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The correspondence between pay grade and rank is technically only one to one within and not necessarily between branches of the armed services. We speak of the two concepts as though they are identical because rank is a more familiar term to lay people and because our measures are based off of pay grade, which is uniform across branches.
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Dichotomizing health in this way is standard in the literature. Ordered logit results were similar, a standard result. We experimented with a quadratic in age and with age categoricals, but we found they did not outperform a basic linear specification. We also explored results using the probit, but because the underlying probability of fair or poor health varied substantially across samples, we prefer the logit for its more easily interpretable and uniformly valid marginal effects. We tried treating self-reported health status as ordered, but we found that the substantive results did not differ from when the outcome is treated as dichotomous.
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