Item Parameter Estimation in Multistage Designs: A Comparison of Different Estimation Approaches for the Rasch Model

Abstract

There is some debate in the psychometric literature about item parameter estimation in multistage designs. It is occasionally argued that the conditional maximum likelihood (CML) method is superior to the marginal maximum likelihood method (MML) because no assumptions have to be made about the trait distribution. However, CML estimation in its original formulation leads to biased item parameter estimates. Zwitser and Maris (2015, Psychometrika) proposed a modified conditional maximum likelihood estimation method for multistage designs that provides practically unbiased item parameter estimates. In this article, the differences between different estimation approaches for multistage designs were investigated in a simulation study. Four different estimation conditions (CML, CML estimation with the consideration of the respective MST design, MML with the assumption of a normal distribution, and MML with log-linear smoothing) were examined using a simulation study, considering different multistage designs, number of items, sample size, and trait distributions. The results showed that in the case of the substantial violation of the normal distribution, the CML method seemed to be preferable to MML estimation employing a misspecified normal trait distribution, especially if the number of items and sample size increased. However, MML estimation using log-linear smoothing lea to results that were very similar to the CML method with the consideration of the respective MST design.