I am dealing with repeated measures data in which there is clearly reason to incorporate random effects to account for each subject having multiple measurements.
A mixed effects model using random intercepts fits my data nicely. I also ran the same model but without the random intercept, thereby making it a standard linear regression. I realized that the population level predictions (based on the fixed effects coefficients) are virtually identical between these two models (standard vs. mixed). Interestingly, however, the Beta coefficients are rather different between these two models.
In general, considering that I am interested in making population level predictions, is the negative consequence of failing to include random intercepts when appropriate that the parameter (Beta) estimates and their associated confidence intervals will be biased?
My understanding is that failure to include random intercepts will cause issues for the assumption of independence of observations in standard multiple regression.