# Selecting link function in GEE with binary dependent variable

In my experiment participants had to make a binary (yes-no) decision about various stimuli. I have two categorical (stimulus characteristics coded as -1 0 and 1 and treatment group coded as 0 1) and three continuous (questionnaire scores) variables.

After useful feedback on a previous question of mine, Difference between generalized linear models & generalized linear mixed models in SPSS, I decided to analyse this dataset with Generalized Estimating Equations (in SPSS). There are several options for selecting link functions that are suitable for binary data. I ran the model with binary logistic binomial identity, binomial Logit, binomial probit and some other ones. If I compare the goodness of fit values (Quasi Likelihood under Independence Model Criterion and Corrected Quasi Likelihood under Independence Model Criterion), these are smallest when I select the link function binomial log complement. Does this mean that this is my best option?

The results actually change a little bit in terms of significance.

In another post I read that I should plot my data. But I don't really know what condition I should put on the x-axis, I don't have a time variable or anything like that. Is looking at the goodness of fit a good idea to do instead?

• This question may be of interest – Macro Jul 27 '12 at 12:05
• One plot you may consider is binning your predictor variable (say, into $k$ evenly spaced bins so that there are a reasonable number of observations in each bin) and calculating the proportion of $1$s, and plotting this proportion against the (binned) predictor. The shape of this plot may inform what would be a more suitable link function. – Macro Jul 27 '12 at 12:47
• Thanks Macro, but I am not sure I understand completely. Do you have some information about what binning exactly is? Also, which predictor variable should I bin? I have multiple. – user9203 Jul 27 '12 at 13:12
• I was imaging, for example, say your predictor ranges from $0$ to $1$. Then, you could estimate $P(Y_i = 1 | X_i \in (0,.1))$ by the sample proportion and do that similarly for other sub-intervals, then plot this function - this is what I meant by binning, since you can't plot the probability continuously as a function of $X_i$ without a model. Having multiple predictors complicates things since you can't visualize that as easily. I'd suggest trying this for one predictor at a time, which may give you some idea of what's going on. – Macro Jul 27 '12 at 13:18
• Ok, I will try to apply the formula. Thanks, it is a very useful answer. But is this better than looking at the model fit and selecting the model with the best fit? Or is there something wrong with that? – user9203 Jul 27 '12 at 13:22