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Bollen, scales for SEM variables

======================Ken Bollen, 17 Feb 1995===========??? From: Ken Bollen <UDEMOC@UNCMVS.OIT.UNC.EDU> Subject: Re: scale for observed variables -Reply - - The original note follows - - The Labovitz ASR piece is unusual in that he looked at the correlation of a categorized variable with the continuous version of itself. The more common situation is that we have two continuous variables that have been collected as categorical variables. The question is how well does the correlation between the categorical variables reproduced the correlation of the continuous variables. K. Barb and I reported a simulation along these lines in American Sociological Review (Bollen and Barb, 1981, "Pearson's R and Coarsely Categorized Measures", Vol.46:232-39). We also found that around 5 to 7 categories led to fairly close correlations. However we only looked at variables that had an underlying normal distribution and we only looked at bivariate correlations. Other studies have looked at this question as well as the issue in the context of SEMs. I review some of these works in Bollen, 1989, Struc. Eqs. with Latent Variables, (NY:Wiley), pages 433-446. Citations to these other studies are in the bibliography. Babakus, Ferguson, & Joreskog, J. of Marketing Research, 1987, is another study on this issue. Overall it is surprising how little work has been done on the robustness of SEM models to ordinal data and how little work there is to evaluate the performance of the WLS (ADF) polychoric solution to the problem. Ken Bollen * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

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