Rotate and Project: Measurement of the Intended Concept with Unidimensional Item Response Theory from...

What to do when item response data are multidimensional but a unidimensional model is preferred in terms of statistical simplicity and ease of interpretability? The projection method for the compensatory logistic multidimensional item response model for dichotomous data leads to a two parameter logistic model with local item dependence. Despite the local item dependence, the model is unidimensional for many practical purposes. Here, Ip's projection method is generalized to the case of the graded response model for polytomous variables, extending the applicability of the method to Likert-type response formats. A secondary aim of the paper is the study of rotation techniques intended for use prior to projection. In contrast to rotations aiming at a simple structure of factor loadings, the proposed techniques increase the variance explained before or after projection, facilitate the interpretation of the projected dimension by variants of target rotations or a mix of both. The method is illustrated with an application to the Highly Sensitive Person Scale and R code is provided.