A Semiparametric Model for Jointly Analyzing Response Times and Accuracy in Computerized Testing

Chun Wang, Zhewen Fan, Hua Hua Chang, Jeffrey A. Douglas

Research output: Contribution to journalArticlepeer-review

33 Scopus citations

Abstract

The item response times (RTs) collected from computerized testing represent an underutilized type of information about items and examinees. In addition to knowing the examinees' responses to each item, we can investigate the amount of time examinees spend on each item. Current models for RTs mainly focus on parametric models, which have the advantage of conciseness, but may suffer from reduced flexibility to fit real data. We propose a semiparametric approach, specifically, the Cox proportional hazards model with a latent speed covariate to model the RTs, embedded within the hierarchical framework proposed by van der Linden to model the RTs and response accuracy simultaneously. This semiparametric approach combines the flexibility of nonparametric modeling and the brevity and interpretability of the parametric modeling. A Markov chain Monte Carlo method for parameter estimation is given and may be used with sparse data obtained by computerized adaptive testing. Both simulation studies and real data analysis are carried out to demonstrate the applicability of the new model.

Original languageEnglish (US)
Pages (from-to)381-417
Number of pages37
JournalJournal of Educational and Behavioral Statistics
Volume38
Issue number4
DOIs
StatePublished - Aug 2013

Bibliographical note

Funding Information:
The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was funded by a grant from the National Science Foundation, NSF-MMS 0960822.

Keywords

  • Cox proportional hazards model
  • Markov chain Monte Carlo
  • partial likelihood
  • response time

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