Matvec Users’ Guide

70 CHAPTER 11. GENERALIZED LINEAR MIXED MODEL ANALYSES
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Figure 11.1: Dose response curves for two different formulations of am antibiotic.
11.1.1 Model Specification
The specification of a generalized linear model consists of descriptors for the linear predictor and the link
function. The linear predictor for our example is:
• µ: intercept
η ij = µ + F i + b x j + b i x j
• F i : main effect of formulation i at x = log 2 (Dose) = 0
• b: linear effect of log 2 (Dose)
• b i : linear interaction between formulation and log 2 (Dose).
In Matvec this linear predictor is denoted by:
M=Model(); // Create a Model object.
M.equation("perc pos=intercept Form log2dose Form*log2dose");
// Linear predictor η ij = µ + F i + b x j + b i x j
M.covariate("log2dose");
M.weight("n");
which is the same as a linear model.
Next the logit link function is specified:
M.link("logit",0)
// Logit link, scale parameter is not estimated.
M.fitdata(D);
// Use Data object D
M.link(‘‘fn’’,nvc) specifies both the link function, ‘‘fn’’, and the number of over-dispersion parameters,
nvc, to estimate. Table 11.2 contains a number link functions that are currently available.