LR test gives contradictory results to R squared I have a difficult decision here. The R squared suggests that model 1 has a better fit than model 2, but the LR test suggests the model 2 has a better fit. How can I resolve this seemingly contradictory result?



Recall that $R^2$ always is at least as large when the model is more complex. The LR test does not say if a model has a better fit, but tests if the additional variables are statistically significant in the more general model.
That said, if I interpret your output correctly, the log likelihood of model 2 is larger, so it should have higher $R^2$, and the p-value of the LR test also says that the inclusion is significant. So there does not appear to be a contradaction here. What kind of model are you fitting/can you post a reproducible example?
