[R] "r-square in LME?

Spencer Graves spencer.graves at pdf.com
Tue Mar 18 18:38:12 CET 2003

In an unpublished note, Sundar Dorai-Raj recently cited the following as 
addressing this question:

Cox, D. R. and Snell, E. J. (1989) The Analysis of Binary Data, Second 
Edition, London: Chapman and Hall.

Nagelkerke, N. J. D. (1991) “A Note on a General Definition of the 
Coefficient of Determination,” Biometrika, 78, 691 -692.

Apparently, Cox and Snell (1989) suggest the following

	  R1.2 = 1-(L(0)/L(b.hat))^(2/n),

where L(b) = log(likelihood(b)).  With a normal likelihood using the 
standard maximum likelihood estimate for the variance, this produces the 
standard formula for the coefficient of determination.

Nagelkerke (1991) suggested the following modification:

	  R2.2 = R1.2/(1-(L(0))^(2/n))

I don't understand this second formula, so I can't comment on it. 
Yesterday, I found a few more recent papers that looked potentially 
relevant in a search of "query.statlib.org" for "coefficient of 
determination".  However, I won't know if they are relevant until I 
actually see them.

Hope this helps.
Best Wishes,
Spencer Graves

Allin Cottrell wrote:
> On Mon, 17 Mar 2003, Daniel Bloch wrote:
>>I analysed data with LME in R. Is there a measure for LME
>>(likelihood estimated) statistics which has an analogous meaning to
>>the coefficient of determination (r-square) estimated by
>>least-square procedure?
> There is not an exact analog, but the log-likelihood is commonly used
> as a figure of merit.
> Allin Cottrell.
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