Dear,
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)
Coefficients:
(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?
I'm not sure about this particular example but in general there is no problem with a negative AIC or a negative deviance just as there is no problem with a positive log-likelihood. It is a common misconception that the log-likelihood must be negative. If the likelihood is derived from a probability density it can quite reasonably exceed 1 which means that log-likelihood is positive, hence the deviance and the AIC are negative.
If you believe that comparing AICs is a good way to choose a model then it would still be the case that the (algebraically) lower AIC is preferred.
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