Nonparametric Item Response Theory Using Stata

Item response theory is a set of models and methods allowing for the analysis of binary or ordinal variables (items) that are influenced by a latent variable or latent trait—that is, a variable that cannot be measured directly. The theory was originally developed in educational assessment but has many other applications in clinical research, ecology, psychiatry, and economics. The Mokken scales have been described by Mokken (1971, A Theory and Procedure of Scale Analysis [De Gruyter]). They are composed of items that satisfy the three fundamental assumptions of item response theory: unidimensionality, monotonicity, and local independence. They can be considered nonparametric models in item response theory. Traces of the items and Loevinger's H coefficients are particularly useful indexes for checking whether a set of items constitutes a Mokken scale. However, these indexes are not available in general statistical packages. We introduce Stata commands to compute them. We also describe the options available and provide examples of output.