The file neurological.dat concerns patients suffering
from a mild neurological disorder. Patients were treated
with one of two drugs or a placebo, and the number recovering
was recorded.
The data consist of five columns: sex, cured or not cured, number on placebo, number on drug A, number on drug B.
> neuro <- read.table("neurological.dat")
> neuro
V1 V2 V3 V4 V5
1 F 1 40 5 26
2 F 0 43 7 32
3 M 1 11 48 52
4 M 0 6 20 20
This is not a good format in S-PLUS. It would be much better
to have ``number cured'' and ``number not cured'' in the same row,
with each of the treatments in a different row. Manipulating
the data into such a form would be complicated, and since
the data set is so small we may as well just do it by hand
(if you have read the handout on objects, you know how
to do this).
> neuro Sex Treatment Cured NotCured 1 F Placebo 40 43 2 F Drug A 5 7 3 F Drug B 26 32 4 M Placebo 11 6 5 M Drug A 48 20 6 M Drug B 52 20Also, we should make sure all of these variables are in the right format:
> neuro$Sex <- as.factor(neuro$Sex) > neuro$Treatment <- as.factor(neuro$Treatment) > neuro$Cured <- as.numeric(neuro$Cured) > neuro$NotCured <- as.numeric(neuro$NotCured)For logistic regression, there are a pair of response variables: the number of successes and the number of failures. Bind the two responses together with
cbind and put them in the model.
> attach(neuro)
> anova(glm(cbind(Cured,NotCured) ~ Sex + Treatment, family=binomial))
Analysis of Deviance Table
Binomial model
Response: cbind(Cured, NotCured)
Terms added sequentially (first to last)
Df Deviance Resid. Df Resid. Dev
NULL 5 19.71457
Sex 1 19.07467 4 0.63990
Treatment 2 0.04528 2 0.59462
It appears that the two drugs were really no different from the
placebo. The big effect was from gender, and looking at
the data above, men were much more likely to recover (70%)
than women (40%).