As far as the Type3 test is concerned, unfortunately, there is no way currently to combine Type3 or CONTRAST tests from MIXED. I have not come across any papers presenting a general methodology on how this could be done. If you happen to find a reference, I would appreciate you passing it along.
From a syntax point of view, you could dummy code the CLASS variable prior to running Proc MIXED and then use the TEST statement in Proc MIANALYZE to get an overall test. Something like the example below would at least show you how it would be coded. But this approach assumes that doing so would be statistically valid, which no one to my knowledge has verified. It essentially treats them as it would any other joint test for parameters and applies the multivariate approach of joint tests using multiply imputed data.
/*Creating Sample Data--Assume that the imputation has already been performed*/
data test;
do _imputation_=1 to 5;
do rep=1 to 100;
do x=1 to 3;
do z=1 to 2;
y=-2+.2*x-.2*z+1.6*x*z+rannor(123);
output;
end;
end;
end;
end;
run;
/*Create the Dummy variables and interactions for X and Z*/
data test;
set test;
x1=(x=1);
x2=(x=2);
z1=(z=1);
x1z1=x1*z1;
x2z1=x2*z1;
run;
proc mixed data=test;
by _imputation_;
model y=x1 x2 z1 x1z1 x2z1/ solution covb;
ods output SolutionF=parms covb=covb;
run;
proc mianalyze parms=parms covb(effectvar=rowcol)=covb;
modeleffects Intercept x1 x2 z1 x1z1 x2z1;
interaxntest:test x1z1=0, x2z1=0/mult;
run;
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