[R] negetative AIC values: How to compare models with negative AIC's
Prof Brian Ripley
ripley at stats.ox.ac.uk
Fri Apr 15 17:05:44 CEST 2005
AICs (like log-likelihoods) can be positive or negative.
However, you fitted a Gaussian and not a binomial glm (as lrm does if
m.arson is binary).
For a discrete response with the usual dominating measure (counting
measure) the log-likelihood is negative and hence the AIC is positive,
but not in general (and it is matter of convention even there).
In any case, Akaike only suggested comparing AIC for nested models, no one
suggests comparing continuous and discrete models.
On Fri, 15 Apr 2005, Jan Verbesselt wrote:
> When fitting the following model
> knots <- 5
> lrm.NDWI <- lrm(m.arson ~ rcs(NDWI,knots)
> I obtain the following result:
> Logistic Regression Model
> lrm(formula = m.arson ~ rcs(NDWI, knots))
> Frequencies of Responses
> 0 1
> 666 35
> Obs Max Deriv Model L.R. d.f. P C Dxy
> Gamma Tau-a R2 Brier
> 701 5e-07 34.49 4 0 0.777 0.553
> 0.563 0.053 0.147 0.045
> Coef S.E. Wald Z P
> Intercept -4.627 3.188 -1.45 0.1467
> NDWI 5.333 20.724 0.26 0.7969
> NDWI' 6.832 74.201 0.09 0.9266
> NDWI'' 10.469 183.915 0.06 0.9546
> NDWI''' -190.566 254.590 -0.75 0.4541
> When analysing the glm fit of the same model
> Call: glm(formula = m.arson ~ rcs(NDWI, knots), x = T, y = T)
> (Intercept) rcs(NDWI, knots)NDWI rcs(NDWI, knots)NDWI'
> rcs(NDWI, knots)NDWI'' rcs(NDWI, knots)NDWI'''
> 0.02067 0.08441 -0.54307
> 3.99550 -17.38573
> Degrees of Freedom: 700 Total (i.e. Null); 696 Residual
> Null Deviance: 33.25
> Residual Deviance: 31.76 AIC: -167.7
> A negative AIC occurs!
> How can the negative AIC from different models be compared with each other?
> Is this result logical? Is the lowest AIC still correct?
Brian D. Ripley, ripley at stats.ox.ac.uk
Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/
University of Oxford, Tel: +44 1865 272861 (self)
1 South Parks Road, +44 1865 272866 (PA)
Oxford OX1 3TG, UK Fax: +44 1865 272595
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