Latent trait models for responses and response times in tests are often pure statistical models without a close connection to features of the assumed response process. In the present paper, a new model is presented that is more closely related to assumptions about the response process. The model is based on two increasing stochastic processes. Each stochastic process represents the accumulation of knowledge with respect to one of two response options, the correct and incorrect response. Both accumulators compete and the accumulator that first exceeds a critical level determines the response. General assumptions about the accumulators result in a race between two response times that follow a bivariate Birnbaum Saunders distribution. The model can be calibrated with marginal maximum likelihood estimation. Feasibility of the estimation approach is demonstrated in a simulation study. Additionally, a test of model fit is proposed. Finally, the model will be used for the analysis of an empirical data set.

Item response theory (IRT) is one of the most widely utilized tools for item response analysis; however, local item and person independence, which is a critical assumption for IRT, is often violated in real testing situations. In this article, we propose a new type of analytical approach for item response data that does not require standard local independence assumptions. By adapting a latent space joint modeling approach, our proposed model can estimate pairwise distances to represent the item and person dependence structures, from which item and person clusters in latent spaces can be identified. We provide an empirical data analysis to illustrate an application of the proposed method. A simulation study is provided to evaluate the performance of the proposed method in comparison with existing methods.

How social networks influence human behavior has been an interesting topic in applied research. Existing methods often utilized scale-level behavioral data (e.g., total number of positive responses) to estimate the influence of a social network on human behavior. This study proposes a novel approach to studying social influence that utilizes item-level behavioral measures. Under the latent space modeling framework, we integrate the two latent spaces for respondents’ social network data and item-level behavior measures into a single space we call ‘interaction map’. The interaction map visualizes the association between the latent homophily among respondents and their item-level behaviors, revealing differential social influence effects across item-level behaviors. We also measure overall social influence by assessing the impact of the interaction map. We evaluate the properties of the proposed approach via extensive simulation studies and demonstrate the proposed approach with a real data in the context of studying how students’ friendship network influences their participation in school activities.

A Bayesian procedure is developed for the estimation of parameters in the two-parameter logistic item response model. Joint modal estimates of the parameters are obtained and procedures for the specification of prior information are described. Through simulation studies it is shown that Bayesian estimates of the parameters are superior to maximum likelihood estimates in the sense that they are (a) more meaningful since they do not drift out of range, and (b) more accurate in that they result in smaller mean squared differences between estimates and true values.

Composite links and exploded likelihoods are powerful yet simple tools for specifying a wide range of latent variable models. Applications considered include survival or duration models, models for rankings, small area estimation with census information, models for ordinal responses, item response models with guessing, randomized response models, unfolding models, latent class models with random effects, multilevel latent class models, models with log-normal latent variables, and zero-inflated Poisson models with random effects. Some of the ideas are illustrated by estimating an unfolding model for attitudes to female work participation.

An item response theory model for dealing with test speededness is proposed. The model consists of two random processes, a problem solving process and a random guessing process, with the random guessing gradually taking over from the problem solving process. The involved change point and change rate are considered random parameters in order to model examinee differences in both respects. The proposed model is evaluated on simulated data and in a case study.

A speeded item response model is proposed. We consider the situation where examinees may retain the harder items to a later test period in a time limit test. With such a strategy, examinees may not finish answering some of the harder items within the allocated time. In the proposed model, we try to describe such a mechanism by incorporating a speeded-effect term into the two-parameter logistic item response model. A Bayesian estimation procedure of the current model using Markov chain Monte Carlo is presented, and its performance over the two-parameter logistic item response model in a speeded test is demonstrated through simulations. The methodology is applied to physics examination data of the Department Required Test for college entrance in Taiwan for illustration.