Matvec Users’ Guide

11.1. GENERALIZED LINEAR MODEL 73
11.1.4 Threshold Model
Matvec can also be used to fit threshold models based on either an underlying normal, Pr(Z ≤ x) = Φ(x),
or logistic, Pr(Z ≤ x) = e x /(1 + e x ) distribution. Suppose data has been collected on calving difficulty to
examine the effect of gender of the calf on calving difficulty. The data are given in Table 11.3.
Table 11.3: Calving difficulty data.
Calving Difficulty
Sex Easy Moderate Difficult
Male 169 16 15
Female 161 23 16
The threshold link function in Matvec requires that ordinal data with c categories be coded as 0, 1, . . . ,
c − 1. The probability that an observation falls in category i is given by
Pr(Y = i) = Pr(τ i−i + η < Z ≤ τ i + η)
where τ −1 = −∞, τ 0 = 0 and τ c = ∞. The data for this study are stored in the file calve.dat:
Male 0 169
Male 1 16
Male 2 15
Female 0 161
Female 1 23
Female 2 16
and are read using:
D=Data();
D.input("calve.dat","Sex $ Score n");
For this example, the linear predictor for observation j will include an intercept and sex main effect. The
threshold between moderate (1) and difficult (2) will only include an intercept. The model is specified by:
M=Model();
M.equation("Score= intercept Sex,Score=intercept");
M.link("thresh",0)
M.param(1);
M.weight("n");
M.fitdata(D);
The M.param(1) indicates that a probit threshold model will be used. Alternatively M.param(0) can be
used to fit a logistic threshold model. The analysis is completed using:
M.glim(20)
M.save("calve.out");
M.contrast("Sex",[1 0 ,-1 0])
Resulting in the following:
Threshold Link Function
Parameters: Probit/Logit (scalar)) 1=probit 0=logit
Terms: Eta1, Thresh1, Thresh2, ...
y 0..numtraits
0
0.48819