Matvec Users’ Guide

11.2. PENALIZED QUASI-LIKELIHOOD 79
Table 11.6: Number of positive tubes out of 10 in a replicated dose response data.
Formulation A
Formulation B
Replication
Replication
Log 2 Dose 1 2 3 4 5 1 2 3 4 5
0 2 9 9 7 8 9 8 9 10 9
1 2 6 8 8 10 7 7 8 8 9
2 2 6 6 8 7 0 1 3 7 7
3 1 3 1 6 6 0 2 0 1 1
4 1 6 0 3 4 0 1 0 0 1
5 0 7 2 1 4 0 0 0 0 0
6 1 1 1 3 3 0 0 0 0 0
Richards.equation("y=intercept,x=intercept,x=intercept,x=intercept");
Init=Vector(700,7,.75,-1);
Richards.init(Init);
Richards.link("richards",1)
Richards.variance("residual",identity(4,4)*1000);
Richards.fitdata(D);
Richards.glim(20)
Richards.vce_aireml(40)
K=identity(4,4);
Richards.contrast(K)
Richards.save("rat_ric.out")
11.2 Penalized Quasi-Likelihood
M.vce aireml() 1 estimates variance components based on the penalized quasi-likelihood function. Consider
an experiment similar to the dose response experiment except that it has been replicated 5 times. The data
are in Table 11.6.
The linear predictor will include as fixed effects an intercept, a main effect for formulation, a covariate
for log dose, and an interaction between formulation and log dose. Replication will be included as a random
effect. Penalized quasi-likelihood estimates of the variance components are obtained using:
D=Data();
D.input("dose_r.dat","rep formul $ logdose n npos perc_pos");
M=Model();
M.equation("perc_pos=intercept formul logdose formul*logdose rep");
M.covariate("logdose");
M.weight("n");
M.variance("rep",2);
M.link("logit",0)
M.fitdata(D);
M.glim();
M.vce_aireml(25,0);
M.info("dose_r.info")
M.vce aireml() takes up to two arguments. The first argument is the maximum number of iterations.
The default number of iterations is 10. The second argument is the stopping criteria. By default the
stopping criteria is to stop when residual log quasi-likelihood is changing by less than 1.e − 4 and will
1 M.vce aireml() is only available for models that include a link function. However, M.link("normal",rvc) can be used to
specify a linear mixed model.