I have a question about the notation you are using for lme4::lmer. Consider your example:
Why did you parameterize multiple variances for the random intercepts as $\sigma^2_{\alpha_j}$ for $j=1,...,J$ rather than assuming a fixed variance, i.e. $\alpha_j \sim N(\mu_{\alpha_j}, \sigma^2_\alpha)$ ?
Perhaps I'm missing something, but my understanding is the model assumes the random intercepts come from a normal distribution with common variance?
I have a question about the notation you are using for
lme4::lmer. Consider your example:Why did you parameterize multiple variances for the random intercepts as$\sigma^2_{\alpha_j}$ for $j=1,...,J$ rather than assuming a fixed variance, i.e. $\alpha_j \sim N(\mu_{\alpha_j}, \sigma^2_\alpha)$ ?
Perhaps I'm missing something, but my understanding is the model assumes the random intercepts come from a normal distribution with common variance?