Parameter Estimation Accuracy of the Effort-Moderated Item Response Theory Model Under Multiple Assumption Violations

Joseph A. Rios, James Soland

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


As low-stakes testing contexts increase, low test-taking effort may serve as a serious validity threat. One common solution to this problem is to identify noneffortful responses and treat them as missing during parameter estimation via the effort-moderated item response theory (EM-IRT) model. Although this model has been shown to outperform traditional IRT models (e.g., two-parameter logistic [2PL]) in parameter estimation under simulated conditions, prior research has failed to examine its performance under violations to the model’s assumptions. Therefore, the objective of this simulation study was to examine item and mean ability parameter recovery when violating the assumptions that noneffortful responding occurs randomly (Assumption 1) and is unrelated to the underlying ability of examinees (Assumption 2). Results demonstrated that, across conditions, the EM-IRT model provided robust item parameter estimates to violations of Assumption 1. However, bias values greater than 0.20 SDs were observed for the EM-IRT model when violating Assumption 2; nonetheless, these values were still lower than the 2PL model. In terms of mean ability estimates, model results indicated equal performance between the EM-IRT and 2PL models across conditions. Across both models, mean ability estimates were found to be biased by more than 0.25 SDs when violating Assumption 2. However, our accompanying empirical study suggested that this biasing occurred under extreme conditions that may not be present in some operational settings. Overall, these results suggest that the EM-IRT model provides superior item and equal mean ability parameter estimates in the presence of model violations under realistic conditions when compared with the 2PL model.

Original languageEnglish (US)
Pages (from-to)569-594
Number of pages26
JournalEducational and Psychological Measurement
Issue number3
StatePublished - Jun 2021

Bibliographical note

Funding Information:
The authors would like to thank Michael Rodriguez from the University of Minnesota and Megan Kuhfeld from NWEA for their helpful comments on an earlier article. The authors received no financial support for the research, authorship, and/or publication of this article.

Publisher Copyright:
© The Author(s) 2020.


  • item response theory
  • noneffortful responding
  • parameter estimation
  • test-taking effort


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