An Evaluation of DIF Tests in Multistage Tests for Continuous Covariates

Multistage tests are a widely used and efficient type of test presentation that aims to provide accurate ability estimates while keeping the test relatively short. Multistage tests typically rely on the psychometric framework of item response theory. Violations of item response models and other assumptions underlying a multistage test, such as differential item functioning, can lead to inaccurate ability estimates and unfair measurements. There is a practical need for methods to detect problematic model violations to avoid these issues. This study compares and evaluates three methods for the detection of differential item functioning with regard to continuous person covariates in data from multistage tests: a linear logistic regression test and two adaptations of a recently proposed score-based DIF test. While all tests show a satisfactory Type I error rate, the score-based tests show greater power against three types of DIF effects.

An Evaluation of DIF Tests in Multistage Tests for Continuous Covariates

Multistage tests are a widely used and efficient type of test presentation that aims to provide accurate ability estimates while keeping the test relatively short. Multistage tests typically rely on the psychometric framework of item response theory. Violations of item response models and other assumptions underlying a multistage test, such as differential item functioning, can lead to inaccurate ability estimates and unfair measurements. There is a practical need for methods to detect problematic model violations to avoid these issues. This study compares and evaluates three methods for the detection of differential item functioning with regard to continuous person covariates in data from multistage tests: a linear logistic regression test and two adaptations of a recently proposed score-based DIF test. While all tests show a satisfactory Type I error rate, the score-based tests show greater power against three types of DIF effects.

Investigating the Impact of Noneffortful Responses on Individual-Level Scores: Can the Effort-Moderated IRT Model Serve as a Solution?

Suboptimal effort is a major threat to valid score-based inferences. While the effects of such behavior have been frequently examined in the context of mean group comparisons, minimal research has considered its effects on individual score use (e.g., identifying students for remediation). Focusing on the latter context, this study addressed two related questions via simulation and applied analyses. First, we investigated how much including noneffortful responses in scoring using a three-parameter logistic (3PL) model affects person parameter recovery and classification accuracy for noneffortful responders. Second, we explored whether improvements in these individual-level inferences were observed when employing the Effort Moderated IRT (EM-IRT) model under conditions in which its assumptions were met and violated. Results demonstrated that including 10% noneffortful responses in scoring led to average bias in ability estimates and misclassification rates by as much as 0.15 SDs and 7% respectively. These results were mitigated when employing the EM-IRT model, particularly when model assumptions were met. However, once model assumptions were violated, the EM-IRT model’s performance deteriorated, though still outperforming the 3PL model. Thus, findings from this study show that: (a) including noneffortful responses when using individual scores can lead to potential unfounded inferences and potential score misuse; and (b) the negative impact that noneffortful responding has on person ability estimates and classification accuracy can be mitigated by employing the EM-IRT model, particularly when its assumptions are met.

Investigating the Impact of Noneffortful Responses on Individual-Level Scores: Can the Effort-Moderated IRT Model Serve as a Solution?

Suboptimal effort is a major threat to valid score-based inferences. While the effects of such behavior have been frequently examined in the context of mean group comparisons, minimal research has considered its effects on individual score use (e.g., identifying students for remediation). Focusing on the latter context, this study addressed two related questions via simulation and applied analyses. First, we investigated how much including noneffortful responses in scoring using a three-parameter logistic (3PL) model affects person parameter recovery and classification accuracy for noneffortful responders. Second, we explored whether improvements in these individual-level inferences were observed when employing the Effort Moderated IRT (EM-IRT) model under conditions in which its assumptions were met and violated. Results demonstrated that including 10% noneffortful responses in scoring led to average bias in ability estimates and misclassification rates by as much as 0.15 SDs and 7%, respectively. These results were mitigated when employing the EM-IRT model, particularly when model assumptions were met. However, once model assumptions were violated, the EM-IRT model’s performance deteriorated, though still outperforming the 3PL model. Thus, findings from this study show that (a) including noneffortful responses when using individual scores can lead to potential unfounded inferences and potential score misuse, and (b) the negative impact that noneffortful responding has on person ability estimates and classification accuracy can be mitigated by employing the EM-IRT model, particularly when its assumptions are met.

