Abstract
In computerized testing, the test takers' responses as well as their response times on the items are recorded. The relationship between response times and response accuracies is complex and varies over levels of observation. For example, it takes the form of a tradeoff between speed and accuracy at the level of a fixed person but may become a positive correlation for a population of test takers. In order to explore such relationships and test hypotheses about them, a conjoint model is proposed. Item responses are modeled by a two-parameter normal-ogive IRT model and response times by a lognormal model. The two models are combined using a hierarchical framework based on the fact that response times and responses are nested within individuals. All parameters can be estimated simultaneously using an MCMC estimation approach. A R-package for the MCMC algorithm is presented and explained.
Highlights
When computerized tests are administered, are the responses to the test items and the times used to produce them are automatically recorded
One approach is to model the response times with time parameters added to a regular item response theory (IRT) model
This product can be considered as a conjoint IRT model for the analysis of discrete and continuous data for measuring test takers’s speed and ability on test items
Summary
When computerized tests are administered, are the responses to the test items and the times used to produce them are automatically recorded. Since the responses and response times are conditionally independent, their joint distribution is the product of a binomial and a normal distribution This product can be considered as a conjoint IRT model for the analysis of discrete and continuous data for measuring test takers’s speed and ability on test items. The beneficial effects of modeling response-time data jointly with response data were assessed by comparing the accuracies of the ability estimates in a stand-alone IRT and a conjoint IRT approach. This was done for different covariances between the speed and ability parameter, different sample sizes, and different numbers of items.
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