I am comparing an offender group with a control group on a certain task in a generalized linear model with accuracy (0-1) as the DV. The reviewers criticized me by mentioning that one group was imprisoned and the other not. I now want to control for the length they are imprisoned but of course, that is also correlated with age. So, I am doubting about the best way to control for this. Length of imprisonment in the control group is zero (not missing). Let’s say I am interested in the interaction between Group*A*B. Than the fixed predictors in the model are:

A, B, Group, A*B, A*Group, B*Group, A*B*Group.

Should the new model look like this:

Age, Imprisonment, A, B, Group, A*B, A*Group, B*Group, A*B*Group.

Or like this:

Age, Imprisonment, A, B, Group, A*B, A*Group, B*Group, A*B*Group A*Imprisonment, B*Imprisonment, 
Group*Imprisonment, A*B*Imprisonment, A*Group*Imprisonment, B*Group*Imprisonment, A*B*Group*Imprisonment.

Or different?

I also included two random factors:

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    $\begingroup$ Is it a strange idea to divide length of imprisonment by age to calculate the proportion of their live they spend in prison? I could than center that proportion and only within the offender group see if this variable influences the interaction between A*B. $\endgroup$ – user9203 Dec 10 '12 at 0:39

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