Generalized Linear Model for Binary Data - Reocities

Using Generalized Linear Model for Dose-response models
The following program features the example on chapter 8 “Binary variable and logistic
regression” in Dobson’s book “An Introduction to Generalized Linear Models”. The data
set includes numbers of insects dead after five hours’ exposure to gaseous carbon
disuphide at various concentrations. There are three variables in the data set: DOSE (logtransformed),
KILLED (number of killed) and N (number of insects).
Using SAS Proc Genmod, several alternative models were fitted to these data:
1. Logistic (with the logit link function)
π
log( ) = β1
+ β 2χ
1−
π
2. Probit (with the inverse cumulative Normal link function Φ -1 )
1
Φ ( ) = β + β χ
−
π 1 2
3. Extreme value (with the complementary log log link function)
log[ − log( 1−
)] = β + β χ
π 1 2
The results from SAS output show that the extreme value model clear provides the best
description of the data based on comparison of predict value with observed value and
based on deviance from SAS output.
Options nodate nonumber;
Title;
Data binary;
input dose killed n;
datalines;
1.6907 6 59
1.7242 13 60
1.7552 18 62
1.7842 28 56
1.8113 52 63
1.8369 53 59
1.8610 61 62
1.8839 60 60
;
/* using Logistic model */
proc genmod data=binary;
make 'OBSTATS' out=obstat1;
model killed/n = dose / dist=bin
link=logit
lrci
waldci
obstat;
run;

data obstats1;
set obstat1 (rename=(yvar1=y yvar2=n));
pred1=pred*n;
run;
/* Using Probit model */
proc genmod data=binary;
make 'OBSTATS' out=obstat2;
model killed/n = dose / dist=bin
link=probit
lrci
waldci
obstat;
run;
data obstats2;
set obstat2 (rename=(yvar1=y yvar2=n));
pred2=pred*n;
run;
/* Using extrme value model */
proc genmod data=binary;
make 'OBSTATS' out=obstat3;
model killed/n = dose / dist=bin
link=cll
lrci
waldci
obstat;
run;
data obstats3;
set obstat3 (rename=(yvar1=y yvar2=n));
pred3=pred*n;
run;
data comp;
merge obstats1 obstats2 obstats3;
keep y n pred1 pred2 pred3;
run;
proc print;
title ‘Comparison of various dose-response models for the beetle
mortality data’;
run;