# GLM model Interpretation

I am interested in the interpretation of a GLM model (my output is from SPSS) I will take the following example:

Suppose that we have a study of alcohol consumption and cirrhosis sufferers. We have the following data:

$\begin{array}{| l l l |}\hline \mbox{Daily Alcohol consumption} & \mbox{Cirrhosis Sufferers} & \mbox{Controls} \\ \hline 0-20 & 3 & 185\\ 21-40 & 10 & 212\\ 41-60 & 15 & 165 \\ 61-80 & 24 & 108 \\ 81-100 & 30 & 58 \\ 101-120 & 23 & 31 \\ 121-140 & 25& 13 \\ 141-160 & 24 & 5 \\ >160 & 30 & 1 \\ \hline \end{array}$

A GLM model is then used in SSPS to model, fitting alcohol as a factor and cirrhosis as the response variable. The output is:

$\begin{array}{| l | l | l |}\hline \mbox{Parameter} & B & \mbox{Std.Error} \\ \mbox{Intercept} & 3.401 & 1.0165 \\ \mbox{[Alcohol=0-20]} & -7.523 & 1.1714 \\ \mbox{[Alcohol=21-40]} & -6.455 & 1.0668 \\ \mbox{[Alcohol=41-60]} & -5.799 & 1.0517 \\ \mbox{[Alcohol=61-80]} & -4.905 & 1.0413 \\ \mbox{[Alcohol=81-100]} & -4.060 & 1.0411 \\ \mbox{[Alcohol=101-120]} & -3.700 & 1.0531 \\ \mbox{[Alcohol=121-140] }& -2.747 & 1.10725 \\ \mbox{[Alcohol=141-160] }& -1.833 & 1.1292 \\ \mbox{[Alcohol=> 160] }& 0 & \\ \mbox{Scale} & 1 & \\ \hline \end{array}$

$\begin{array}{|c|c|c|c|}\hline \mbox{Source} & \mbox{Wald-Chi Square} & df & Sig \\ \hline \mbox{(Intercept)} & 19.714& 1& .000 \\ \mbox{Alcohol} & 177.349 & 8 & .000 \\ \hline \end{array}$

So first off we notice that the reference group is the highest alcohol intake. Having noticed this we can then see that the affect of alcohol consumption decreases ass the intake is lowered.

From the test of model effects table we can see that both the intercept and the affect of alcohol are significant factors in the prediction of cirrhosis.

I was wondering if there is anything else that I can conclude from the data? Is there any way for me to test the significance of each level of alcohol consumption? If this was linear regression I could carry out a $t$-test with statistic $\frac{\hat{\beta}}{s.e(\beta)}$, which would seem to lead me to conclude that all of these are significant?

Is there any way for me to test the significance of each level of alcohol consumption? If this was linear regression I could carry out a $t$-test with statistic $\frac{\hat{\beta}}{s.e(\beta)}$, which would seem to lead me to conclude that all of these are significant?