On the Speed Sensitivity Parameter in the Lognormal Model for Response Times and Implications for High-Stakes Measurement Practice

In high-stakes testing, often multiple test forms are used and a common time limit is enforced. Test fairness requires that ability estimates must not depend on the administration of a specific test form. Such a requirement may be violated if speededness differs between test forms. The impact of not taking speed sensitivity into account on the comparability of test forms regarding speededness and ability estimation was investigated. The lognormal measurement model for response times by van der Linden was compared with its extension by Klein Entink, van der Linden, and Fox, which includes a speed sensitivity parameter. An empirical data example was used to show that the extended model can fit the data better than the model without speed sensitivity parameters. A simulation was conducted, which showed that test forms with different average speed sensitivity yielded substantial different ability estimates for slow test takers, especially for test takers with high ability. Therefore, the use of the extended lognormal model for response times is recommended for the calibration of item pools in high-stakes testing situations. Limitations to the proposed approach and further research questions are discussed.

Semisupervised Learning Method to Adjust Biased Item Difficulty Estimates Caused by Nonignorable Missingness in a Virtual Learning Environment

In data collected from virtual learning environments (VLEs), item response theory (IRT) models can be used to guide the ongoing measurement of student ability. However, such applications of IRT rely on unbiased item parameter estimates associated with test items in the VLE. Without formal piloting of the items, one can expect a large amount of nonignorable missing data in the VLE log file data, and this is expected to negatively affect IRT item parameter estimation accuracy, which then negatively affects any future ability estimates utilized in the VLE. In the psychometric literature, methods for handling missing data have been studied mostly around conditions in which the data and the amount of missing data are not as large as those that come from VLEs. In this article, we introduce a semisupervised learning method to deal with a large proportion of missingness contained in VLE data from which one needs to obtain unbiased item parameter estimates. First, we explored the factors relating to the missing data. Then we implemented a semisupervised learning method under the two-parameter logistic IRT model to estimate the latent abilities of students. Last, we applied two adjustment methods designed to reduce bias in item parameter estimates. The proposed framework showed its potential for obtaining unbiased item parameter estimates that can then be fixed in the VLE in order to obtain ongoing ability estimates for operational purposes.

Improving the Precision of Ability Estimates Using Time-On-Task Variables: Insights From the PISA 2012 Computer-Based Assessment of Mathematics

Log-file data from computer-based assessments can provide useful collateral information for estimating student abilities. In turn, this can improve traditional approaches that only consider response accuracy. Based on the amounts of time students spent on 10 mathematics items from the PISA 2012, this study evaluated the overall changes in and measurement precision of ability estimates and explored country-level heterogeneity when combining item responses and time-on-task measurements using a joint framework. Our findings suggest a notable increase in precision with the incorporation of response times and indicate differences between countries in how respondents approached items as well as in their response processes. Results also showed that additional information could be captured through differences in the modeling structure when response times were included. However, such information may not reflect the testing objective.

Bayesian modeling of item heterogeneity in dichotomous recognition memory data and prospects for computerized adaptive testing

Most current models of recognition memory fail to separately model item and person heterogeneity which makes it difficult to assess ability at the latent construct level and prevents the administration of adaptive tests. Here we propose to employ a General Condorcet Model for Recognition (GCMR) in order to estimate ability, response bias and item difficulty in dichotomous recognition memory tasks. Using a Bayesian modeling framework and MCMC inference, we perform 3 separate validation studies comparing GCMR to the Rasch model from IRT and the 2-High-Threshold (2HT) recognition model. First, two simulations demonstrate that recovery of GCMR ability estimates with varying sparsity and test difficulty is more robust and thatestimates improve from the two other models under common test scenarios. Then, using a real dataset, face validity is confirmed by replicating previous findings of general and domain-specific age effects (Güsten et al., 2021). Using cross-validation we show better out-of-sample prediction for the GCMR as compared to Rasch and 2HT model. Finally, an adaptive test using the GCMR is simulated, showing that the test length necessary to obtain reliable ability estimates can be significantly reduced compared to a non-adaptive procedure. The GCMR allows to model trial-by-trial performance and to increase the efficiency and reliability of recognition memory assessments.