I am using propensity scores for IPW in a logistic GLM in R. Two of the propensities are quite small and thus the resulting weights are quite large - much larger than all the others. I expected these two observations to have a large impact on the modelling results. This is indeed the case when using a binomial model with just the exposure as covariate. However, when including all the covariates used for creating the propensities, there is virtually no influence of these two highly-weighted observations. When removing the two observations, the fitted model stays almost precisely the same.
Investigating this further, it turns out that the working weights of the glm model for these observations are very small when including additional covariates, but not when using just the exposure. I am aware that glm adjusts the weights in some way to arrive at the working weights, but I am not sure how. Can you give me insights on why the weights become very small when including additional covariates?
The dataset is quite large (8500 rows), but I am happy to share it if this gives additional insights. I assume this is mostly a theoretical question, so I am not including the dataset for now. The code I used is simply
glm(outcome ~ exposure, weights = 1/propensity, family = "binomial")
(or the same line with additional covariates added).