Abstract
Recent versions of LISREL (Joreskög and Sorbom, 1983) contain procedures for estimating polyserial and polychoric correlations from crude rank category measures. In this paper, the accuracy of these procedures for estimating the relationship between constructs in both a single and a multiple indicator model is compared to that of using Pearsonian correlations based on equal distance scoring of the rank categories. In these comparisons, a variety of multivariate nonnormal distributions were simulated and the average bias and average absolute error of the estimated relationships between underlying constructs were calculated. These estimates were affected by the number of rank categories for each measure, the correlations among measures, their skewness and kurtosis, and the correlation between underlying constructs. The most important finding is that although the polychoric procedure can be helpful in estimating the correlation between unobserved variables in single indicator models, it does not improve estimates based on Pearsonian correlations in the multiple indicator model.
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Homer, P., O'Brien, R.M. Using LISREL models with crude rank category measures. Qual Quant 22, 191–201 (1988). https://doi.org/10.1007/BF00223041
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DOI: https://doi.org/10.1007/BF00223041