A Sensitivity Analysis of Gibbs Sampling for 3PNO IRT Models: Effects of Prior Specifications on Parameter Estimates

Abstract

The performance of the Gibbs sampling procedure for the three-parameter normal ogive (3PNO) IRT model was investigated using Monte Carlo simulations. Model parameters were estimated for tests with 10, 20, and 40 items and samples of 100, 300, 500, and 1000 examinees, where different actual values and prior specifications were considered for the item parameters. Summary statistics showed that this procedure was more affected by the choice of the prior distributions for the three-parameter model than the two-parameter model. For the 3PNO model, appropriate informative priors with relatively small spread should be adopted for the slope and intercept parameters to obtain more efficient and accurate MCMC estimates when sample sizes are not large and/or tests are not long enough. When it is not clear whether the prior information is appropriate, informative priors with small prior variances are not recommended.