I agree with Tim, with this kind of design, as long as there are few missing data cells, the full mixed model doesn't really buy you much over the simpler and more traditional analysis. If there's a lot of missing data the mixed model might make more sense.

Jake

> From: tim.cole@ucl.ac.uk
> To: r-sig-mixed-models@r-project.org
> Date: Wed, 5 Feb 2014 11:27:31 +0000
> Subject: Re: [R-sig-ME] model specification for 2x2x2 factorial between-subjects design with repeated measures
> 
> Bruce,
> 
> Since your DV has only two levels you can do a much simpler analysis, avoiding repeated measures entirely. Make the second DV your outcome, and adjust for the first DV as a baseline covariate along with adjustments for c1, c2 and c3.
> 
> Best wishes,
> Tim Cole
> 
> From: Bruce Gilstrap <bruce@gilstraps.org<mailto:bruce@gilstraps.org>>
> 
> My colleagues and I are interested in analyzing a dataset generated by a
> 2x2x2 factorial design where each of the 3 factors are between-subjects
> factors, each consisting of 2 levels, which results in 8 experimental
> conditions. Therefore, each subject was randomly assigned to 1 of these
> conditions. Additionally, the DV was measured twice, so our design includes
> a repeated measure. Basically, then, the data look like this (in so-called
> *long* form):
> 
> subj  c1  c2  c3  time   dv
>    1   0   0   0     1  1.1
>    2   0   0   1     1  3.2
>    3   0   1   0     1  4.4
> 
> So far, this is a relatively straightforward design. However, it is
> complicated by the fact that the third condition is essentially a
> treatment. That is, it was unknown to the subjects when the DV was measured
> at time 1. After the first measurement of the DV, they were presented with
> a treatment, and then we measured the DV at time 2. Therefore, the design
> includes a pre-/post-test element as well. Our research question is focused
> on the effect of the treatment (c3), and we are not directly interested in
> the effects of c1 and c2. We included these conditions because prior
> research suggests that they may affect our DV. Therefore, we are planning
> to treat these conditions as covariates.
> 
> [snip]
> 
> We would appreciate receiving advice about our plans for analyzing these
> data, and are particularly interested in comments about the following
> issues:
> 
>    1. Is our intended approach to treat c1 and c2 as covariates defensible?
>    2. If so, will our R-specific model specifications allow us to answer
>    our research question?
>    3. In any case, are there any better approaches?
> 
> Thanks,
> 
> Bruce
> 
> ---
>  Phone +44(0)20 7905 2666 Fax +44(0)20 7905 2381
> Centre for Paediatric Epidemiology and Biostatistics
> UCL Institute of Child Health, London WC1N 1EH, UK
> 
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