The probability that an examinee chooses a particular option within an item is estimated by averaging over the responses to that item of examinees with similar response patterns for the whole test. The approach does not presume any latent variable structure or any dimensionality. But simulated and actual data analyses are presented to show that when the responses are determined by a latent ability variable, this similarity-based smoothing procedure can reveal the dimensionality of ability very satisfactorily.

The posterior distribution of the bivariate correlation is analytically derived given a data set where x is completely observed but y is missing at random for a portion of the sample. Interval estimates of the correlation are then constructed from the posterior distribution in terms of highest density regions (HDRs). Various choices for the form of the prior distribution are explored. For each of these priors, the resulting Bayesian HDRs are compared with each other and with intervals derived from maximum likelihood theory.

This paper presents an analysis, based on simulation, of the stability of principal components. Stability is measured by the expectation of the absolute inner product of the sample principal component with the corresponding population component. A multiple regression model to predict stability is devised, calibrated, and tested using simulated Normal data. Results show that the model can provide useful predictions of individual principal component stability when working with correlation matrices. Further, the predictive validity of the model is tested against data simulated from three non-Normal distributions. The model predicted very well even when the data departed from normality, thus giving robustness to the proposed measure. Used in conjunction with other existing rules this measure will help the user in determining interpretability of principal components.

A theorem is proved stating that the set of all “minimax links”, defined as links minimizing, over paths, the maximum length of links in any path connecting a pair of objects comprising nodes in an undirected weighted graph, comprise the union of all minimum spanning trees of that graph. This theorem is related to methods of fitting network models to dissimilarity data, particularly a method called “Pathfinder” due to Schvaneveldt and his colleagues, as well as to single linkage clustering, and results concerning the relationship between minimum spanning trees and single linkage hierarchical trees.

Residuals for check of model fit in the polytomous Rasch model are examined. Comparisons are made between using counts for all response pattern and using item totals for score groups for the construction of the residuals. Comparisons are also, for the residuals based on score group totals, made between using as basis the item totals, or using the estimated item parameters. The developed methods are illustrated by two examples, one from a psychiatric rating scale, one from a Danish Welfare Study.

Numerous types of analyses for factorial designs having unequal cell frequencies have been discussed in the literature. These analyses test either weighted or unweighted marginal means which, in turn, correspond to different model comparisons. Previous research has indicated, however, that these analyses result in biased (liberal or conservative) tests when cell variances are heterogeneous. We show how to obtain a generally robust and powerful analysis with any of the recommended nonorthogonal solutions by adapting a modification of the Welch-James procedure for comparing means when population variances are heterogeneous.

When the process of publication favors studies with small p-values, and hence large effect estimates, combined estimates from many studies may be biased. This paper describes a model for estimation of effect size when there is selection based on one-tailed p-values. The model employs the method of maximum likelihood in the context of a mixed (fixed and random) effects general linear model for effect sizes. It offers a test for the presence of publication bias, and corrected estimates of the parameters of the linear model for effect magnitude. The model is illustrated using a well-known data set on the benefits of psychotherapy.

Varimax rotation consists of iteratively rotating pairs of columns of a matrix to a maximal sum (over columns) of variances of squared elements of the matrix. Without loss of optimality, the two rotated columns can be permuted and/or reflected. Although permutations and reflections are harmless for each planar rotation per se, they can be harmful in Varimax rotation. Specifically, they often give rise to the phenomenon that certain pairs of columns are consistently skipped in the iterative process, whence Varimax will be terminated at a nonstationary point. The skipping phenomenon is demonstrated, and it is shown how to prevent it.