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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;

and

* Model 2: Intercept NOT significant -

proc mixed data=etc...;
    class lab DIRECTION;
    model ca = p t s DIRECTION/ solution ;
    random lab;
run;
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It means that DIRECTION is not independent of the mean value of ca. Changing the parameterization of DIRECTION will have different effects on the intercept. This is not substantively important but it can change the interpretation.

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  • $\begingroup$ Thank you very much for your answer. But just to clarify - isn't that the case for all of the predictors (that is, if they are independent of the mean then won't they be irrelevant to the model)? $\endgroup$ – lithic Jan 28 '15 at 21:02
  • $\begingroup$ Yes, but categorical variables (and how they are parameterized) affect the intercept in more obvious ways. It's similar to what happens if you center a continuous variable. $\endgroup$ – Peter Flom - Reinstate Monica♦ Jan 29 '15 at 10:27

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