Using Covariance Modeling for Estimating Reliability on Scales with Ordered Polytomous Variables

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Abstract
This study explores the use of covariance modeling for estimating reliability on ordered polytomous variable models. Using Browne's (1984) general family of fit functions, the writer employed three different correlation matrices (PEARSON, POLYCHORIC, and TOBIT) to obtain reliability estimates. Based on the results of a Monte Carlo study using different levels of variable asymmetry, reliability estimates obtained from the PEARSON matrix did not perform so well as estimates obtained from the POLYCHORIC or TOBIT matrices across the different asymmetry levels. Little difference was detected between the use of the POLYCHORIC and TOBIT matrices, with both providing small bias in the estimates of reliability.