[R-sig-ME] The effects of adding by-subject or by-item random intercepts

[John Maindonald]

Think of the intercept (probably at the mean of x)  and slope 
of the fitted lines as statistics that you want to compare between 
groups.  You might use a t-test the test for no significant 
difference in intercept between the two groups. Similarly
for the slope, if you look at that on its own.

If the intercepts do differ between subjects, then the difference
in intercepts must, to be real, be greater than can be explained
by within group variation in intercepts.  Similarly for the slopes.

John Maindonald             email: john.maindonald at anu.edu.au
phone : +61 2 (6125)3473    fax  : +61 2(6125)5549
Centre for Mathematics & Its Applications, Room 1194,
John Dedman Mathematical Sciences Building (Building 27)
Australian National University, Canberra ACT 0200.
http://www.maths.anu.edu.au/~johnm

On 08/12/2009, at 6:15 PM, Antoine Tremblay wrote:

> Dear all,
> 
> This question is about the effects of adding by-subject or by-item
> random intercepts to a model.
> 
> If we are contrasting a single condition between two subject groups,
> say ReactionTime ~ Sex,
> is it warranted (or necessary or ill-advised) to include by-subjects
> random intercepts,
> since this could (if I'm understanding it correctly) adjust the mean
> reaction time for each subject (and thus for
> each condition) towards the grand mean, thus reducing or
> eliminating the difference in the condition between subjects? And
> similarly if we are contrasting a
> single condition between two sets of items, say ReactionTime ~ Frequency?
> 
> I believe that the addition of the random effect may reduce the effect
> of the fixed effect, but should
> not remove it entirely. Is this right?
> 
> The question would then become: Why would the addition of say by-item
> random intercepts to a model
> take away an effect that was present in a model without by-item random
> intercepts?
> 
> Thank you again, your help is well appreciated.
> 
> -- 
> Antoine Tremblay
> Department of Neuroscience
> Georgetown University
> Washington DC
> 
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