Journal of Educational Measurement最新文献

Explanatory item response models (EIRMs) have been applied to investigate the effects of person covariates, item covariates, and their interactions in the fields of reading education and psycholinguistics. In practice, it is often assumed that the relationships between the covariates and the logit transformation of item response probability are linear. However, this linearity assumption obscures the differential effects of covariates over their range in the presence of nonlinearity. Therefore, this paper presents exploratory plots that describe the potential nonlinear effects of person and item covariates on binary outcome variables. This paper also illustrates the use of EIRMs with smooth functions to model these nonlinear effects. The smooth functions examined in this study include univariate smooths of continuous person or item covariates, tensor product smooths of continuous person and item covariates, and by-variable smooths between a continuous person covariate and a binary item covariate. Parameter estimation was performed using the mgcv R package through the maximum penalized likelihood estimation method. In the empirical study, we identified a nonlinear effect of the person-by-item covariate interaction and discussed its practical implications. Furthermore, the parameter recovery and the model comparison method and hypothesis testing procedures presented were evaluated via simulation studies under the same conditions observed in the empirical study.

In a recently published article in this journal, Becker et al. claim that, because of a missing slope parameter, the lognormal model for response times on test items almost never holds in practice. However, the authors' critique rests on a misrepresentation of the model, which already does have the equivalent of a slope parameter. More importantly, their extra parameter spoils the interpretation of the parameters for the test-takers' speed and labor intensity of the items necessary for a response-time model to be empirically meaningful while their proposed interpretation of the extra parameter seems unwarranted. An analysis of the authors' earlier empirical comparison between the original and their alternative version of the model does not seem to support much of a conclusion about the relative fit of the two models. Also, their simulation study conducted to demonstrate the necessity of the extra slope parameter appears to be based on data simulated in favor of their parameter.

Recently, Bayesian diagnostic classification modeling has been becoming popular in health psychology, education, and sociology. Typically information criteria are used for model selection when researchers want to choose the best model among alternative models. In Bayesian estimation, posterior predictive checking is a flexible Bayesian model evaluation tool, which allows researchers to detect Q-matrix misspecification. However, model selection methods using posterior predictive checking (PPC) for Bayesian DCM are not well investigated. Thus, this research aims to propose a novel model selection approach using posterior predictive checking with limited-information statistics for selecting the correct Q-matrix. A simulation study was conducted to examine the performance of the proposed method. Furthermore, an empirical example was provided to illustrate how it can be used in real scenarios.

As part of the effort to develop an improved oral reading fluency (ORF) assessment system, Kara et al. estimated the ORF scores based on a latent variable psychometric model of accuracy and speed for ORF data via a fully Bayesian approach. This study further investigates likelihood-based estimators for the model-derived ORF scores, including maximum likelihood estimator (MLE), maximum a posteriori (MAP), and expected a posteriori (EAP), as well as their standard errors. The proposed estimators were demonstrated with a real ORF assessment dataset. Also, the estimation of model-derived ORF scores and their standard errors by the proposed estimators were evaluated through a simulation study. The fully Bayesian approach was included as a comparison in the real data analysis and the simulation study. Results demonstrated that the three likelihood-based approaches for the model-derived ORF scores and their standard error estimation performed satisfactorily.

Item difficulty and dimensionality often correlate, implying that unidimensional IRT approximations to multidimensional data (i.e., reference composites) can take a curvilinear form in the multidimensional space. Although this issue has been previously discussed in the context of vertical scaling applications, we illustrate how such a phenomenon can also easily occur within individual tests. Measures of reading proficiency, for example, often use different task types within a single assessment, a feature that may not only lead to multidimensionality, but also an association between item difficulty and dimensionality. Using a latent regression strategy, we demonstrate through simulations and empirical analysis how associations between dimensionality and difficulty yield a nonlinear reference composite where the weights of the underlying dimensions change across the scale continuum according to the difficulties of the items associated with the dimensions. We further show how this form of curvilinearity produces systematic forms of misspecification in traditional unidimensional IRT models (e.g., 2PL) and can be better accommodated by models such as monotone-polynomial or asymmetric IRT models. Simulations and a real-data example from the Early Childhood Longitudinal Study—Kindergarten are provided for demonstration. Some implications for measurement modeling and for understanding the effects of 2PL misspecification on measurement metrics are discussed.

In this study, we introduced a cross-classified multidimensional nominal response model (CC-MNRM) to account for various response styles (RS) in the presence of cross-classified data. The proposed model allows slopes to vary across items and can explore impacts of observed covariates on latent constructs. We applied a recently developed variant of the Metropolis-Hastings Robbins-Monro (MH-RM) algorithm to address the computational challenge of estimating the proposed model. To demonstrate our new approach, we analyzed empirical student evaluation of teaching (SET) data collected from a large public university with three models: a CC-MNRM with RS, a CC-MNRM with no RS, and a multilevel MNRM with RS. Results indicated that the three models led to different inferences regarding the observed covariates. Additionally, in the example, ignoring/incorporating RS led to changes in student substantive scores, while the instructor substantive scores were less impacted. Misspecifying the cross-classified data structure resulted in apparent changes on instructor scores. To further evaluate the proposed modeling approach, we conducted a preliminary simulation study and observed good parameter and score recovery. We concluded this study with discussions of limitations and future research directions.

The Lognormal Response Time (LNRT) model measures the speed of test-takers relative to the normative time demands of items on a test. The resulting speed parameters and model residuals are often analyzed for evidence of anomalous test-taking behavior associated with fast and poorly fitting response time patterns. Extending this model, we demonstrate the connection between the existing LNRT model parameters and the “level” component of profile similarity, and we define two new parameters for the LNRT model representing profile “dispersion” and “shape.” We show that while the LNRT model measures level (speed), profile dispersion and shape are conflated in model residuals, and that distinguishing them provides meaningful and useful parameters for identifying anomalous testing behavior. Results from data in a situation where many test-takers gained preknowledge of test items revealed that profile shape, not currently measured in the LNRT model, was the most sensitive response time index to the abnormal test-taking behavior patterns. Results strongly support expanding the LNRT model to measure not only each test-taker's level of speed, but also the dispersion and shape of their response time profiles.