[R] Penalized likelihood-ratio chi-squared statistic: L.R. model for Goodness of fit?

[Frank E Harrell Jr]

Jan Verbesselt wrote:
> Dear R list,
> 
>  
> 
> From the lrm() binary logistic model we derived the G2 value or the
> likelihood-ratio chi-squared statistic given as L.R. model, in the output of
> the lrm().

> How can this value be penalized for non-linearity (we used splines in the
> lrm function)?
> 

> lrm.iRVI <- lrm(arson ~ rcs(iRVI,5),
> penalty=list(simple=10,nonlinear=100,nonlinear.interaction=4)) 
> 
> This didn’t work properly.

Please following the posting guide.  What do you mean by 'work' and what 
is the output?

You are attempting to penalize for nonexistent interaction terms.

Differential penalization is only appropriate if there are many similar 
terms being penalized (e.g., you fit a multivariable model and want to 
penalize all nonlinear terms in all variables combined).

> The aim is to obtain a value that can be used to compare the goodness of fit
> of the different univariate binary logistic models. 

By univariate I assume you mean univariable.  Penalization is primarily 
used to fit multivariable models.  It allows you to fit "bigger" models.

But for your purpose comparing AIC of various models might be entertained.

Frank

> 
> (The lower the value, the better the fit)
> 
> Kind regards,
> 
> Jan
> 
> ____________________________________________________________________
> Ir. Jan Verbesselt
> Research Associate
> Group of Geomatics Engineering
> Department Biosystems ~ M³-BIORES
> Vital Decosterstraat 102, 3000 Leuven, Belgium
> Tel: +32-16-329750   Fax: +32-16-329760
> http://gloveg.kuleuven.ac.be/
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-- 
Frank E Harrell Jr   Professor and Chair           School of Medicine
                      Department of Biostatistics   Vanderbilt University