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I have a modeling situation that I am not 100% sure how to approach. I have two independent variables, information and time, with time being a repeated measure. The dependent measure is difference. When analyzing summary measures of difference collapsed across time, and as theory would suggest, there is a quadratic relationship between information and difference.

Information increases the difference up to a peak, past which higher information results in a smaller difference. I would like to build a model to incorporate time so that I do not have to collapse down to summary measures. Theory and previous data would suggest a linear relationship between time and difference. How should I model this? Currently I have this for my full theory driven model:

full_model_ml <- lmerTest::lmer(difference ~ 
       I((time - 54)/10)*(cinformation + cinformation2) +             
       (I((time - 54)/10) | id), data = df, REML = FALSE,
       control = lme4::lmerControl(optimizer ="Nelder_Mead")).

But I'm not sure is this is the correct approach given the expected polynomial relationship between information and difference, and linear relationship between time and difference.

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  • $\begingroup$ You write about a quadratic effect of information, so I am assuming cinformation2 is cinformation squared? Where do the 54 and 10 constants come from? Are you sure you need a fixed pre-specified functional form? Or do you simply want to allow for capturing non-linear effects, whatever their shape or form? Then I would advice smoothing splines with GAM, as these can also incorporate random effects. But it would probably be helpful if you address the questions above, and specify as clearly as possible your research questions or hypotheses. $\endgroup$
    – Marjolein Fokkema
    Commented Oct 24 at 19:58

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