Suppose I have an LMER output (using Grunfeld data from plm package) as:
summary(lmer(inv ~ value + capital + (1|firm), data = Grunfeld)) > Random effects: Groups Name Variance Std.Dev. Corr firm (Intercept) 7367 85.83 Residual 2781 52.74 0.831 Number of obs: 200, groups: firm, 10 Fixed effects: Estimate Std. Error t value (Intercept) -57.86442 29.37776 -1.97 value 0.10979 0.01053 10.43 capital 0.30819 0.01717 17.95 Correlation of Fixed Effects: (Intr) value value -0.328 capital -0.019 -0.368
I know we can write a Level 1/Level 2 model based on this as:
Level 1: y = alpha_0 + alpha_1 * value + alpha_2 * capital + eps Level 2: alpha_0 = gamma_00 + u_0 alpha_1 = gamma_01 + u_1 alpha_2 = gamma_02 + u_2
The level 1 model should have alpha_0=-57.864, alpha_1=0.109, alpha_2=0.308.
Now, I'm actually not sure if this is the correct form of the level 2 model. Im wondering what exactly the level 1/2 models would be here (for example, are the gammas in the level 2 model concrete values, or are they RV's. For example, here, it is not clear what those values are supposed to be). And also what the correlation of the fixed effects means versus the correlation of random effects. I can't seem to find definitive answers online.