Comparisons of order analysis and factor analysis in assessing the dimensionality of binary data

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 analysis procedures. Comparisons were based on eight datasets with known dimensionality and two multidimensional sets of mathematics data. Two of the order analysis procedures fared poorly in reproducing the factor structure of the datasets. The third procedure reproduced the factors for datasets with orthogonal factors but failed to reproduce the factors for datasets containing oblique factors. Reasons for the differences between these procedures are discussed