[R] Goodness of fit of binary logistic model

[David Winsemius]

On Aug 5, 2011, at 9:47 AM, Paul Smith wrote:

> Dear All,
>
> I have just estimated this model:
> -----------------------------------------------------------
> Logistic Regression Model
>
> lrm(formula = Y ~ X16, x = T, y = T)
>
>                     Model Likelihood     Discrimination    Rank  
> Discrim.
>                        Ratio Test            Indexes          Indexes
>
> Obs            82    LR chi2      5.58    R2       0.088    C        
> 0.607
> 0             46    d.f.            1    g        0.488    Dxy      
> 0.215
> 1             36    Pr(> chi2) 0.0182    gr       1.629    gamma    
> 0.589
> max |deriv| 9e-11                         gp       0.107    tau-a    
> 0.107
>                                          Brier    0.231
>
>          Coef    S.E.   Wald Z Pr(>|Z|)
> Intercept -1.3218 0.5627 -2.35  0.0188
> X16=1      1.3535 0.6166  2.20  0.0282
> -----------------------------------------------------------
>
> Analyzing the goodness of fit:
>
> -----------------------------------------------------------
>> resid(model.lrm,'gof')
> Sum of squared errors     Expected value|H0                    SD
>         1.890393e+01          1.890393e+01          6.073415e-16
>                    Z                     P
>        -8.638125e+04          0.000000e+00
> -----------------------------------------------------------
>
>> From the above calculated p-value (0.000000e+00), one should discard
> this model. However, there is something that is puzzling me: If the
> 'Expected value|H0' is so coincidental with the 'Sum of squared
> errors', why should one discard the model? I am certainly missing
> something.

It's hard to tell what you are missing, since you have not described  
your reasoning at all. So I guess what is at error is your expectation  
that we would have drawn all of the unstated inferences that you draw  
when offered the output from lrm. (I certainly did not draw the  
inference that "one should discard the model".)

resid is a function designed for use with glm and lm models. Why  
aren't you  using residuals.lrm?

-- 


David Winsemius, MD
West Hartford, CT