[R] Goodness of fit of binary logistic model

[Paul Smith]

On Fri, Aug 5, 2011 at 4:54 PM, David Winsemius <dwinsemius at comcast.net> wrote:
>> 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?

----------------------------------------------------------
> residuals.lrm(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
>