Inaccurate Individual Ability Estimates with Three-Parameter Item Response Models in Mixture Settings

ABSTRACT

It is demonstrated that the popular three-parameter logistic model can lead to markedly inaccurate individual ability level estimates for mixture populations. A theoretically and empirically important setting is initially considered where (a) in one of two subpopulations (latent classes) the two-parameter logistic model holds for each item in a measuring instrument, while (b) this model as well as the three-parameter logistic model for an item with guessing are valid for the instrument in the second class. Fitting the respective hybrid models then to the overall data set, with the three-parameter logistic model assumed for that item, is found to lead to notably inaccurate individual trait score estimates in either class. The implications of the reported results for contemporary empirical educational and behavioral research are finally discussed.

KEYWORDS:

• Individual ability level
• latent class
• mixture
• pseudo-guessing parameter
• two-parameter logistic model
• three-parameter logistic model