Alternative Approaches to Structural Modeling of Ordinal Data: A Monte Carlo Study

In practice, several measures of association are used when analyzing structural equation models with ordinal variables: ordinary Pearson correlations (PE approach), polychoric and polyserial correlations (PO approach), and conditional polychoric correlations (CPO approach). In the case of structural equation models without latent variables, the literature has shown that the PE approach is outperformed by the alternatives. In this article we report a Monte Carlo study showing the comparative performance of the aforementioned alternative approaches under deviations from their respective assumptions in the case of structural equation models with latent variables when attention is restricted to point estimates of model parameters. The CPO approach is shown to be the most robust against nonnormality. It is also robust to randomness of the exogenous variables, but not to the existence of measurement errors in them. The PO approach lacks robustness against nonnormality. The PE approach lacks robustness against transformation errors but otherwise it can perform about as well as the alternative approaches.