# Repeated Measures model with Covariates

#### cecilia

##### New Member
Hi Everyone, i am struggling with finding a good way to analyze a dataset. The design is this: I have 25(n) subjects, all of them are tested in an experiment under 9 conditions. I estimate an electrophysiological index (idx) in every condition for each subject. Now I want to ask whether the volume of brain structures a,b,c has an effect on this index(idx) and whether this differs between conditions.
What I think is that this is a repeated measures model where i have for every subject the output of the 9 conditions (9 *idx), and for every of them I have a value for brain structure a,b,c. The model I am trying to fit is:
y1-y9 ~ a,b,c
where (y1-y9) = indices in the nine conditions for every subject. a,b,c = volume of structure a,b,c for every subject.
I am not sure though this is the right way to do this and also I am not sure how to interpret the results. I specify a within subject model, is this right? Another possibility could be using a linear model where:
idx ~ (a+b+c)*factor1*factor2 where idx=column vector of all indices , and factor 1 and 2 are categorical values (covariates) specifying the levels of factors for every row (i.e. idx ). a,b,c are repeated (since they are the same across conditions).
Any help would be very appreciated! I am not an expert in this topic, please if need more info ask!
Thank you in advance! Cecilia

#### mmercker

##### Member
Hi Cecilia, as far as I see you can use a mixed regression model (or mixed ANOVA) of this type:

idx ~ brain_structure + condition + brain_structure:condition,

with "subject_ID" as a random factor. Thus, the outcome related to "brain_structure" tells you if brain structure effects the index, analogous for "condition" and the interaction term "brain_structure:condition" tells you if the dependency of the index on brain_structure differs under different conditions respectively the dependency of the index on condition changes with different brain structures.