Comparisons of Order Analysis and Factor Analysis in Assessing the Dimensionality of Binary Data

Abstract

Previous research has not shown a clear relationship between order analytic and factor analytic approaches to assessing the dimensionality of binary data. This study compared factor analysis with three order analy sis procedures. Comparisons were based on eight data sets with known dimensionality and two multidimen sional sets of mathematics data. Two of the order analysis procedures fared poorly in reproducing the factor structure of the datasets. The third procedure re produced the factors for datasets with orthogonal fac tors but failed to reproduce the factors for datasets containing oblique factors. Reasons for the differences between these procedures are discussed.