Some historical background and preliminary technical information are first presented, and then a number of hidden, but important, methodological aspects of dual scaling are illustrated and discussed: normed versus projected weights, the amount of information accounted for by each solution, a perfect solution to the problem of multidimensional unfolding, multidimensional quantification space, graphical display, number-of-option problems, option standardization versus item standardization, and asymmetry of symmetric (dual) scaling. Contrary to the common perception that dual scaling and similar quantification methods are now mathematically transparent, the present study demonstrates how much more needs to be clarified for routine use of the method to arrive at valid conclusions. Data analysis must be carried out in such a way that common sense, intuition and sound logic will prevail.

Multitrait-Multimethod (MTMM) matrices are often analyzed by means of confirmatory factor analysis (CFA). However, fitting MTMM models often leads to improper solutions, or non-convergence. In an attempt to overcome these problems, various alternative CFA models have been proposed, but with none of these the problem of finding improper solutions was solved completely. In the present paper, an approach is proposed where improper solutions are ruled out altogether and convergence is guaranteed. The approach is based on constrained variants of components analysis (CA). Besides the fact that these methods do not give improper solutions, they have the advantage that they provide component scores which can later on be used to relate the components to external variables. The new methods are illustrated by means of simulated data, as well as empirical data sets.

Loglinear unidimensional and multidimensional Rasch models are considered for the analysis of repeated observations of polytomous indicators with ordered response categories. Reparameterizations and parameter restrictions are provided which facilitate specification of a variety of hypotheses about latent processes of change. Models of purely quantitative change in latent traits are proposed as well as models including structural change. A conditional likelihood ratio test is presented for the comparison of unidimensional and multiple scales Rasch models. In the context of longitudinal research, this renders possible the statistical test of homogeneity of change against subject-specific change in latent traits. Applications to two empirical data sets illustrate the use of the models.

The purpose of this paper is to present a hypothesis testing and estimation procedure, Crossing SIBTEST, for detecting crossing DIF. Crossing DIF exists when the difference in the probabilities of a correct answer for the two examinee groups changes signs as ability level is varied. In item response theory terms, crossing DIF is indicated by two crossing item characteristic curves. Our new procedure, denoted as Crossing SIBTEST, first estimates the matching subtest score at which crossing occurs using least squares regression analysis. A Crossing SIBTEST statistic then is used to test the hypothesis of crossing DIF. The performance of Crossing SIBTEST is evaluated in this study.

In a broad class of item response theory (IRT) models for dichotomous items the unweighted total score has monotone likelihood ratio (MLR) in the latent trait θ. In this study, it is shown that for polytomous items MLR holds for the partial credit model and a trivial generalization of this model. MLR does not necessarily hold if the slopes of the item step response functions vary over items, item steps, or both. MLR holds neither for Samejima's graded response model, nor for nonparametric versions of these three polytomous models. These results are surprising in the context of Grayson's and Huynh's results on MLR for nonparametric dichotomous IRT models, and suggest that establishing stochastic ordering properties for nonparametric polytomous IRT models will be much harder.

The solution of weakly constrained regression problems typically requires the iterative search, in a given interval, of a point where a certain function has a zero derivative. This note deals with improved bounds for the interval to be searched.