Two methods of estimating parameters in the Rasch model are compared. It is shown that estimates for a certain loglinear model for the score × item × response table are equivalent to the unconditional maximum likelihood estimates for the Rasch model.

The DEDICOM model is a model for representing asymmetric relations among a set of objects by means of a set of coordinates for the objects on a limited number of dimensions. The present paper offers an alternating least squares algorithm for fitting the DEDICOM model. The model can be generalized to represent any number of sets of relations among the same set of objects. An algorithm for fitting this three-way DEDICOM model is provided as well. Based on the algorithm for the three-way DEDICOM model an algorithm is developed for fitting the IDIOSCAL model in the least squares sense.

Harshman's DEDICOM model providesa framework for analyzing square but asymmetric materices of directional relationships among n objects or persons in terms of a small number of components. One version of DEDICOM ignores the diagonal entries of the matrices. A straight-forward computational solution for this model is offered in the present paper. The solution can be interpreted as a generalized Minres procedure suitable for handing asymmetric matrices.

Saito and Otsu (1988) compared their OSMOD method of nonmetric principal-component analysis to an early and incorrect implementation of the PRINCIPALS algorithm of Young, Takane, and de Leeuw (1978). In this comment we present results from the current, correct implementations of the algorithm.

In FACTALS an alternating least squares algorithm is utilized. Mooijaart (1984) has shown that this algorithm is based upon an erroneous assumption. This paper gives a proper solution for the loss function used in FACTALS.

An old problem in personnel psychology is to characterize distributions of test validity correlation coefficients. The proposed model views histograms of correlation coefficients as observations from a mixture distribution which, for a fixed sample size n, is a conditional mixture distribution h(r|n) = Σjλjh(r; ρj, n), where R is the correlation coefficient, ρj are population correlation coefficients and λj are the mixing weights. The associated marginal distribution of R is regarded as the parent distribution underlying histograms of empirical correlation coefficients. Maximum likelihood estimates of the parameters ρj and λj can be obtained with an EM algorithm solution and tests for the number of components t are achieved after the (one-component) density of R is replaced with a tractable modeling density h(r; ρj, n). Two illustrative examples are provided.

An algorithm is presented for computing a test statistic for comparing medians based on a small-sample size estimate of the variance of the usual sample median.