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I have a dataset that it is clearly need a multilevel model approach -observations from different regions-. However, I am not interesting in population parameters of regions, but overall parameters for covariates and intercept.

Is applying multilevel model in the described case worth doing? I know that if I acount for inner class correlations, I would have more realistic variance estimates...

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Generally speaking, it is no problem to get 'overall' parameters using mixed models. Typically, in this case I think you would take up the regions as a random effect and the overall predictor variables of interest as fixed effects.

E.g., for a linear mixed model using lme4: model <- lmer(Dependent ~ Predictor1 + Predictor2 + (1|Region), data = data) for a simple model without interactions.

The resulting output should get you both the 'overall' (fixed) effects estimates, as well as the random effects (associated with the particular regions - in this example random intercepts only).

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