Theoretical models specifying indirect or mediated effects are common in the social sciences. An indirect effect exists when an independent variable's influence on the dependent variable is mediated through an intervening variable. Classic approaches to assessing such mediational hypotheses (Baron & Kenny, 1986; Sobel, 1982) have in recent years…

Cognitive diagnostic models (CDMs) attempt to uncover latent skills or attributes that examinees must possess in order to answer test items correctly. The DINA (deterministic input, noisy "and") model is a popular CDM that has been widely used. It is shown here that a logistic version of the model can easily be fit with standard software for…

Doubly bounded continuous data are common in the social and behavioral sciences. Examples include judged probabilities, confidence ratings, derived proportions such as percent time on task, and bounded scale scores. Dependent variables of this kind are often difficult to analyze using normal theory models because their distributions may be quite…

Response time has been regarded as an important source for investigating the relationship between human performance and response speed. It is important to examine the relationship between response time and item characteristics, especially in the perspective of the relationship between response time and various factors that affect examinee's…

Sample size ranks as one of the most important factors that affect the item calibration task. However, due to practical concerns (e.g., item exposure) items are typically calibrated with much smaller samples than what is desired. To address the need for a more flexible framework that can be used in small sample item calibration, this article…

Longitudinal data describe developmental patterns and enable predictions of individual changes beyond sampled time points. Major methodological issues in longitudinal data include modeling random effects, subject effects, growth curve parameters, and autoregressive residuals. This study embedded the longitudinal model within a multigroup…

A Bayesian inference approach using Markov Chain Monte Carlo (MCMC) is developed for the logistic positive exponent (LPE) model proposed by Samejima and for a new skewed Logistic Item Response Theory (IRT) model, named Reflection LPE model. Both models lead to asymmetric item characteristic curves (ICC) and can be appropriate because a symmetric…

Association models constitute an attractive alternative to the usual log-linear models for modeling the dependence between classification variables. They impose special structure on the underlying association by assigning scores on the levels of each classification variable, which can be fixed or parametric. Under the general row-column (RC)…

The application of multidimensional item response theory models to repeated observations has demonstrated great promise in developmental research. It allows researchers to take into consideration both the characteristics of item response and measurement error in longitudinal trajectory analysis, which improves the reliability and validity of the…

Using data from the international Teacher Education and Development Study: Learning to Teach Mathematics (TEDS-M), the measurement equivalence of teachers' beliefs across countries is investigated for the case of "mathematics-as-a fixed-ability". Measurement equivalence is a crucial topic in all international large-scale assessments and…

Bayesian multidimensional scaling (MDS) has attracted a great deal of attention because: (1) it provides a better fit than do classical MDS and ALSCAL; (2) it provides estimation errors of the distances; and (3) the Bayesian dimension selection criterion, MDSIC, provides a direct indication of optimal dimensionality. However, Bayesian MDS is not…

A dominant theme in modeling human perceptual judgments is that sensory neural activity is summed or integrated until a critical bound is reached. Such models predict that, in general, the shape of response time distributions change across conditions, although in practice, this shape change may be subtle. An alternative view is that response time…

This study tests the extent to which giving credit for African American English (AAE) responses on a General American English sentence imitation test mitigates dialect effects. Forty-eight AAE-speaking second graders completed the Recalling Sentences subtest of the Clinical Evaluation of Language Fundamentals-Third Edition (1995). A Bayesian…

A. Redish et al. (2007) proposed a reinforcement learning model of context-dependent learning and extinction in conditioning experiments, using the idea of "state classification" to categorize new observations into states. In the current article, the authors propose an interpretation of this idea in terms of normative statistical inference. They…

This study uses a new psychometric model (mixture item response theory-MIMIC model) that simultaneously estimates differential item functioning (DIF) across manifest groups and latent classes. Current DIF detection methods investigate DIF from only one side, either across manifest groups (e.g., gender, ethnicity, etc.), or across latent classes…