polychoric, by any other 'namelist'
Polychoric correlation is the correlation between two ordinal variables obtained as the maximum likelihood estimate under the assumption that the ordinal variables are obtained by coarsening a bivariate normal distribution. I developed a suite of polychoric correlation matrix analysis and a follow-up principal component analysis in early 2000s for a common application of scoring households on their socio-economic status based on categorical proxies of wealth, such as materials used in the house (dirt floor vs. wooden floor vs. tile or cement floor), and presence or absence of certain assets (TV, radio, bike, car, etc.). Even though my -polychoric- program from circa 2004 appears to be finding some good use in Stata world, it lacks a number of important features. I will describe how the modern Stata tools complement and enhance what -polychoric- was purported to achieve. While -polychoric- only deals with pairwise correlations, David Roodmanâ€™s -cmp- provides better justifiable joint correlations based on numerical multivariate integration. Also, while plugging the principal components obtained from -polychoric- into regression models leads to underaccounting of sampling errors in regression coefficient estimates because of the generated regressors problem, generalized structural equation modeling with -gsem- provides the capability of simultaneous estimation of models that utilize the SES index as a predictor of a substantive outcome. I will review a stylized example from Bollen, Glanville and Stecklov seminal papers on the use of latent variable models in analyzing socio-economic status, and demonstrate how these different programs can be used to that effect.
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