asymmetrical mixed anova?

[Matej Hruska]

Dear fellow modelers,

I am trying to figure out whether it is possible to make a mixed anova model asymmetrical (meaning having an “independent” control group) – my design is 2×2 factors + (possibly) 1 control group (so 5 experimental conditions), repeated measures pre-test / post-test (in each condition).
Or is there some other more sensible way to measure group differences and interactions?

Thanks,
Matej

[henrik]

In principle mixed models have the same constraint as all statistical models that you cannot estimate parameters for cells or conditions where you have no data at all (i.e., structurally missing). For example, when your control condition does not interact with one other factor (e.g., for your factor A, the control condition only exists for level a1 and not for level a2) then you cannot have an interaction of A with control.

As far as I understand your design you have 5 between-subjects or independent-samples groups. For each unit of observation in this group you furthermore have pre-test and post-test observations. This would allow to model the data as a 5 x 2 design with factors group and test_time: ~ group*test_time + (test_time|id) (note that the random effects structure assumes that you have replicates for each unit of observation and test_time condition, which you probably should have)

The problem with this approach is obviously that it flattens out the 2 x 2 design underlying 4 of your 5 groups. I do not see a way how to incorporate this structure with the control in one model. I think there are two ways to address the 2 x 2 structure subsequently, once you have run the initial model and have determined how the control group relates to the other 4 groups. You could either test the 2 x 2 design from the initial model using lsmeans (using a combination of lsmeans, contrast, and test) or run a second model on the reduced data that has a 2 x 2 x 2 design (i.e., your 4 groups times the repeated-measures factor). The second approach seems somewhat more straight forward to implement.

• This reply was modified 7 years, 6 months ago by henrik. Reason: clarified ranom effects structure

[Matej Hruska]

Dear Henrik,
thanks for your answer! sorry for a delayed reaction, I didnt receive an email notification…
It looks like we will simplify the design and maybe do two separate experiments, so the structure will be more straightforward.
Best,
Matej

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