[R] negetative AIC values: How to compare models with negative AIC's

[Jan Verbesselt]

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?


Thanks,
Jan

_______________________________________________________________________
ir. Jan Verbesselt 
Research Associate 
Lab of Geomatics Engineering K.U. Leuven
Vital Decosterstraat 102. B-3000 Leuven Belgium 
Tel: +32-16-329750   Fax: +32-16-329760
http://gloveg.kuleuven.ac.be/