Matvec Users’ Guide

72 CHAPTER 11. GENERALIZED LINEAR MIXED MODEL ANALYSES
Kp=[0 1, -1 0 0 0
0 0 0 0 1 , -1]
"Estimate ",est=M.estimate(Kp)
"Kp*bhat ",Kp*bhat
with the result:
Estimate
1.51543
-1.51994
Kp*bhat
1.51543
-1.51994
Wald tests and standard errors can be obtained using the M.contrast(Kp) member function. For example,
to test for a formulation effect:
"\nFormulation Effect p-value="+string(pval=M.contrast(Kp))
with the result:
RESULTS FROM CONTRAST(S)
----------------------------------------------------------
Contrast MME_addr K_coef Raw_data_code
---------------------------------------------
1 2 1 Form:A
1 3 -1 Form:B
estimated value (K’b-M) = 1.51543 +- 2.31358
Prob(|t| > 0.655017) = 0.512532 (p_value)
2 5 1 Form*log2dose:A*log2dose
2 6 -1 Form*log2dose:B*log2dose
estimated value (K’b-M) = -1.51994 +- 1.03644
Prob(|t| > 1.46651) = 0.142666 (p_value)
----------------------------------------------------------
joint hypothesis test H: K’b = M
Prob(F > 3.67092) = 0.0254529 (p_value)
Formulation Effect p-value=0.0254529
A likelihood ratio test can also be performed by fitting a reduced model with the restriction K ′ β = 0
and comparing the log-likelihoods of the full and reduced models. For example, to calculate the likelihood
ratio test for a formulation effect:
M.glim(20,Kp);
string("\nReduced Log Like=",RL=M.log_like())
Chi2=StatDist("ChiSquare",2);
string("\nLRT =",TS=2*(L-RL),"\n","P-value=",1-Chi2.cdf(TS))
with the result:
Reduced Log Like=-38.2602
LRT =12.3139
P-value=0.00211866