multivariate analysis of covariance (MANCOVA) and repeated measurements designs. After a review of the basic full-rank model, an extension is described which allows restrictions of a more general nature. This model is useful in the…

A single conceptual and theoretical framework for sampling any configuration of data from one or more population matrices is presented, integrating past designs and discussing implications for more general designs. The theory is based upon a generalization of the generalized symmetric mean approach for single matrix samples. (Author/CTM)

The multivariate general linear hypothesis (MGLH) has received relatively little utilization in educational research and evaluation. This is surprising in view of the fact that recent publications have made the MGLH tractable by practitioners. This paper seeks to stimulate interest in the MGLH by reviewing recent applications, emphasizing the…