R help - Aug 2005 - HowTo derive a correct likelihood-ratio chi-squared statistic from lrm() with a rsc() ?

Dear R helpers,

 
>From the lrm( ) model used for binary logistic regression, we used the L.R.
model value (or the G2 value, likelihood-ratio chi-squared statistic)  to
evaluate the goodness-of-fit of the models. The model with the lowest G2
value consequently, has the best performance and the highest accuracy.

 

However our model includes rsc() functions to account for non-linearity. We
would like to penalize the L.R. model function for the non-linearity because
the L.R. model value we obtain from different models are just the inverse of
the derived c-index and AIC (from the lrm) (?!). So the L.R. Model is higher
for the best model and not lower as explained above…

 

The models:

 

These are the models

                knots                      <- 5

    lrm.iRVI                              <- lrm(arson ~ rcs(iRVI,knots))

    lrm.ARND                          <- lrm(arson ~ rcs(ARND,knots))

    lrm.ARNDiRVI <- lrm(arson ~ rcs(ARND,knots)+rcs(iRVI,knots))

 

and the L.R. model values are bigger, the better the model becomes (it is
the inverse of our derived AIC and c-index). Normally, the best model should
have the lowest G2 value.

 

Could we solve this by penalizing the model or is there another way to
derive a correct G2 value when rcs() functions are used in an lrm() model?

 

e.g., lrm.iRVI <- lrm(arson ~ rcs(iRVI,knots),
penalty=list(simple=10,nonlinear=100,nonlinear.interaction=4)) 

but this does not work. 

 

Is the AIC value a good approx for the L.R. model? (see function below)

 

dAIC <- function(fit){

    logl        <- oos.loglik(fit) # derive -2*logL of the model

    k           <- 2

    edf         <- fit$stats[4]

    # 'edf' is the equivalent degrees of freedom (i.e., the number of
parameters for usul parametric models) of 'fit'.

    lrmAIC      <- logl + k*edf

    return(lrmAIC)

    }

 

 

Best regards,

Jan

 

 

 

_______________________________________________________________________
Ir. Jan Verbesselt
Research Associate
Group of Geomatics Engineering
Department Biosystems ~ M³-BIORES
Vital Decosterstraat 102, 3000 Leuven, Belgium
Tel: +32-16-329750   Fax: +32-16-329760
http://gloveg.kuleuven.ac.be/
_______________________________________________________________________

 


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