[R] mixed effects or fixed effects?

[Andrew Robinson]

Hi Dan,

this is an interesting and intricate question, but only marginally
related to the subject line.

On Wed, Jan 24, 2007 at 03:25:39PM +0000, dan kumpik wrote:
> Hi,
> 
> I am running a learning experiment in which both training subjects and 
> controls complete a pretest and posttest. All analyses are being 
> conducted in R. We are looking to compare two training methodologies, 
> and so have run this experiment twice, once with each methodology. 
> Methodology is a between-subjects factor. Trying to run this analysis 
> with every factor included (ie, subject as a random factor, session 
> nested within group nested within experiment) seems to me (after having 
> tried) to be clumsy and probably uninterpretable.
> 	My favoured model for the analysis is a linear mixed-effects model, and 
> to combine the data meaningfully, I have collated all the pretest data 
> for controls and trained subjects from each experiment, and assumed this 
> data to represent a population sample for naive subjects for each 
> experiment. I have also ditched the posttest data for the controls, and 
> assumed the posttest training data to represent a population sample for 
> trained subjects for each experiment. I have confirmed the validity of 
> these assumptions by ascertaining that a) controls and trained listeners 
> did not differ significantly at pretest for either experiment; and b) 
> control listeners did not learn significantly between pretest and 
> posttest (and therefore their posttest data are not relevant). This was 
> done using a linear mixed-effects model for each experiment, with 
> subject as a random factor and session (pretest vs posttest) nested 
> within Group (trained vs control).

I don't agree with ditching the posttest data for the controls.
Although you may have failed to detect a lack of statistically
significant learning, that doesn't mean that there isn't enough
learning to imperil your inference.  

Also, under an appropriate model, posttest control data could
contribute to estimating the variance components, so by discarding
data you risk losing power. And by your description of the strategy,
you lose balance, but this is not such a problem as far as I am
aware. 

> 	Therefore, the model I want to use to analyse the data would ideally be 
> a linear mixed-effects model, with subject as a random factor, and 
> session (pre vs post) nested within experiment. Note that my removal of 
> the Group (Trained vs Control) factor simplifies the model somewhat, and 
> makes it more interpretable in terms of evaluating the relative effects 
> of each experiment.

I see that it simplifies the interpretation but not necessarily in a
constructive way!  

> 	What I would like to know is- a) would people agree that this is a 
> meaningful way to combine my data? I believe the logic is sound, but am 
> slightly concerned that I am ignoring a whole block of posttest data for 
> the controls (even though this does not account for a significant amount 
> of the variance); and b) given that each of my trained subjects appear 
> twice- one in the pretest and once in the posttest, and the controls 
> only appear once- in the pretest sample, is there any problem with 
> making subject a random factor? Conceptually, I see no problem with 
> this, but I would like to be sure before I finish writing up.
> 
> Many thanks for your time

I think that you need to make the model structure match the
experiment.  I hope that this is useful for you!

Andrew
-- 
Andrew Robinson  
Department of Mathematics and Statistics            Tel: +61-3-8344-9763
University of Melbourne, VIC 3010 Australia         Fax: +61-3-8344-4599
http://www.ms.unimelb.edu.au/~andrewpr
http://blogs.mbs.edu/fishing-in-the-bay/