Statistical Inference Based on Latent Ability Estimates

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Abstract
The quality of approximations to first and second order moments (e.g., statistics like means, variances, regression coefficients) based on latent ability estimates is being discussed. The ability estimates are obtained using either the Rasch, or the two-parameter logistic model. Straightforward use of such statistics to make inferences with respect to true latent ability is not recommended, unless we account for the fact that the basic quantities are estimates. In this paper true score theory is used to account for the latter; the counterpart of observed/true score being estimated/true latent ability. It is shown that statistics based on the true score theory are virtually unbiased if the number of items presented to each examinee is larger than fifteen. Three types of estimators are compared: maximum likelihood, weighted maximum likelihood, and Bayes modal. Furthermore, the (dis)advantages of the true score method and direct modeling of latent ability is discussed.