The Schwarz or Bayesian information criterion (BIC) is one of the most widely used tools for model comparison in social science research. The BIC, however, is not suitable for evaluating models with order constraints on the parameters of interest. This article explores two extensions of the BIC for evaluating order-constrained models, one where a…

In item response theory (IRT) modeling, the Fisher information matrix is used for numerous inferential procedures such as estimating parameter standard errors, constructing test statistics, and facilitating test scoring. In principal, these procedures may be carried out using either the expected information or the observed information. However, in…

In this article, we adjust the Kuk randomized response model for collecting information on a sensitive characteristic for increased protection and efficiency by making use of forced "yes" and forced "no" responses. We first describe Kuk's model and then the proposed adjustment to Kuk's model. Next, by means of a simulation…

Despite wide applications of both mediation models and missing data techniques, formal discussion of mediation analysis with missing data is still rare. We introduce and compare four approaches to dealing with missing data in mediation analysis including list wise deletion, pairwise deletion, multiple imputation (MI), and a two-stage maximum…

Intra-individual variability over a short period of time may contain important information about how individuals differ from each other. In this article we begin by discussing diverse indicators for quantifying intra-individual variability and indicate their advantages and disadvantages. Then we propose an alternative method that models…

Data from the ALEKS-based placement program at the University of Illinois is presented visually in several ways. The placement exam (an ALEKS assessment) contains precise item-specific information and the data show many interesting properties of the student populations of the placement courses, which include Precalculus, Calculus, and Business…

Markov chain Monte Carlo (MCMC) methods enable a fully Bayesian approach to parameter estimation of item response models. In this simulation study, the authors compared the recovery of graded response model parameters using marginal maximum likelihood (MML) and Gibbs sampling (MCMC) under various latent trait distributions, test lengths, and…

A latent variable modeling approach for examining population similarities and differences in observed variable relationship and mean indexes in incomplete data sets is discussed. The method is based on the full information maximum likelihood procedure of model fitting and parameter estimation. The procedure can be employed to test group identities…

Davidian-curve item response theory (DC-IRT) is introduced, evaluated with simulations, and illustrated using data from the Schedule for Nonadaptive and Adaptive Personality Entitlement scale. DC-IRT is a method for fitting unidimensional IRT models with maximum marginal likelihood estimation, in which the latent density is estimated,…

This study linked nonlinear profile analysis (NPA) of dichotomous responses with an existing family of item response theory models and generalized latent variable models (GLVM). The NPA method offers several benefits over previous internal profile analysis methods: (a) NPA is estimated with maximum likelihood in a GLVM framework rather than…

An exploratory study of the value of ridge regression for interactive models is reported. Assuming that the linear terms in a simple interactive model are centered to eliminate non-essential multicollinearity, a variety of common models, representing both ordinal and disordinal interactions, are shown to have "orientations" that are…

The mixture index of fit (T. Rudas et al, 1994) is used to estimate the fraction of a population for which differential item functioning (DIF) occurs, and this approach is compared to the Mantel Haenszel test of DIF. The proposed noniterative procedure provides information about data portions contributing to DIF. (SLD)

Two methods of estimating parameters in the Rasch model are compared. The equivalence of likelihood estimations from the model of G. J. Mellenbergh and P. Vijn (1981) and from usual unconditional maximum likelihood (UML) estimation is demonstrated. Mellenbergh and Vijn's model is a convenient method of calculating UML estimates. (SLD)

Properties of the pseudolikelihood method of estimating Rasch model item parameters, which is based on comparing responses to pairs of items without regard to other items, are studied. Simulation found pseudolikelihood estimates comparable to conditional and marginal maximum likelihood estimates. (SLD)

In psychometrics, it is often the case that one encounters data that may not be considered random but selected in a systematic way according to some explanatory variable. In this article, maximum likelihood estimation is considered when data are supposed to arise from a bivariate normal distribution that is truncated in an extreme way. Two methods…