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Abstract:
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Partial association measures the relationship between two variables Y1 and Y2 after adjusting a set of covariates X. It remains unknown how to fully characterize such an association if both Y1 and Y2 are recorded on ordinal scales. The classical polychoric correlation is known to be inadequate, as it requires the bivariate normality of the latent variables and it only reflects linear association. We propose a general measure to characterize ordinal-ordinal partial association. It is based on surrogate residuals (Liu and Zhang, JASA, 2018) derived from fitting cumulative link regression models for each Y1 and Y2. The measure has the following properties: (1) its size reflects the strength of association for ordinal data, rather than the hypothetical latent variables; (2) it does not rely on the normality assumption or models with the probit link, but instead it broadly applies to models with any link functions; and (3) it can capture non-linear association and has potential to detect any complex dependence. The research is motivated by and applied to a national election study where the partisanship effect on the voting behavior is assessed and interesting patterns are revealed.
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