Include two correlated factors in mixed model?

Question

In my experiment in which participants make a yes-no decision, I use two measures of empathy because I predict these to be both of influence. The two questionnaire scales are weakly correlated but do not measure exactly the same. Can I include these two scales in my mixed model ANOVA or will they sort of average each other out and should I, if I want to use both measures of empathy run two separate models?

MIXED decision BY treatment target WITH empathic_concern perspective_taking
 /CRITERIA=CIN(95) MXITER(100) MXSTEP(10) SCORING(1) SINGULAR(0.000000000001) HCONVERGE(0, ABSOLUTE) LCONVERGE(0, ABSOLUTE) PCONVERGE(0.000001, ABSOLUTE) 
  /FIXED=treatment target empathic_concern perspective_taking
treatment * target perspective_taking
treatment * empathic_concern
treatment * perspective_taking
empathic_concern * perspective_taking
treatment * perspective_taking * empathic_concern 
 | SSTYPE(3) 
  /METHOD=ML 
  /PRINT=CORB DESCRIPTIVES  SOLUTION 
  /RANDOM=INTERCEPT | SUBJECT(id) COVTYPE(VC) 
  /EMMEANS=TABLES(OVERALL). 

Answer 1

Whether you should include correlated independent variables is really a question about collinearty. In SAS (which it looks like you are using) you can check for collinearity in PROC REG with the COLLIN option. For this purpose, it is OK to use REG even here.

If the highest condition index is over 30, it is often thought to be problematic. In that case, you would look at the proportion of variance explained by the collinearity with that condition index and see where the problem was.

(After Andrea's comment, and a little more coffee, it's clear this isn't SAS code)