Regression and decomposition with ordinal health outcomes

Although ordinal health outcome values are categories like "poor" health or "moderate" depression, they are often assigned values 1,2,3,… for convenience. We provide results on interpretation of subsequent analysis based on ordinary least squares (OLS) regression. For description, unlike for prediction, the OLS estimand's interpretation does not require that the 1,2,3,… are cardinal values: it is always the "best linear approximation" of a summary of the conditional survival functions. Further, for Blinder-Oaxaca-type decomposition, the OLS-based estimator is numerically equivalent to a certain counterfactual-based decomposition of the survival function, again regardless of any cardinal values. Empirically, with 2022 U.S. data for working-age adults, we estimate a higher incidence of depression in the rural population, and we decompose the rural-urban difference. Including a nonparametric estimator that we describe, estimators agree that 33%-39% of the rural-urban difference is statistically explained by income, education, age, sex, and geographic region. The OLS-based detailed decomposition shows this is mostly from income.