I have been analyzing a longitudinal dataset and came across a peculiar finding. I have been using a marginal logistic regression GEE to analyze the regression coefficients, standard errors, Z-scores and p-values from my model. Then, when I tried running a standard logistic regression model (ignoring that the data are longitudinal in nature), my output yielded nearly the same regression coefficient estimates, but much smaller standard errors (and therefore larger Z-scores and smaller p-values).
I understand that using a standard logistic regression model for longitudinal data is inherently wrong, due to the correlated nature of the repeated measures among subjects and the heterogeneity of variances across measurements. However - why would only the standard errors be affected (smaller) in the standard logistic regression results, and not the coefficient estimates themselves?