Both the speed and accuracy of responding are important measures of performance. A well-known interpretive difficulty is that participants may differ in their strategy, trading speed for accuracy, with no change in underlying competence. Another difficulty arises when participants respond slowly and inaccurately (rather than quickly but inaccurately), e.g., due to a lapse of attention. We introduce an approach that combines response time and accuracy information and addresses both situations. The modeling framework assumes two latent competing processes. The first, the error-free process, always produces correct responses. The second, the guessing process, results in all observed errors and some of the correct responses (but does so via non-specific processes, e.g., guessing in compliance with instructions to respond on each trial). Inferential summaries of the speed of the error-free process provide a principled assessment of cognitive performance reducing the influences of both fast and slow guesses. Likelihood analysis is discussed for the basic model and extensions. The approach is applied to a data set on response times in a working memory test.

Glickman, Gray, and Morales (this issue) propose a statistical model for measuring the unobserved latency of stimulus-controlled processes. The model accounts for both speed and accuracy and does so by assuming that participants set an internal deadline. If a stimulus-controlled response is not produced by the deadline, the participant then guesses. The applicability of the model is discussed in this comment. The deadline model yields specific predictions for the case in which stimulus difficulty is manipulated in a within-block manner. In this case, it is reasonable to assume that stimulus difficulty does not affect the deadline. It is shown that in common perceptual and cognitive domains, extant data do not fully meet these predictions. Hence, practitioners need be aware of the possibility and consequences of model misspecification.

For the exploratory analysis of a matrix of proximities or (dis)similarities between objects, one often uses cluster analysis (CA) or multidimensional scaling (MDS). Solutions resulting from such analyses are sometimes interpreted using external information on the objects. Usually the procedures of CA, MDS and using external information are carried out independently and sequentially, although combinations of two of the three procedures (CA and MDS, or MDS and using external information) have been proposed in the literature. The present paper offers a procedure that combines all three procedures in one analysis, using a model that describes a partition of objects with cluster centroids represented in a low-dimensional space, which in turn is related to the information in the external variables. A simulation study is carried out to demonstrate that the method works satisfactorily for data with a known underlying structure. Also, to illustrate the method, it is applied to two empirical data sets.

Several hierarchical classes models can be considered for the modeling of three-way three-mode binary data, including the INDCLAS model (Leenen, Van Mechelen, De Boeck, and Rosenberg, 1999), the Tucker3-HICLAS model (Ceulemans, Van Mechelen, and Leenen, 2003), the Tucker2-HICLAS model (Ceulemans and Van Mechelen, 2004), and the Tucker1-HICLAS model that is introduced in this paper. Two questions then may be raised: (1) how are these models interrelated, and (2) given a specific data set, which of these models should be selected, and in which rank? In the present paper, we deal with these questions by (1) showing that the distinct hierarchical classes models for three-way three-mode binary data can be organized into a partially ordered hierarchy, and (2) by presenting model selection strategies based on extensions of the well-known scree test and on the Akaike information criterion. The latter strategies are evaluated by means of an extensive simulation study and are illustrated with an application to interpersonal emotion data. Finally, the presented hierarchy and model selection strategies are related to corresponding work by Kiers (1991) for principal component models for three-way three-mode real-valued data.

Two generalizations of the Rasch model are compared: the between-item multidimensional model (Adams, Wilson, and Wang, 1997), and the mixture Rasch model (Mislevy & Verhelst, 1990; Rost, 1990). It is shown that the between-item multidimensional model is formally equivalent with a continuous mixture of Rasch models for which, within each class of the mixture, the item parameters are equal to the item parameters of the multidimensional model up to a shift parameter that is specific for the dimension an item belongs to in the multidimensional model. In a simulation study, the relation between both types of models also holds when the number of classes of the mixture is as small as two. The relation is illustrated with a study on verbal aggression.

In the present paper, a new family of item response theory (IRT) models for dichotomous item scores is proposed. Two basic assumptions define the most general model of this family. The first assumption is local independence of the item scores given a unidimensional latent trait. The second assumption is that the odds-ratios for all item-pairs are constant functions of the latent trait. Since the latter assumption is characteristic of the whole family, the models are called constant latent odds-ratios (CLORs) models. One nonparametric special case and three parametric special cases of the general CLORs model are shown to be generalizations of the one-parameter logistic Rasch model. For all CLORs models, the total score (the unweighted sum of the item scores) is shown to be a sufficient statistic for the latent trait. In addition, conditions under the general CLORs model are studied for the investigation of differential item functioning (DIF) by means of the Mantel-Haenszel procedure.

A necessary and sufficient condition is given in this paper for the existence and uniqueness of the maximum likelihood (the so-called joint maximum likelihood) estimate of the parameters of the Partial Credit Model. This condition is stated in terms of a structural property of the pattern of the data matrix that can be easily verified on the basis of a simple iterative procedure. The result is proved by using an argument of Haberman (1977).

Although the Bock–Aitkin likelihood-based estimation method for factor analysis of dichotomous item response data has important advantages over classical analysis of item tetrachoric correlations, a serious limitation of the method is its reliance on fixed-point Gauss-Hermite (G-H) quadrature in the solution of the likelihood equations and likelihood-ratio tests. When the number of latent dimensions is large, computational considerations require that the number of quadrature points per dimension be few. But with large numbers of items, the dispersion of the likelihood, given the response pattern, becomes so small that the likelihood cannot be accurately evaluated with the sparse fixed points in the latent space. In this paper, we demonstrate that substantial improvement in accuracy can be obtained by adapting the quadrature points to the location and dispersion of the likelihood surfaces corresponding to each distinct pattern in the data. In particular, we show that adaptive G-H quadrature, combined with mean and covariance adjustments at each iteration of an EM algorithm, produces an accurate fast-converging solution with as few as two points per dimension. Evaluations of this method with simulated data are shown to yield accurate recovery of the generating factor loadings for models of up to eight dimensions. Unlike an earlier application of adaptive Gibbs sampling to this problem by Meng and Schilling, the simulations also confirm the validity of the present method in calculating likelihood-ratio chi-square statistics for determining the number of factors required in the model. Finally, we apply the method to a sample of real data from a test of teacher qualifications.

A central theme of research on human development and psychopathology is whether a therapeutic intervention or a turning-point event, such as a family break-up, alters the trajectory of the behavior under study. This paper lays out and applies a method for using observational longitudinal data to make more confident causal inferences about the impact of such events on developmental trajectories. The method draws upon two distinct lines of research: work on the use of finite mixture modeling to analyze developmental trajectories and work on propensity scores. The essence of the method is to use the posterior probabilities of trajectory group membership from a finite mixture modeling framework, to create balance on lagged outcomes and other covariates established prior to t for the purpose of inferring the impact of first-time treatment at t on the outcome of interest. The approach is demonstrated with an analysis of the impact of gang membership on violent delinquency based on data from a large longitudinal study conducted in Montreal.

The asymptotic standard deviation (SD) of the alpha coefficient with standardized variables is derived under normality.The research shows that the SD of the standardized alpha coefficient becomes smaller as the number of examinees and/or items increase. Furthermore, this research shows that the degree of the dependence of the SD on the number of items is a function of the average correlation coefficients. When the average correlation approaches 1, the SD of the alpha coefficient decreases rapidly as the number of items increase, with the order of p. On the other hand, when the items are only weakly correlated, increasing the number of items decreases the SD of the alpha coefficient at a much slower rate.