Several themes which are common to both econometrics and psychometrics are surveyed. The themes are illustrated by reference to permanent income hypotheses, simultaneous equation models, adaptive expectations and partial adjustment schemes, and by reference to test score theory, factor analysis, and time-series models.

Various models for sets of congeneric tests are considered, including models appropriate for the analysis of multitrait-multimethod data. All models are illustrated with real data. The special cases when two or more tests within a set are tau-equivalent or parallel are also considered. All data analyses are done within the framework of a general model by Jöreskog [1970].

A paired composition is a response (upon a dependent variable) to the ordered pair <j, k> of stimuli, treatments, etc. The present paper develops an alternative analysis for the paired compositions layout previously treated by Bechtel's [1967] scaling model. The alternative model relaxes the previous one by including row and column scales that provide an expression of bias for each pair of objects. The parameter estimation and hypothesis testing procedures for this model are illustrated by means of a small group analysis, which represents a new approach to pairwise sociometrics and personality assessment.

In the factor-analytic model, let some of the factors be known (i.e., the factor loadings are given in advance; they may e.g. be obtained from some previous analyses). However, their covariance matrix may, or may not, be known. The remaining factors (if any) are assumed to be uncorrelated among themselves and to the first set. For this model, the maximum likelihood equations are obtained and an iterative method for the solution is proposed.

In calculations of the discriminating-power parameter of the normal ogive model, Bock and Lieberman compared estimates derived from their maximum-likelihood solution with those derived from the heuristic solution. The two sets of estimates were in excellent agreement provided the heuristic solution used accurate tetrachoric correlation coefficients. Three computer methods for the calculation of the tetrachoric correlation were examined for accuracy and speed. The routine by Saunders was identified as an acceptably accurate method for calculating the tetrachoric correlation coefficient.

The oblimax, promax, maxplane, and Harris-Kaiser techniques are compared. For five data sets, of varying reliability and factorial complexity, each having a graphic oblique solution (used as criterion), solutions obtained using the four methods are evaluated on (1) hyperplane-counts, (2) agreement of obtained with graphic within-method primary factor correlations and angular separations, (3) angular separations between obtained and corresponding graphic primary axes. The methods are discussed and ranked (descending order): Harris-Kaiser, promax, oblimax, maxplane. The Harris-Kaiser procedure—independent cluster version for factorially simple data, P'P proportional to Φ, with equamax rotations, for complex—is recommended.

This paper gives a rigorous and greatly simplified proof of Guttman's theorem for the least upper-bound dimensionality of arbitrary real symmetric matrices S, where the points embedded in a real Euclidean space subtend distances which are strictly monotone with the off-diagonal elements of S. A comparable and more easily proven theorem for the vector model is also introduced. At most n-2 dimensions are required to reproduce the order information for both the distance and vector models and this is true for any choice of real indices, whether they define a metric space or not. If ties exist in the matrices to be analyzed, then greatest lower bounds are specifiable when degenerate solutions are to be avoided. These theorems have relevance to current developments in nonmetric techniques for the monotone analysis of data matrices.