# In propensity score matching, what violations or implications may result from having fitted propensity scores that are not centered at 0.5?

I currently have a procedure doing propensity score matching, and I use the fitted propensity scores (obtained via a glm call) and match on those. It turns out that I have about 60-70% more fitted values that are less than 0.5 than those greater than 0.5.

Hence, my fitted scores are skewed left. I am wondering if this violates any rules or what the implications might be from this and if it is something that can be assumed away? Thanks.

• There is no reason for fitted propensity scores to have mean or median equal to 0.50. No assumption is violated. At first instance, "clip them" slightly (i.e. drop instance outside $[0.025, 0.0975]$) and use the PS as planned (through IPTW, inclusion as additional covariate, etc.). – usεr11852 says Reinstate Monic Nov 27 '18 at 23:59

1. if the range of the estimated PS is too narrow this might suggest that a potentially confounder is unaccounted for. Simply put, we do not have ignorability. The potential outcomes $$Y$$ are not independent of the treatment variable $$A$$ even if we condition on some other variables $$X$$.
3. we might simply overfit our treatment assignment data $$A$$. This would have the direct consequence that our PS estimates are artificially over-determined. We should focus into getting a well-calibrated and properly estimated method to estimate the PS to begin with.