'Translate' ANOVA comparison on regression parameters into linear mixed model

Cross Validated Asked by Laurie on August 13, 2020

I am analysing data from a medication study. Participants did the same task twice; in one session they were given a certain drug and a placebo in the other one. The order of the sessions was perfectly counterbalanced, meaning that some participants did the drug condition first whereas others participated in the placebo condition first. Therefore, we have repeated measures data from each participant in both conditions. In the task, we assume that three different factors (delay, reward magnitude and previous choice) influence current choice. I used to fit a logistic regression model and compared the regression weights between conditions with a 2×2 ANOVA (drug x order).
However, for various reasons I would rather analyse the same data with a linear mixed model in R. Since I am new to mixed model analysis, I would love to hear your opinions on how I set up the model. As I said, we are specifically interested in how the drug affects the influence of reward parameters on choice. For example: Does the delay has a different influence on choice given drug vs/placebo, so the interaction between both. I set up the model in the following way: Choice~1+ delay*drug+reward_mag:drug+previous_choice:drug+reward_mag+previous_choice+(1+delay+reward_mag+previous_choice+drug+session| subj). I was specifically wondering whether I would need to specify the interaction effects as random effects as well?

Every help would be vry much appreciated!



One Answer

The model:

Choice~1+ delay*drug+reward_mag:drug+previous_choice:drug+reward_mag+previous_choice+(1+delay+reward_mag+previous_choice+drug+session| subj)

has a very complex random structure. It would not surprise me if it converges with a singular fit or some other problem. But you might be lucky. Do you have a priori reasons to think that all the main effects should vary by subject ?

If you have reason to believe that the interactions should also vary by subject then of course you can also include them in the random structure, but again, don't be surprised if you get convergence problems.

Answered by Robert Long on August 13, 2020

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