The increasing use of diary methods calls for the development of appropriate statistical methods. For the resulting panel data, latent Markov models can be used to model both individual differences and temporal dynamics. The computational burden associated with these models can be overcome by exploiting the conditional independence relations implied by the model. This is done by associating a probabilistic model with a directed acyclic graph, and applying transformations to the graph. The structure of the transformed graph provides a factorization of the joint probability function of the manifest and latent variables, which is the basis of a modified and more efficient E-step of the EM algorithm. The usefulness of the approach is illustrated by estimating a latent Markov model involving a large number of measurement occasions and, subsequently, a hierarchical extension of the latent Markov model that allows for transitions at different levels. Furthermore, logistic regression techniques are used to incorporate restrictions on the conditional probabilities and to account for the effect of covariates. Throughout, models are illustrated with an experience sampling methodology study on the course of emotions among anorectic patients.

Scalability coefficients play an important role in Mokken scale analysis. For a set of items, scalability coefficients have been defined for each pair of items, for each individual item, and for the entire scale. Hypothesis testing with respect to these scalability coefficients has not been fully developed. This study introduces marginal modelling as a framework to derive the standard errors for the scaling coefficients and test hypotheses about these coefficients. Several examples demonstrate the possibilities of marginal modelling in Mokken scale analysis. These possibilities include testing whether Mokken’s criteria for a scale are satisfied, testing whether scalability coefficients of different items are equal, and testing whether scalability coefficients are equal across different groups.

According to the recent Nation’s Report Card, 12th-graders failed to produce gains on the 2005 National Assessment of Educational Progress (NAEP) despite earning better grades on average. One possible explanation is that 12th-graders were not motivated taking the NAEP, which is a low-stakes test. We develop three Bayesian IRT mixture models to describe the results from a group of examinees including both nonguessers and partial guessers. The first assumes that the guesser answers questions based on his or her knowledge up to a certain test item, and guesses thereafter. The second model assumes that the guesser answers relatively easy questions based on his or her knowledge and guesses randomly on the remaining items. The third is constructed to describe more general low-motivation behavior. It assumes that the guesser gives less and less effort as he or she proceeds through the test. The models can provide not only consistent estimates of IRT parameters but also estimates of each examinee’s nonguesser/guesser status and degree of guessing behavior. We show results of a simulation study comparing the performance of the three guessing models to the 2PL-IRT model. Finally, an analysis of real data from a low-stakes test administered to university students is presented.

In this paper implicit function-based parameterizations for orthogonal and oblique rotation matrices are proposed. The parameterizations are used to construct Newton algorithms for minimizing differentiable rotation criteria applied to m factors and p variables. The speed of the new algorithms is compared to that of existing algorithms and to that of Newton algorithms based on alternative parameterizations. Several rotation criteria were examined and the algorithms were evaluated over a range of values for m. Initial guesses for Newton algorithms were improved by subconvergence iterations of the gradient projection algorithm. Simulation results suggest that no one algorithm is fastest for minimizing all criteria for all values of m. Among competing algorithms, the gradient projection algorithm alone was faster than the implicit function algorithm for minimizing a quartic criterion over oblique rotation matrices when m is large. In all other conditions, however, the implicit function algorithms were competitive with or faster than the fastest existing algorithms. The new algorithms showed the greatest advantage over other algorithms when minimizing a nonquartic component loss criterion.

Conjoint choice experiments are used widely in marketing to study consumer preferences amongst alternative products. We develop a class of choice models, belonging to the class of Poisson race models, that describe a ‘random utility’ which lends itself to a process-based description of choice. The models incorporate a dependence structure which captures the relationship between the attributes of the choice alternatives and which appropriately moderates the randomness inherent in the race. The new models are applied to conjoint choice data and are shown to have performance markedly superior to that of independent Poisson race models and of the multinomial logit model.

The achievement level is a variable measured with error, that can be estimated by means of the Rasch model. Teacher grades also measure the achievement level but they are expressed on a different scale. This paper proposes a method for combining these two scores to obtain a synthetic measure of the achievement level based on the theory developed for regression with covariate measurement error. In particular, the focus is on ordinal scaled grades, using the SIMEX method for measurement error correction. The result is a measure comparable across subjects with smaller measurement error variance. An empirical application illustrates the method.

The use of Candecomp to fit scalar products in the context of INDSCAL is based on the assumption that the symmetry of the data matrices involved causes the component matrices to be equal when Candecomp converges. Ten Berge and Kiers gave examples where this assumption is violated for Gramian data matrices. These examples are believed to be local minima. It is now shown that, in the single-component case, the assumption can only be violated at saddle points. Chances of Candecomp converging to a saddle point are small but still nonzero.

The aim of this paper is to study the analysis of contingency tables with one heavyweight column or one heavyweight entry by taxicab correspondence analysis (TCA). Given that the mathematics of TCA is simpler than the mathematics of correspondence analysis (CA), the influence of one heavyweight column on the outputs of TCA is studied explicitly without recourse to asymptotics as done by Benzécri (Les Cahiers de L’Analyse des Données 4:413–16, 1979). A reweighting of the heavyweight column is proposed, which can also be applied to CA. A real data set is analyzed.

Recent advances in data recording technology have given researchers new ways of collecting on-line and continuous data for analyzing input-output systems. For example, continuous response digital interfaces are increasingly used in psychophysics. The statistical problem related to these input-output systems reduces to linking time-varying covariates to a continuous response variate. Using real-time data obtained from an experiment in psychoacoustics, we showcase new statistical tools that incorporate dynamical elements of an input-output system. We employ functional data analysis (FDA) methods and a simple differential equation to analyze and model the continuous responses. Furthermore, we outline the issues involved in analyzing input-output systems when the exact form of the underlying mathematical model is not known. Finally, we develop a calibration method to facilitate inter-subject and intra-subject comparisons.