[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In an unpublished note, Sundar Dorai-Raj recently cited the following as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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