[R] HOWTO compare univariate binomial glm lrm models which are not nested

[Jan Verbesselt]

Thanks a lot for the input!

I forgot to add family=binomial, for a binomial glm. Now the AIC's are
positive!

I was planning to use AIC (from the binomial glm) and c-index (lrm) to
compare and rank different uni-variate (one continue explanatory variable)
logistic models to evaluate the 'performance' of the different explanatory
variables in the different models.

What is the best technique to compare these lrm.models, which are not
nested? I found in literature that ranking based on different parameters
(goodness of fit and predictability) that these can be used to compare
uni-variate models.

Thanks in advance,
Regards,
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/
_______________________________________________________________________

-----Original Message-----
From: Prof Brian Ripley [mailto:ripley at stats.ox.ac.uk] 
Sent: Friday, April 15, 2005 5:06 PM
To: Jan Verbesselt
Cc: r-help at stat.math.ethz.ch
Subject: Re: [R] negetative AIC values: How to compare models with negative
AIC's

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:

>
> 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?

-- 
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