Journal of Educational and Behavioral Statistics current issue

A Nonlinear Mixed Effects Model for Latent Variables

Harring, J. R. — Fri, 11 Sep 2009 12:18:02 PDT

The nonlinear mixed effects model for continuous repeated measures data has become an increasingly popular and versatile tool for investigating nonlinear longitudinal change in observed variables. In practice, for each individual subject, multiple measurements are obtained on a single response variable over time or condition. This structure can be adapted to examine the change in latent variables rather than modeling change in manifest variables. This article considers a nonlinear mixed effects model for describing nonlinear change of a latent construct over time, where the latent construct of interest is measured by multiple indicators gathered at each measurement occasion. To accomplish this, the nonlinear mixed effects model is modified to include a measurement model that explicitly expresses the relationship of the observed variables to the latent constructs. A method for marginal maximum likelihood estimation of this model is presented and discussed. An example using education data is provided to illustrate the utility of the model.

Using Dominance Analysis to Determine Predictor Importance in Logistic Regression

Azen, R., Traxel, N. — Fri, 11 Sep 2009 12:18:02 PDT

This article proposes an extension of dominance analysis that allows researchers to determine the relative importance of predictors in logistic regression models. Criteria for choosing logistic regression R² analogues were determined and measures were selected that can be used to perform dominance analysis in logistic regression. A simulation study, using both simple random sampling from a known population and bootstrap sampling from a single (parent) random sample, was performed to evaluate the bias, sampling distribution, and confidence intervals of quantitative dominance measures as well as the reproducibility of qualitative dominance measures. Results indicated that the bootstrap procedure is feasible and can be used in applied research to generalize logistic regression dominance analysis results to the population of interest. The procedures for determining and interpreting the general dominance of predictors in a logistic regression context are illustrated with an empirical example.

An Integrated Bayesian Model for DIF Analysis

Soares, T. M., Goncalves, F. B., Gamerman, D. — Fri, 11 Sep 2009 12:18:02 PDT

In this article, an integrated bayesian model for differential item functioning (DIF) analysis is proposed. The model is integrated in the sense of modeling the responses along with the DIF analysis. This approach allows DIF detection and explanation in a simultaneous setup. Previous empirical studies and/or subjective beliefs about the item parameters, including differential functioning behavior, may be conveniently expressed in terms of prior distributions. Values of indicator variables are estimated in the model, indicating which items have DIF and which do not; as a result, the data analyst may not be required to specify an "anchor set" of items that do not exhibit DIF a priori to identify the model. It reduces the iterative procedures that are commonly used for proficiency purification and DIF detection and explanation. Examples demonstrate the efficiency of this method in simulated and real situations.

A Bivariate Lognormal Response-Time Model for the Detection of Collusion Between Test Takers

van der Linden, W. J. — Fri, 11 Sep 2009 12:18:02 PDT

A bivariate lognormal model for the distribution of the response times on a test by a pair of test takers is presented. As the model has parameters for the item effects on the response times, its correlation parameter automatically corrects for the spuriousness in the observed correlation between the response times of different test takers because of variation in the time intensities of the items. This feature suggests using the model in a routine check of response-time patterns for possible collusion between test takers using an estimate of the correlation parameter or a statistical test of a hypothesis about it. Closed-form expressions for the maximum-likelihood estimations of the model parameters and a Lagrange multiplier test for the correlation parameter are presented. As in any type of statistical decision making, results from such procedures should be corroborated by evidence from other sources, for example, results from a response-based analysis or observations during the test session. The effectiveness of the model in removing the spuriousness from correlated response times is illustrated using empirical response-time data.

Linda S. Gottfredson

Wainer, H., Robinson, D. H. — Fri, 11 Sep 2009 12:18:02 PDT