The use of item responses from questionnaire data is ubiquitous in social science research. One side effect of using such data is that researchers must often account for item level missingness. Multiple imputation (Rubin, 1987) is one of the most widely used missing data handling techniques. The traditional multiple imputation approach in…

This research is concerned with two topics in assessing model fit for categorical data analysis. The first topic involves the application of a limited-information overall test, introduced in the item response theory literature, to Structural Equation Modeling (SEM) of categorical outcome variables. Most popular SEM test statistics assess how well…

This research concerns a new proposal for calculating student growth percentiles (SGP, Betebenner, 2009). In Betebenner (2009), quantile regression (QR) is used to estimate the SGPs. However, measurement error in the score estimates, which always exists in practice, leads to bias in the QR-­based estimates (Shang, 2012). One way to address this…

The present study was motivated by the recognition that standard errors (SEs) of item response theory (IRT) model parameters are often of immediate interest to practitioners and that there is currently a lack of comparative research on different SE (or error variance-covariance matrix) estimation procedures. The present study investigated item…

The main purpose of this study is to improve estimation efficiency in obtaining maximum marginal likelihood estimates of contextual effects in the framework of nonlinear multilevel latent variable model by adopting the Metropolis-Hastings Robbins-Monro algorithm (MH-RM). Results indicate that the MH-RM algorithm can produce estimates and standard…

The main purpose of this study is to improve estimation efficiency in obtaining maximum marginal likelihood estimates of contextual effects in the framework of nonlinear multilevel latent variable model by adopting the Metropolis-Hastings Robbins-Monro algorithm (MH-RM; Cai, 2008, 2010a, 2010b). Results indicate that the MH-RM algorithm can…

Differential item functioning (DIF) occurs when the probability of responding in a particular category to an item differs for members of different groups who are matched on the construct being measured. The identification of DIF is important for valid measurement. This research evaluates an improved version of Lord's X[superscript 2] Wald test for…

Model-based multiple imputation has become an indispensable method in the educational and behavioral sciences. Mean and covariance structure models are often fitted to multiply imputed data sets. However, the presence of multiple random imputations complicates model fit testing, which is an important aspect of mean and covariance structure…

Typically a longitudinal growth modeling based on item response theory (IRT) requires repeated measures data from a single group with the same test design. If operational or item exposure problems are present, the same test may not be employed to collect data for longitudinal analyses and tests at multiple time points are constructed with unique…

We propose a new limited-information goodness of fit test statistic C[subscript 2] for ordinal IRT models. The construction of the new statistic lies formally between the M[subscript 2] statistic of Maydeu-Olivares and Joe (2006), which utilizes first and second order marginal probabilities, and the M*[subscript 2] statistic of Cai and Hansen…