Say I have the following output:
Fixed effects: intercept: Estimate = 50 X1: Estimate = 20 X2: Estimate = -10 Random effects: intercept: Variance = 16, SD=4 X1: Variance = 9, SD = 3 Corr = -.5 X2: Variance = 4, SD = 2 Corr = .5 Residual Variance = 4
In interpreting this, can I say that a one standard deviation increase in the intercept yields a half standard deviation decrease in the slope with respect to X1? For example, if obs 1's intercept is 58 (2 SD's above the mean) then the slope estimate with respect to X1 is 17 (i.e. 20 -(2 X -.5 X 3)). Is that a correct interpretation of the change in estimates?
where SD = standard deviation and Corr = correlation between the random effect and intercept