I have a categorical dataset where the outcome is nominal (with three categories). There are 300 observations, and each individual contributes two observations to the dataset.
When I analyzed the data assuming independence (using multinomial regression through the
nnet package in R), my standard errors for $\beta$ coefficients were slightly larger than when modeling with a GEE with a time-exchangeable odds ratio dependence structure between the correlated observations (through the
This was a very surprising result to me. Shouldn't standard errors assuming independence be smaller than when a dependence structure is assumed? Are there ever cases where it can be backwards, like this?
All the coefficients from the GEE-based estimation were almost the exact same as the multinomial coefficients, but in the opposite direction (negative where the multinomial coefficients were positive). I am also quite confused by this result. Is there a fundamental difference in the modeling here?
UPDATE: I have found this reference, where pages 47-50 (pages 5-7 on the pdf) show that the standard errors of the GEE estimates are smaller. However, I do not understand their reasoning on page 50: "Standard errors are smaller because regressor (time) is changing within an individual." Any clarification would be extremely helpful.