### asymmetrical mixed anova?

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This topic contains 2 replies, has 2 voices, and was last updated by  Matej Hruska 7 months, 2 weeks ago.

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• #72

Matej Hruska
Participant

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

• #73

henrik
Keymaster

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 months, 3 weeks ago by  henrik. Reason: clarified ranom effects structure
• #84

Matej Hruska
Participant

Dear Henrik,