B0884
Title: The role of the distribution of categorical responses to survey questions on psychometric dimensionality assessment
Authors: Bruno Zumbo - University of British Columbia (Canada) [presenting]
Abstract: It is well-known that the parameter space of the (phi) correlation among binary variables is not [-1, 1] in most bivariate settings, as the marginal distributions may impose different upper and/or lower bounds. A past study generalized this finding for binary variables to variables with multiple categories by highlighting that these bounds for binary variables are, in fact, the Frechet-Hoeffding (FH) bounds for two jointly distributed Bernoulli random variables. They then derived a general form of the FH bounds for binary or multi-categorical discrete variables. In addition, they described an approach to characterize the covariance matrix among these discrete variable types or their combination. Some of the key points of the derivation of the general form of the FH bounds are discussed. Then, it is used to demonstrate the impact of the shape of the binary, categorical, and mixed cases of item response distributions on the dimensionality analysis of the item response data for the (i) ratio or difference between the first two eigenvalues and the parallel analysis, and (ii) interpretation of the factor(s) using the item factor loadings from the conventional exploratory principal axis factor analysis.
