Egret® Example 1
Logistic Regression with Random Effects
Logistic regression with random effects should be used in any situation involving grouped binary data in which the observations within individual groups are correlated. In this example, the individual groups are litters of rats, and we are interested survival rates of the rat pups. There are two treatments, applied to 16 mothers each, hence two groups of 16 litters each. The variables, the variable names used in the data set (available on the Egret trial CD (Williams.cyl), and the data themselves are as follows:
There is likely to be within-litter correlation: a pair of offspring in the same litter are more likely to share the same outcome than are two offspring chosen from different litters. As a result, the proportions of offspring in a litter surviving are more variable than is explained by the binomial distribution. There is "extra-binomial variation" or "overdispersion." We are not interested in modeling a "litter effect" (knowing that a particular mother had a higher offspring survival rate than another is not of use to this study), but we must still adjust for the effect of the litter on the response (survival) rate. We will model the responses using Egret's betabinomial logistic regression with random effects option.
1. Select DefineModel > Logistic regression with random effects > Betabinomial regression
2. In the dialog that follows, select denom as the group size variable and outcome as the outcome variable. The dialog now looks like this:
3. Now that the model is defined, we proceed to Egret's Analyze menu, where we choose New .
4. In the dialog that follows, we add group to the regression terms (this is the effect we want to model) and leave the Include Scale box checked (this will adjust for the litter effect).
5. Click OK and the results are displayed:
With a p-value of 0.148, the evidence for a group effect on outcome is insufficient to pass the threshold of statistical significance.
6. The importance of using an analysis that accounts for random effects can be seen from the results from an ordinary logistic regression (i.e. if we fail to include the Scale parameter). This ordinary logistic regression yields a p-value of 0.004, which would have been misleading:
