Logistic regression shows negative adj. (McFadden's) R2 but statistically sig. coefficient for main predictor variable. How to interpret?

[Gate Nucht]

As the title says, I have a logistic regression model with a negative adjusted R2 (McFadden's), but my main predictor variable is statistically significant. This is true for the basic model that only includes x and y as well as for models that include multiple predictors.

Is it sound to conclude that x is associated with y even though my model does not fit according to the adjusted R2? Or does poor model fit mean that the statistically significant coefficients are not meaningful?

Thanks!

[FernandoRios]

can you show your results?
I can think ofa case when the PR2 would be negative. Can you post your result to see what are you facing? Namely, can you show the results of a logit without any covariate, and one with your main covariates?

[Gate Nucht]

Thanks for the quick response! Below are the results for one of my outcome variables.

. logistic becamehl i.wasdetained

Logistic regression                             Number of obs     =      1,532
                                                LR chi2(1)        =       4.86
                                                Prob > chi2       =     0.0275
Log likelihood = -179.22844                     Pseudo R2         =     0.0134

------------------------------------------------------------------------------
    becamehl | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
 wasdetained |
          0  |          1  (base)
          1  |   2.862325   1.228674     2.45   0.014     1.234054    6.639013
             |
       _cons |   .0230714   .0041253   -21.08   0.000     .0162508    .0327546
------------------------------------------------------------------------------
Note: _cons estimates baseline odds.

. fitstat

Measures of Fit for logistic of becamehl

Log-Lik Intercept Only:     -181.659     Log-Lik Full Model:         -179.228
D(1529):                     358.457     LR(1):                         4.862
                                         Prob > LR:                     0.027
McFadden's R2:                 0.013     McFadden's Adj R2:            -0.003
Maximum Likelihood R2:         0.003     Cragg & Uhler's R2:            0.015
McKelvey and Zavoina's R2:     0.022     Efron's R2:                    0.004
Variance of y*:                3.365     Variance of error:             3.290
Count R2:                      0.975     Adj Count R2:                  0.000
AIC:                           0.238     AIC*n:                       364.457
BIC:                      -10855.733     BIC':                          2.473

. logistic becamehl i.wasdetained rage adatoarr adatow1 i.convicted i.h3a blrent blevict h2_1 e1

Logistic regression                             Number of obs     =      1,402
                                                LR chi2(10)       =      20.56
                                                Prob > chi2       =     0.0244
Log likelihood = -167.87489                     Pseudo R2         =     0.0577

------------------------------------------------------------------------------
    becamehl | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
 wasdetained |
          0  |          1  (base)
          1  |    2.78561   1.240647     2.30   0.021      1.16363    6.668465
             |
        rage |   .9892609   .0150464    -0.71   0.478     .9602057    1.019195
    adatoarr |   1.027631   .2966059     0.09   0.925     .5836522     1.80934
     adatow1 |   1.004718   .0068533     0.69   0.490     .9913753    1.018241
             |
   convicted |
          0  |          1  (base)
          1  |   1.285578    .964681     0.33   0.738      .295371    5.595373
             |
         h3a |
          0  |          1  (base)
   1. Alone  |   .7177582   .3379728    -0.70   0.481     .2852137    1.806283
             |
      blrent |   .5537232    .236645    -1.38   0.167     .2396151    1.279591
     blevict |   4.859672   2.042834     3.76   0.000     2.132023      11.077
        h2_1 |   1.229243   .4934245     0.51   0.607     .5597077    2.699694
          e1 |   1.270503   .4414346     0.69   0.491     .6430233    2.510294
       _cons |   .0157691   .0140079    -4.67   0.000     .0027649    .0899373
------------------------------------------------------------------------------
Note: _cons estimates baseline odds.

. fitstat

Measures of Fit for logistic of becamehl

Log-Lik Intercept Only:     -178.154     Log-Lik Full Model:         -167.875
D(1388):                     335.750     LR(10):                       20.558
                                         Prob > LR:                     0.024
McFadden's R2:                 0.058     McFadden's Adj R2:            -0.021
Maximum Likelihood R2:         0.015     Cragg & Uhler's R2:            0.065
McKelvey and Zavoina's R2:     0.108     Efron's R2:                    0.026
Variance of y*:                3.688     Variance of error:             3.290
Count R2:                      0.972     Adj Count R2:                  0.000
AIC:                           0.259     AIC*n:                       363.750
BIC:                       -9721.219     BIC':                         51.898

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