Homogeneity analysis (multiple correspondence analysis), which is usually applied to "k" separate variables, was applied to sets of variables by using sums within sets. The resulting technique, OVERALS, uses optimal scaling. The corresponding OVERALS computer program minimizes a least squares loss function via an alternating least…

Maximum likelihood procedures are presented for a general model to unify the various models and techniques that have been proposed for item analysis. Unconditional maximum likelihood estimation, proposed by Wright and Haberman, and conditional maximum likelihood estimation, proposed by Rasch and Andersen, are shown as important special cases. (JAZ)

Practical problems with multilevel techniques are discussed. These problems relate to terminology, computer programs employing different algorithms, and interpretations of the coefficients in either one or two steps. The usefulness of hierarchical linear models (HLMs) in common situations in educational research is explored. While elegant, HLMs…

A non-linear version of redundancy analysis is introduced. The technique is called REDUNDALS. It is implemented within the computer program for canonical correlation analysis called CANALS. The REDUNDALS algorithm is of an alternating least square (ALS) type. The technique is defined as minimization of a squared distance between criterion…

An alternating least squares method for iteratively fitting the longitudinal reduced-rank regression model is proposed. For social and behavioral science applications, the developed algorithm does not rely on the assumption of multinomial errors and allows for scaling of input and output variables. (SLD)