When I fit any model in
summary identifies a correlation between fixed effect(s) and the (fixed) intercept. How should I interpret this, and why is it not $0$? In my way of thinking any correlation between the intercept and a fixed effect should be zero, since, in the design matrix $X$, the intercept term is just a column of $1$s, and therefore constant. There is a related post on this topic (lmer interpretation of correlation), but it doesn't help me much. Below is model
summary output, so you can see what I mean. See the block labeled
Correlation of Fixed Effects:, at the very bottom.
>summary(exp2modFull) Linear mixed model fit by REML ['lmerMod'] Formula: RT_log ~ Condition + (Condition | Subject) + (Condition | Item) Data: exp2 REML criterion at convergence: -1978.6 Scaled residuals: Min 1Q Median 3Q Max -3.7080 -0.5775 -0.0634 0.4801 7.8186 Random effects: Groups Name Variance Std.Dev. Corr Subject (Intercept) 0.0261472 0.16170 Conditionoddman 0.0028821 0.05369 -0.21 Conditionhetero 0.0037356 0.06112 -0.46 0.80 Item (Intercept) 0.0018914 0.04349 Conditionoddman 0.0002885 0.01699 -0.97 Conditionhetero 0.0010140 0.03184 -0.65 0.81 Residual 0.0320147 0.17893 Number of obs: 3600, groups: Subject, 20; Item, 12 Fixed effects: Estimate Std. Error t value (Intercept) 6.583310 0.038622 170.46 Conditionoddman -0.009109 0.014883 -0.61 Conditionhetero 0.021487 0.018018 1.19 Correlation of Fixed Effects: (Intr) Cndtnd Conditnddmn -0.309 Conditinhtr -0.472 0.722