Goodness of Fit for Logistic Regression

[Fariha Zaman]

I am running a logistic regression on a binary dependent variable. I got the following answers after applying the following code:

 estat classification

Logistic model for improved

              -------- True --------
Classified |         D            ~D  |      Total
-----------+--------------------------+-----------
     +     |      4362          2617  |       6979
     -     |      3899          7113  |      11012
-----------+--------------------------+-----------
   Total   |      8261          9730  |      17991

Classified + if predicted Pr(D) >= .5
True D defined as improved != 0
--------------------------------------------------
Sensitivity                     Pr( +| D)   52.80%
Specificity                     Pr( -|~D)   73.10%
Positive predictive value       Pr( D| +)   62.50%
Negative predictive value       Pr(~D| -)   64.59%
--------------------------------------------------
False + rate for true ~D        Pr( +|~D)   26.90%
False - rate for true D         Pr( -| D)   47.20%
False + rate for classified +   Pr(~D| +)   37.50%
False - rate for classified -   Pr( D| -)   35.41%
--------------------------------------------------
Correctly classified                        63.78%
--------------------------------------------------

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. lroc

Logistic model for improved

number of observations =    17991
area under ROC curve   =   0.6835

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. lfit, group(10) table

Logistic model for improved, goodness-of-fit test

  (Table collapsed on quantiles of estimated probabilities)
  +----------------------------------------------------------+
  | Group |   Prob | Obs_1 |  Exp_1 | Obs_0 |  Exp_0 | Total |
  |-------+--------+-------+--------+-------+--------+-------|
  |     1 | 0.2610 |   419 |  430.4 |  1418 | 1406.6 |  1837 |
  |     2 | 0.3300 |   659 |  685.8 |  1634 | 1607.2 |  2293 |
  |     3 | 0.3389 |   464 |  431.3 |   817 |  849.7 |  1281 |
  |     4 | 0.4072 |   615 |  698.5 |  1255 | 1171.5 |  1870 |
  |     5 | 0.4315 |   752 |  724.4 |   969 |  996.6 |  1721 |
  |-------+--------+-------+--------+-------+--------+-------|
  |     6 | 0.4984 |   895 |  844.5 |   931 |  981.5 |  1826 |
  |     7 | 0.5227 |  1013 |  964.9 |   869 |  917.1 |  1882 |
  |     8 | 0.5948 |   969 |  995.5 |   763 |  736.5 |  1732 |
  |     9 | 0.6732 |  1230 | 1199.1 |   654 |  684.9 |  1884 |
  |    10 | 0.9740 |  1245 | 1286.7 |   420 |  378.3 |  1665 |
  +----------------------------------------------------------+

       number of observations =     17991
             number of groups =        10
      Hosmer-Lemeshow chi2(8) =        43.71
                  Prob > chi2 =         0.0000

How can I know if my model is fit or not? As my Prob > chi2 = 0.0000 but my number of observation is large, how can I interpret my goodness of fit for this?

[Felix Bittmann]

Logit reports Pseudo R², which you can use. An alternative is fitstat

ssc install fitstat, replace
logit ...
fitstat

[Fariha Zaman]

Thank you, I have used the code. But I am not sure how to interpret the results.

fitstat

Measures of Fit for logit of improved

Log-Lik Intercept Only:   -12410.371     Log-Lik Full Model:       -11452.652
D(17973):                  22905.305     LR(12):                     1915.437
                                         Prob > LR:                     0.000
McFadden's R2:                 0.077     McFadden's Adj R2:             0.076
Maximum Likelihood R2:         0.101     Cragg & Uhler's R2:            0.135
McKelvey and Zavoina's R2:     0.134     Efron's R2:                    0.102
Variance of y*:                3.798     Variance of error:             3.290
Count R2:                      0.638     Adj Count R2:                  0.211
AIC:                           1.275     AIC*n:                     22941.305
BIC:                     -153187.444     BIC':                      -1797.865

[Felix Bittmann]

These numbers need to be seen as relational. For example, take McFaddens R2. This means that your predictors explain about 7.7% of the variation in the dependent variable. Is this low or high? Depends on your research question and related research. I would attempt to compare with result to previous research from the literature.