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

[Thierry Onkelinx]

Dear Koen,

Have you tried writing down the model you envision as a (set of)
mathematical expressions? This can help to better understand what you want
and how you can fit it.

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 13:31 GMT+01:00 Koen Neijenhuijs <kn.journal.news op gmail.com>:

> 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 op 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 op 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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