# Why age-matched groups for difference between groups in generalized linear model?

I have a question about GLM. For example: I create the model with the formula like this:

Volume=group+age+sex+age*group+random-effect(kinship)

I am not a statistician and trying to understand the theory of GLM, My interest is to find the significant difference between groups and also the interaction between group and age(age*group),so I have these question: 1) what is a factor and covariates in my model(group to be factor and age, sex to be covariates???)

2) if we consider the the age and sex to be covariates into our model, that means the model consider the variances contribution from these covariates, right? So why people always create their model with age-matched or sex-matched between groups when they build the model(I understand this for univariate(group) comparison), is that because in GLM, the model consider just linear effect for age and sex? the model still have non-linear effect for these covariates?

3) More specifically, I have two groups, presymptomatic(34 PS) and patients(13 PT), and I run the model above to find the difference between groups and also the interaction between group and age, basically for age, we have two approaches: first one, we use the real age for PS and PT which are very different; secondly, for PT, we use the duration of disease(age_baseline - age_of_onset), for PS, we use estimated distance to age of onset(age_baseline - everage_age_of_onset_of_family), we created the same model for these two approaches:

Use real age:

of onset(age_baseline - everage_age_of_onset_of_family)** and duration of disease(age_baseline - age_of_onset)

So, my question is that in my model using age-dismatched groups, does the model really find the difference between groups, not because the difference caused from the age(It is normal when you get old, the brain volume will be smaller)? Also, for the age approach, which one is better?? duration of disease(age_baseline - age_of_onset) or estimated distance to age of onset(age_baseline - everage_age_of_onset_of_family)??? The two approached gave different results.

4) Plus, can someone explain me what the random-effect does in the model, because I found that the random-effect really gives different in my model.

5) Still, even we can not truly trust the difference between the groups, but the interaction between age and group(age*group) looks irrelevant with the range of age for PS and PT, at least we can give trust this part in our model? non??

I know that for PT, I dont have too many subjects(13), But I wanna know more if I create the model in the right way and how to interpret it.