I am running a logistic model for catastrophic health expenditure (CHE) in Argentina. The sample size is 22500. I followed Xu et al. methodology to define CHE and adjusted for 8 socioeconomic variables. The are all significant. Then I assessed the goodness of fit by looking at the H-L statistic (p-value>0.05) and the test indicates that the model fits the data well. Then, to assess the discrimination of the fitted model I estimated the area under the ROC curve, which is 78.1%. So far the model looks good. Unfortunately when looking at predicted probabilities and residuals I realized that the predicted probabilities are very low. They range between .0001645 and .3187172. Therefore I have very large residuals and leverage. Of course this also translates into a large number of influential observations.
Any suggestions why this could be happening? I have some ideas but I am not sure they are the right explanation: Is it possible that the proportion of households with CHE==1 is very low (3%) in the sample and this could be affecting the results?
Can I still use this model as a descriptive model of CHE in Argentina?
Thanks you! Mercedes