When I add a categorical fixed effect to my mixed model (with one random effect and three continuous fixed effects) the intercept is no longer statistically significant. Does this mean that the newly added categorical fixed effect is not independent of the random effect?
In this case, the random effect corresponds to the laboratories that performed the analysis and the categorical fixed effect is the measurement configuration ("DIRECTION")...
In SAS Proc Mixed the models are:
* Model 1: Intercept significant - proc mixed data=etc...; class lab; model ca = p t s / solution ; random lab; run;
* Model 2: Intercept NOT significant - proc mixed data=etc...; class lab DIRECTION; model ca = p t s DIRECTION/ solution ; random lab; run;