Combinatorial optimization problems in the social and behavioral sciences are frequently associated with a variety of alternative objective criteria. Multiobjective programming is an operations research methodology that enables the quantitative analyst to investigate tradeoffs among relevant objective criteria. In this paper, we describe an interactive procedure for multiobjective asymmetric unidimensional seriation problems. This procedure uses a dynamic-programming algorithm to partially generate the efficient set of sequences for small to medium-sized problems, and a multioperation heuristic to estimate the efficient set for larger problems. The interactive multiobjective procedure is applied to an empirical data set from the psychometric literature. We conclude with a discussion of other potential areas of application in combinatorial data analysis.

By assuming a distribution for the subject weights in a diagonal metric (INDSCAL) multidimensional scaling model, the subject weights become random effects. Including random effects in multidimensional scaling models offers several advantages over traditional diagonal metric models such as those fitted by the INDSCAL, ALSCAL, and other multidimensional scaling programs. Unlike traditional models, the number of parameters does not increase with the number of subjects, and, because the distribution of the subject weights is modeled, the construction of linear models of the subject weights and the testing of those models is immediate. Here we define a random effects diagonal metric multidimensional scaling model, give computational algorithms, describe our experiences with these algorithms, and provide an example illustrating the use of the model and algorithms.

This paper presents a synthesis of Bock's (1972) nominal categories model and Luce's (1959) choice model for mixed-effects analyses of rank-ordered data. It is shown that the proposed ranking model is both parsimonious and flexible in accounting for preference heterogeneity as well as fixed and random effects of covariates. Relationships to other approaches, including Takane's (1987) ideal point discriminant model and Croon's (1989) latent-class version of Luce's ranking model, are also discussed. The application focuses on a ranking study of behavioral traits that parents find desirable in children.

Corrections of correlations for range restriction (i.e., selection) and unreliability are common in psychometric work. The current rule of thumb for determining the order in which to apply these corrections looks to the nature of the reliability estimate (i.e., restricted or unrestricted). While intuitive, this rule of thumb is untenable when the correction includes the variable upon which selection is made, as is generally the case. Using classical test theory, we show that it is the nature of the range restriction, not the nature of the available reliability coefficient, that determines the sequence for applying corrections for range restriction and unreliability.

An important assumption in IRT model-based adaptive testing is that matching difficulty levels of test items with an examinee's ability makes a test more efficient. According to Lord, “An examinee is measured most effectively when the test items are neither too difficult nor too easy for him”. This assumption is examined and challenged through a class of one-parameter IRT models including those of Rasch and the normal ogive. It is found that for a specific model, the validity of the fundamental assumption is closely related to the so-called van Zwet tail ordering of symmetric distributions. In this connection, the cosine distribution serves as the borderline between those satisfying the assumption and those violating the assumption. Graphic and numerical illustrations are presented to demonstrate the theoretic results.

Two new methods for improving the measurement precision of a general test factor are proposed and evaluated. One new method provides a multidimensional item response theory estimate obtained from conventional administrations of multiple-choice test items that span general and nuisance dimensions. The other method chooses items adaptively to maximize the precision of the general ability score. Both methods display substantial increases in precision over alternative item selection and scoring procedures. Results suggest that the use of these new testing methods may significantly enhance the prediction of learning and performance in instances where standardized tests are currently used.

A special rotation procedure is proposed for the exploratory dynamic factor model for stationary multivariate time series. The rotation procedure applies separately to each univariate component series of a q-variate latent factor series and transforms such a component, initially represented as white noise, into a univariate moving-average. This is accomplished by minimizing a so-called state-space criterion that penalizes deviations of the rotated solution from a generalized state-space model with only instantaneous factor loadings. Alternative criteria are discussed in the closing section. The results of an empirical application are presented in some detail.

Researchers studying item response models are often interested in examining the effects of local dependency on the validity of the resulting conclusion from statistical inference. This paper focuses on the detection of local dependency. We provide a framework for viewing local dependency within dichotomous and polytomous items that are clustered by design, and present a testing procedure that allows researchers to specifically identify individual item pairs that exhibit local dependency, while controlling for false positive rate. Simulation results from the study indicate that the proposed method is effective. In addition, a discussion of its relation to other existing methods is provided.

In this paper, we propose a Bayesian framework for estimating finite mixtures of the LISREL model. The basic idea in our analysis is to augment the observed data of the manifest variables with the latent variables and the allocation variables. The Gibbs sampler is implemented to obtain the Bayesian solution. Other associated statistical inferences, such as the direct estimation of the latent variables, establishment of a goodness-of-fit assessment for a posited model, Bayesian classification, residual and outlier analyses, are discussed. The methodology is illustrated with a simulation study and a real example.