[R] Repeated measures logistic regression

[Andy Fugard]

Dear all,

Thanks to everyone who replied off list to my (rambling) question  
earlier this year!  I have put pointers to things I found useful over  
here:

   http://tinyurl.com/yvvvn9

Thought it might be helpful to share as now and again I receive  
emails from people wondering if I ever made progress.

Best wishes,

Andy


On 25 Feb 2007, at 19:58, Andy Fugard wrote:

> Dear all,
>
> I'm struggling to find the best (set of?) function(s) to do repeated
> measures logistic regression on some data from a psychology  
> experiment.
>
> An artificial version of the data I've got is as follows.  Firstly,
> each participant filled in a questionnaire, the result of which is a
> score.
>
>> questionnaire
>     ID Score
> 1   1     6
> 2   2     5
> 3   3     6
> 4   4     2
> ...
>
> Secondly, each participant did a task which required a series of
> button-pushes.  The response is binary.  The factors CondA and CondB
> describe the structure of the stimulus:
>
>> experiment
>      ID CondA CondB Response
> 1    1    a1    b1        1
> 2    1    a2    b2        0
> 3    1    a3    b1        0
> 4    1    a4    b2        0
> 5    1    a1    b1        1
> 6    1    a2    b2        0
> 7    1    a3    b1        0
> 8    1    a4    b2        0
> 9    2    a1    b1        1
> 10   2    a2    b2        0
> 11   2    a3    b1        0
> 12   2    a4    b2        0
> 13   2    a1    b1        1
> 14   2    a2    b2        0
> 15   2    a3    b1        0
> 16   2    a4    b2        0
>
> I would like to model how someone's score on the questionnaire
> relates to the responses they give in the button-pushing.  I'm
> particularly interested in interactions between the type of the
> stimulus and the score.
>
> I combined the experiment and the questionnaire dataframe with a
> merge so now there an additional column.
>
>> exp.q
>      ID Score CondA CondB Response
> 1    1     6    a1    b1        1
> 2    1     6    a2    b2        0
> 3    1     6    a3    b1        0
> 4    1     6    a4    b2        0
> 5    1     6    a1    b1        1
> 6    1     6    a2    b2        0
> 7    1     6    a3    b1        0
> 8    1     6    a4    b2        0
> 9    2     5    a1    b1        1
> 10   2     5    a2    b2        0
> 11   2     5    a3    b1        0
> 12   2     5    a4    b2        0
> ...
>
> Eventually, via glm, glmmPQL, and a few others, I ended up with
> lmer.  My questions follow.  I suspect (or hope) that I need to be
> pointed towards the relevant literature.  I own Faraway's "Extending
> the Linear Model with R" and Crawley's "Statistics: An Introduction
> using R".
>
> 1. Is the way I've combined the tables okay?  I'm concerned that the
> repetition of the score is Bad but can't think of any other way to
> code things.
>
> 2. Is lmer the most appropriate function to use?
>
> 3. If so, does the following call capture what I'm trying to model?
>
> model1 = lmer(Response ~ CondA * CondB * Score + (1|Subject),
>                data =exp.q,
>                family = binomial)
>
> I just want to tell lmer, "Look, this set of responses all comes from
> the same person: tell me the within-subject stuff that's going on and
> how that's affected by their score!"
>
> 4. Is there any way to do stepwise model simplification?  In the real
> data I have, there are several more predictors, including more than
> one questionnaire score and subscores.  I have specific hypotheses
> about what could be going on, so I can live with manual editing of
> the formulae, but it's nice for exploratory purposes to do stepwise
> simplification.
>
> 5. What's the best way to discover and report the relative
> contribution of each predictor?  I'm after an analogue of
> standardized betas (though I recently learned that they're thoroughly
> evil).
>
> 6. Is there anyway to get a p-value for goodness of fit?
>
> Many thanks for any help,
>
> Andy
>
> --
> Andy Fugard, Postgraduate Research Student
> Psychology (Room F15), The University of Edinburgh,
>    7 George Square, Edinburgh EH8 9JZ, UK
> Mobile: +44 (0)78 123 87190   http://www.possibly.me.uk
>
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--
Andy Fugard, Postgraduate Research Student
Psychology (Room F15), The University of Edinburgh,
   7 George Square, Edinburgh EH8 9JZ, UK
Mobile: +44 (0)78 123 87190   http://www.possibly.me.uk