[R] mixed effects or fixed effects?

dan kumpik daniel.kumpik at physiol.ox.ac.uk
Wed Jan 24 16:25:39 CET 2007


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).
	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.
	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


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