Polytomous multilevel testlet models for testlet-based assessments with complex sampling designs

A Multi-Rater Latent Growth Curve Model

To avoid the subjectivity of having a single person evaluate a construct of interest (e.g., a student's self-efficacy in school), multiple raters are often used. Increasingly, data that use multiple raters to evaluate psychological and social-emotional constructs over time are available. While a range of models to address measurement issues that arise when using multiple raters have been presented, including a small number for longitudinal data, few if any models are available to estimate growth in the presence of multiple raters. In this study, we provide a model that removes all but the shared perceptions of raters at a given timepoint (i.e., removes unique rater variance), then adds on a latent growth curve model across timepoints. Through simulation and empirical studies, we examine the performance of the model in terms of recovering true growth parameters, and relative to more crude approaches like estimating growth based on a single rater. Our results indicate that the model we propose performs quite well along these dimensions, and shows promise for use by researchers who want to estimate growth based on longitudinal multi-rater data.

Examining the Performance of the Trifactor Model for Multiple Raters

Researchers in the social sciences often obtain ratings of a construct of interest provided by multiple raters. While using multiple raters provides a way to help avoid the subjectivity of any given person's responses, rater disagreement can be a problem. A variety of models exist to address rater disagreement in both structural equation modeling and item response theory frameworks. Recently, a model was developed by Bauer et al. (2013) and referred to as the "trifactor model" to provide applied researchers with a straightforward way of estimating scores that are purged of variance that is idiosyncratic by rater. Although the intent of the model is to be usable and interpretable, little is known about the circumstances under which it performs well, and those it does not. We conduct simulation studies to examine the performance of the trifactor model under a range of sample sizes and model specifications and then compare model fit, bias, and convergence rates.

The Bayesian Multilevel Trifactor Item Response Theory Model

Advancements in item response theory (IRT) have led to models for dual dependence, which control for cluster and method effects during a psychometric analysis. Currently, however, this class of models does not include one that controls for when the method effects stem from two method sources in which one source functions differently across the aspects of another source (i.e., a nested method-source interaction). For this study, then, a Bayesian IRT model is proposed, one that accounts for such interaction among method sources while controlling for the clustering of individuals within the sample. The proposed model accomplishes these tasks by specifying a multilevel trifactor structure for the latent trait space. Details of simulations are also reported. These simulations demonstrate that this model can identify when item response data represent a multilevel trifactor structure, and it does so in data from samples as small as 250 cases nested within 50 clusters. Additionally, the simulations show that misleading estimates for the item discriminations could arise when the trifactor structure reflected in the data is not correctly accounted for. The utility of the model is also illustrated through the analysis of empirical data.

A general Bayesian multilevel multidimensional IRT model for locally dependent data

Many item response theory (IRT) models take a multidimensional perspective to deal with sources that induce local item dependence (LID), with these models often making an orthogonal assumption about the dimensional structure of the data. One reason for this assumption is because of the indeterminacy issue in estimating the correlations among the dimensions in structures often specified to deal with sources of LID (e.g., bifactor and two-tier structures), and the assumption usually goes untested. Unfortunately, the mere fact that assessing these correlations is a challenge for some estimation methods does not mean that data seen in practice support such orthogonal structure. In this paper, a Bayesian multilevel multidimensional IRT model for locally dependent data is presented. This model can test whether item response data violate the orthogonal assumption that many IRT models make about the dimensional structure of the data when addressing sources of LID, and this test is carried out at the dimensional level while accounting for sampling clusters. Simulations show that the model presented is effective at carrying out this task. The utility of the model is also illustrated on an empirical data set.

Joint Testlet Cognitive Diagnosis Modeling for Paired Local Item Dependence in Response Times and Response Accuracy

In joint models for item response times (RTs) and response accuracy (RA), local item dependence is composed of local RA dependence and local RT dependence. The two components are usually caused by the same common stimulus and emerge as pairs. Thus, the violation of local item independence in the joint models is called paired local item dependence. To address the issue of paired local item dependence while applying the joint cognitive diagnosis models (CDMs), this study proposed a joint testlet cognitive diagnosis modeling approach. The proposed approach is an extension of Zhan et al. (2017) and it incorporates two types of random testlet effect parameters (one for RA and the other for RTs) to account for paired local item dependence. The model parameters were estimated using the full Bayesian Markov chain Monte Carlo (MCMC) method. The 2015 PISA computer-based mathematics data were analyzed to demonstrate the application of the proposed model. Further, a brief simulation study was conducted to demonstrate the acceptable parameter recovery and the consequence of ignoring paired local item dependence.