Regression and decomposition with ordinal health outcomes
研究了有序健康结果（如健康等级）在普通最小二乘回归和Blinder-Oaxaca分解中的解释，发现OLS估计量不要求数值为基数，并用2022年美国数据分解了城乡抑郁差异，其中33%-39%由收入等因素解释。
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.