[R-sig-ME] statistical basis for using mixed model in a situation

[Steven J. Pierce]

Here's a paper advocating for the simpler approach when the additional
parameters offered by the mixed model are not of intrinsic interest. 

Murtaugh, P. A. (2007). Simplicity and complexity in ecological data
analysis. Ecology, 88(1), 56-62. doi:
10.1890/0012-9658(2007)88[56:SACIED]2.0.CO;2

Anyone have example papers advocating for the other side of this issue?

Steven J. Pierce, Ph.D. 
Associate Director 
Center for Statistical Training & Consulting (CSTAT) 
Michigan State University 
E-mail: pierces1 at msu.edu 
Web: http://www.cstat.msu.edu 

-----Original Message-----
From: John Maindonald [mailto:john.maindonald at anu.edu.au] 
Sent: Wednesday, May 30, 2012 8:32 PM
To: Juliet Hannah
Cc: r-sig-mixed-models at r-project.org
Subject: Re: [R-sig-ME] statistical basis for using mixed model in a
situation

The two approaches (but doing the t-test with var.equal=TRUE) should 
give the same final result, unless the between sample component of
variance happens to be estimated to be zero. If you average the triplicates,

you get output that is easier to interpret.  The t-test output will give you
the 
number of degrees of freedom for the t-test.

Thinking in terms of averaging the triplicates hints at the possibility
that some other form of summary might in one or other circumstance
be preferable, e.g., work with a median.

The mixed model is needed if you want the variance information that, 
if it can be estimated with enough accuracy to be useful, allows 
prediction of the manner in which the SEDs will change when, e.g., 
each sample is measured 5 times. 

It is a "horses for courses" matter!

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 31/05/2012, at 6:44 AM, Juliet Hannah wrote:

> All,
> 
> Consider a simple two-group design in which one wants to test if the
> means of these two groups are different. Assume a simple
> t-test (un-paired) is sufficient. Let's say there are 10 samples in
> Group A and 10 in group B.
> 
> Now, let's say each sample was measured in triplicate so that Group A
> has 30 arising from 10 measured in triplicate.
> 
> Here is my question:
> 
> We could average the triplicates and proceed with the t-test.
> 
> But I have also observed people fitting a mixed model with a random
> intercept for the triplicates.
> 
> What is the statistical basis for selecting one approach over the other?
> 
> Off the top of my head, this seems a little different from examples
> such as students nested within classes and so on, but
> I am unable to properly characterize it statistically.
> 
> Thanks,
> 
> Juliet
> 
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