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

[Koen Neijenhuijs]

Dear Thierry,

thanks for the quick response! That would be the easiest model, but I'm not
entirely sure whether this model represents motivation the way we envision
it. In essence what you propose is a model where we test whether adherence
has changed from week1&week2 to week3, and whether this change is different
for the two different groups. However, this model does not have a concrete
moderation of the individual differences inside of the fixed effect, which
is what we're after. In essence, the research question isn't so much about
the two different groups (the groups merely exist to balance the experiment
itself, and is thus a control variable), but what the effect of the
manipulation is for participants of different intrinsic motivations. Our
problem is that intrinsic motivation is inherently intertwined with the
dependent variable, and while putting time in the model as you propose is
one way to approach the question, the interaction of BeforeAfter*Treatment
doesn't allow us to disentagle the question regarding motivation.

Kind regards,

Koen

2016-12-02 13:23 GMT+01:00 Thierry Onkelinx <thierry.onkelinx at inbo.be>:

> Dear Koen,
>
> I think you can fit this in a single model. Here a a few options:
>
> with lme4:
> Adherence ~ BeforeAfter * Treatment + (1 + BeforeAfter|Participant)
> Adherence ~ BeforeAfter * Treatment + (1| Participant:BeforeAfter)
>
> with INLA:
> Adherence ~ BeforeAfter * Treatment + f(Time, model = "rw1", replicate =
> Participant)
>
> The BeforeAfter:Treatment interaction is the effect you are interested in.
> The lme4 random effect allow for an additional treatment effect for
> individual participants. The INLA random effect allows for correlated
> random intercept along Time for the individual participant. rw1 stands for
> random walk of order 1, which models the differences between consecutive
> time points.
>
> Best regards,
>
>
> ir. Thierry Onkelinx
> Instituut voor natuur- en bosonderzoek / Research Institute for Nature and
> Forest
> team Biometrie & Kwaliteitszorg / team Biometrics & Quality Assurance
> Kliniekstraat 25
> 1070 Anderlecht
> Belgium
>
> To call in the statistician after the experiment is done may be no more
> than asking him to perform a post-mortem examination: he may be able to say
> what the experiment died of. ~ Sir Ronald Aylmer Fisher
> The plural of anecdote is not data. ~ Roger Brinner
> The combination of some data and an aching desire for an answer does not
> ensure that a reasonable answer can be extracted from a given body of data.
> ~ John Tukey
>
> 2016-12-02 12:03 GMT+01:00 Koen Neijenhuijs <kn.journal.news at gmail.com>:
>
>> 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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>>
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>

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