A FORTRAN Program for Assessing Unidimensionality of Binary Data Using Holland and Rosenbaum's Methodology

Unidimensionality is one of the important assumptions the data should satisfy in order to apply unidimensional item response models. There are several methodologies available to date to assess the dimensionality of the latent space underlying binary item responses. Rosenbaum (1984) and Holland and Rosenbaum (1986) have proved theorems concerning conditional associations that can be applied to assess dimensionality. Holland and Rosenbaum's method has been applied to assess dimensionality by Zwick (1987), Ben- Simon and Cohen (1990), and Nandakumar (1991) to various test situations. This article outlines the Holland and Rosenbaum's (1986) methodology to assess unidimensionality, illustrates the procedure through a simulated data set, and describes how to interpret the results.