Matvec Users’ Guide

80 CHAPTER 11. GENERALIZED LINEAR MIXED MODEL ANALYSES
reduce the step size if the residual log quasi-likelihood decreases by more than 1.e − 4. If the second
argument is zero, then the stopping criteria is EPSILON (the default value of EPSILON is 1.e − 14) and it
does not reduce the step size when the log likelihood increases. The EPSILON parameter can be set using
this.parameter("EPSILON",value). M.vce aireml() returns a nr×(nr+1) matrix, where nr is the number
of variance components. The first column of the matrix contains the estimated variance components. The
remaining columns of the matrix contains the asymptotic covariance matrix.
The M.info() is similar to M.save() except it does not include the estimated fixed effects or predicted
random effects. The resulting file dose r.info:
some extra information in the model
--------------------------------------------------------
AI REML converged
maximum log restricted likelihood = -297.196
variance for rep =
0.801036
residual variance =
1
MME dimension : 11
non-zeros in MME: 52
basic statistics for dependent variables
-----------------------------------------------------
trait-name n mean std
perc_pos 70 0.371429 0.348139
--------------------------------------------------------
The residual log quasi-likelihood can also be obtained using M.residual log like().
11.2.1 Correlated random effects
In the previous example, it was assumed that the only effect of blocks was a change in the intercept. An
alternative model would also allow the slope to change also. In the following Matvec code a random block
by logdose is added to the model.
M=Model();
M.equation("perc pos=intercept formul logdose formul*logdose rep"+\
"rep*logdose");
M.covariate("logdose");
M.weight("n");
M.variance("rep",2);
M.variance("rep*logdose",.1);
M.link("logit",0)
M.fitdata(D);
However, the random intercept and random slope may be correlated. M.variance(effect 1,effect 2,covariance)
2 is used to designate that the random effects are correlated. The complete Matvec code is now:
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"+\
" rep*logdose");
M.covariate("logdose");
2 Correlated random effects do not require a link function.