Traditional statistical model evaluation typically relies on goodness-of-fit testing and quantifying model complexity by counting parameters. Both of these practices may result in overfitting and have thereby contributed to the generalizability crisis. The information-theoretic principle of minimum description length addresses both of these…

Nonlinear mixed-effects models are models in which one or more coefficients of the growth model enter in a nonlinear manner, such as appearing in the exponent of the growth function. In their applications, the within-individual residuals are often assumed to be independent with constant variance across time, an assumption that implies that the…

The frequent practice of overall fit evaluation for latent variable models in educational and behavioral research is reconsidered. It is argued that since overall plausibility does not imply local plausibility and is only necessary for the latter, local misfit should be considered a sufficient condition for model rejection, even in the case of…

The application of diagnostic classification models (DCMs) in the field of educational measurement is getting more attention in recent years. To make a valid inference from the model, it is important to ensure that the model fits the data. The purpose of the present study was to investigate the performance of the limited information…

The present guide provides a practical guide to conducting latent profile analysis (LPA) in the Mplus software system. This guide is intended for researchers familiar with some latent variable modeling but not LPA specifically. A general procedure for conducting LPA is provided in six steps: (a) data inspection, (b) iterative evaluation of models,…

This study compares two missing data procedures in the context of ordinal factor analysis models: pairwise deletion (PD; the default setting in Mplus) and multiple imputation (MI). We examine which procedure demonstrates parameter estimates and model fit indices closer to those of complete data. The performance of PD and MI are compared under a…

S-X[superscript 2] is a popular item fit index that is available in commercial software packages such as "flex"MIRT. However, no research has systematically examined the performance of S-X[superscript 2] for detecting item misfit within the context of the multidimensional graded response model (MGRM). The primary goal of this study was…

Education researchers frequently have to choose between statistical models for their data, and in many cases the candidate models or parameters can be listed in a sequence, m=1,...,M, from less preferable choices to more. For instance, in choosing a bandwidth for regression discontinuity designs, researchers would favor the largest possible…

Analysts of discrete data often face the challenge of managing the tendency of inflation on certain values. When treated improperly, such phenomenon may lead to biased estimates and incorrect inferences. This study extends the existing literature on single-value inflated models and develops a general framework to handle variables with more than…

Attribute structure is an explicit way of presenting the relationship between attributes in diagnostic measurement. The specification of attribute structures directly affects the classification accuracy resulted from psychometric modeling. This study provides a conceptual framework for understanding misspecifications of attribute structures. Under…

Cognitive diagnosis models (CDMs) estimate student ability profiles using latent attributes. Model fit to the data needs to be ascertained in order to determine whether inferences from CDMs are valid. This study investigated the usefulness of some popular model fit statistics to detect CDM fit including relative fit indices (AIC, BIC, and CAIC),…

In 1995, Huffman and Heller used exploratory factor analysis to draw into question the factors of the Force Concept Inventory (FCI). Since then several papers have been published examining the factors of the FCI on larger sets of student responses and understandable factors were extracted as a result. However, none of these proposed factor models…

Although differences in goodness-of-fit indices (?GOFs) have been advocated for assessing measurement invariance, studies that advanced recommended differential cutoffs for adjudicating invariance actually utilized a very limited range of values representing the quality of indicator variables (i.e., magnitude of loadings). Because quality of…

In this paper, we investigate two purported problems with Bayesian Knowledge Tracing (BKT), a popular statistical model of student learning: "identifiability" and "semantic model degeneracy." In 2007, Beck and Chang stated that BKT is susceptible to an "identifiability problem"--various models with different…

The purpose of this article is to develop a statistical model that best explains variability in the number of school days suspended. Number of school days suspended is a count variable that may be zero-inflated and overdispersed relative to a Poisson model. Four models were examined: Poisson, negative binomial, Poisson hurdle, and negative…