[R-sig-ME] Using individual differences from model A as predictor in model B

[Koen Neijenhuijs]

Dear all,


we've run an experiment with two groups, which we followed for 3 weeks.
Each participant got three trials per week, and our dependent variable is
the adherence, defined as whether they replied to the trial or not. In the
third week, we introduced a manipulation, which was balanced across the two
groups. We want to test the effect of the manipulation, moderated for
intrinsic motivation to adhere to the trials. We are struggling with the
operationalization of intrinsic motivation.

We ran a binomial mixed-effect model on the data of the first two weeks, to
estimate intrinsic motivation. So far, we've come up with three methods to
do so, but each comes with their own concerns. I was hoping to hear your
thoughts on this.

1. The first method is simply to use the aggregated (sum) adherence of each
participant. This method would be seemingly valid, as the model on the
first two weeks shows no main effect of time, group, nor the interaction
time*group. However, I am reluctant to go this route as this method is less
detailed than the other options.

2. The second method is to extract the random-adjusted intercept and
random-adjusted slope of time (random effects + fixed effects), per
participant. The interaction of these two represent intrinsic motivation as
it inherits both the intercept of adherence as well as its' development
over time; this combination is capable of representing every possible
motivation timeline (start high and go lower over time; start high and stay
high over time; start low and go up over time; etc). However, using this
method, to test the effect we're interested in will result in a three-way
interaction (intercept*slope*manipulation), and a four-way interaction to
check moderation of prior group characteristics. It is unlikely we have
enough power to test this, as our sample size is limited.

3. The third method is to extract the prediction equation from the model of
the first two weeks and apply this to the data of the third week. This
method will give us one representation of motivation instead of two, which
does include both fixed and random effects. However, as the method is
applied to data of the third week, I am uncertain whether it is valid as a
representation of intrinsic motivation over the first two weeks.

Sorry for the long wall of text. What are your thoughts on this? Are there
other ways of operationalizing individual differences on adherence in the
first two weeks to use as an independent variable on adherence in the third
week?

Cheers,

Koen

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