Use propensity score or logit propensity score as distance metric for control group selection?

Question

My question is a bit of a general one (and my first on here). I'm researching different matching methods for selecting a control group in an observational study, and when checking SAS's options for proc PSMATCH, there's an option to use either the raw propensity score (PS) or the logit propensity score (LPS) as the distance metric between control and program group members.

My question is - in what situations would it be appropriate to use the PS as a distance metric as opposed to the LPS? Or, maybe more broadly, how might I determine when it's appropriate with a given set of data?

Answer 1

The only criterion that should help you determine which distance metric to use is whichever one yields the best balance on your covariates while retaining as many matched units as possible. There are no theoretical reasons to prefer one over the other. See Ho, Imai, King, & Stuart (2007) for a discussion of what they call the "propensity score tautology".

A valid propensity score (i.e., a distance metric) will tend to yield balance on covariates when matched on; the way you know a propensity score (i.e., distance metric) is valid is by examining whether it achieves balance. Because the goal of propensity score matching is balance, balance is the criterion that will help you decide how to proceed.

Though there was some early work appearing to display a preference for using the logit of the propensity score rather than the propensity score, that work is largely irrelevant in light of the commonly accepted notion that covariate balance is the primary goal of matching.