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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