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Mixed (aka multilevel or hierarchical) models are linear models that include both fixed effects and random effects. They are used to model longitudinal or nested data.
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Including Time Invariant Covariates in a Random Intercept Model
As long as the variable $x_i$ varies across $i$, meaning there are deviations from the mean that will help in explaining or shifting the regression line, it does not need to vary across $t$ for it to …