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Fixed vs random effects with lme4

Hello,

Is there a way to conduct the Hausman test on models which have been
estimated using lme4?

To be more specific,

My model assumption is that the plot size(X covariate) is correlated with
the random intercept ( estimated from Household_ID) which will be
estimated. So I have to find out how to tell lmer to consider this
correlation. I would also, similarly, want to carry random effects where
this correlation assumption is done away with. Finally, I want to conduct
the Hausman test for model choice.

Thank you,

Regards,
Yashree