[R-sig-ME] R2 measure in mixed models? (Steve Candy) [Sec=Unclassified]

[Steve Candy]

A further complication is that there could be information about a fixed effect at more than one sampling level in a LMM.
So how does one combine %variance explained across multiple levels to give an overall "strength" of a fixed effect?

The classic example is the incomplete block design analysis with recovery of inter-block information. There is information on treatment means and comparisons in both the plots within-blocks and in the block totals.


On Mon, 1 Mar, 2010 at 17:55:59 PM, Juliet Hannah <juliet.hannah at gmail.com> wrote:

>How does one try and summarize the "strength" of a fixed effect in the mixed model setting?
>It is this question that had led me to try and understand the various pseudo R-squares.
>I'm curious how others do this (for any definition of strength).


>>On Fri, Feb 26, 2010 at 10:27 AM, Nick Isaac <njbisaac at googlemail.com> wrote:
>> Thanks for these pertinent comments.
>>
>> I can't comment on the motivation for the original post. I have always
>> felt that a single dimensionless Rsq was fairly meaningless in the
>> context of mixed models.
>>
>> Gelman & Pardoe's formula summarizes the fit at each level in the
>> model separately. This has more intuitive appeal, especially since I
>> tend to fit models containing fixed effects at the group level. The
>> motivation then would be to write a sentence along the lines of
>> 'gender explains 5% of the among-subject variance in orthodontic
>> growth curves; age explains 80% of the within-subject variation'.
>>
>> Incidentally, G&P also state that negative Rsqs might be expected (for
>> their
>> index): essentially it means that adding a fixed effect causes the variance
>> of a random effect to increase..
>>
>> Best wishes, Nick

Regards Steve

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Steven G Candy
Senior Applied Statistician
Southern Ocean Ecosystems
Australian Antarctic Division
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