Wald Test

[Luke Brown]

Good morning users,
I am using the following logistic regression and i want to see if adding the variable "crisis" I have significant improvement to my model. To do so, I used the Wald test for only that variable.

logit hequity hhsex i.Age i.Educ i.Race logincome logwealth crisis

Iteration 0:   log likelihood = -18808.808  
Iteration 1:   log likelihood = -12504.414  
Iteration 2:   log likelihood = -11899.219  
Iteration 3:   log likelihood = -11874.807  
Iteration 4:   log likelihood = -11874.744  
Iteration 5:   log likelihood = -11874.744  

Logistic regression                               Number of obs   =      28816
                                                  LR chi2(15)     =   13868.13
                                                  Prob > chi2     =     0.0000
Log likelihood = -11874.744                       Pseudo R2       =     0.3687

-----------------------------------------------------------------------------------------
                hequity |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
------------------------+----------------------------------------------------------------
                  hhsex |   .1263082   .0404188     3.12   0.002     .0470887    .2055277
                        |
                    Age |
                 31-40  |  -.0635375   .0615691    -1.03   0.302    -.1842107    .0571357
                 41-50  |  -.2001831   .0610567    -3.28   0.001    -.3198521   -.0805142
                 51-60  |  -.3630659   .0630575    -5.76   0.000    -.4866562   -.2394755
                 61-70  |  -.7231996    .068211   -10.60   0.000    -.8568906   -.5895086
                   >70  |  -1.078588   .0719979   -14.98   0.000    -1.219702   -.9374752
                        |
                   Educ |
           High school  |   1.049553   .1544172     6.80   0.000     .7469009    1.352205
       College diploma  |   1.450958   .1560823     9.30   0.000     1.145043    1.756874
    Bachelor or higher  |   1.883296   .1567473    12.01   0.000     1.576077    2.190515
                        |
                   Race |
Black/African American  |  -.3783898   .0512918    -7.38   0.000    -.4789198   -.2778599
              Hispanic  |  -.8111242   .0597963   -13.56   0.000    -.9283227   -.6939256
       Asian and other  |  -.5625384    .078592    -7.16   0.000    -.7165759   -.4085008
                        |
              logincome |   .6113415   .0245721    24.88   0.000     .5631811    .6595019
              logwealth |   .4307844     .01204    35.78   0.000     .4071863    .4543824
                 crisis |  -.0855568   .0322764    -2.65   0.008    -.1488175   -.0222962
                  _cons |  -12.38672   .2929917   -42.28   0.000    -12.96098   -11.81247
-----------------------------------------------------------------------------------------

Wald test:

test crisis

 ( 1)  [hequity]crisis = 0

           chi2(  1) =    7.03
         Prob > chi2 =    0.0080

I was also wondering if the fact that my variable is significant should lead to the same result and so that it provides a statistically significant improvement in the fit of the model.

Thank you in advanced
Luke Brown

[Rich Goldstein]

the post-hoc test you did is exactly the same as the test that is part of the logit output (and the chi-squared value is the square of the z statistic)

fit can be defined in more than one way so I can't answer your second question meaningfully

[William Lisowski]

Can you tell us what the variables "hhsex" and "crisis" are? I have the feeling that they might be 0/1 categorical variables, in which case using the i. prefix on them as well would have been appropriate, especially if you are going to use the margins command - highly recommended - to help understand your results.

You may find much of use regarding analysis of categorical data and interpretation of the results - including use of the margins command - in the course notes prepared by Richard Williams, a frequent contributor here, at https://www3.nd.edu/~rwilliam/xsoc73994/ .

You could consider reporting odds ratios rather than coefficients - see help logistic for a good explanation of the difference.

[Luke Brown]

logistic hequity i.hhsex i.Age i.Educ i.Race logincome logwealth i.crisis

Logistic regression                               Number of obs   =      28816
                                                  LR chi2(15)     =   13868.13
                                                  Prob > chi2     =     0.0000
Log likelihood = -11874.744                       Pseudo R2       =     0.3687

-----------------------------------------------------------------------------------------
                hequity | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
------------------------+----------------------------------------------------------------
                2.hhsex |   1.134632   .0458605     3.12   0.002     1.048215    1.228173
                        |
                    Age |
                 31-40  |   .9384389   .0577788    -1.03   0.302     .8317605      1.0588
                 41-50  |   .8185808   .0499799    -3.28   0.001     .7262564    .9226418
                 51-60  |   .6955406    .043859    -5.76   0.000     .6146783    .7870405
                 61-70  |   .4851973   .0330958   -10.60   0.000     .4244799    .5545998
                   >70  |   .3400752   .0244847   -14.98   0.000     .2953183    .3916153
                        |
                   Educ |
           High school  |   2.856374   .4410732     6.80   0.000     2.110449    3.865941
       College diploma  |   4.267202   .6660347     9.30   0.000     3.142576    5.794296
    Bachelor or higher  |   6.575141   1.030636    12.01   0.000     4.835947    8.939816
                        |
                   Race |
Black/African American  |   .6849634    .035133    -7.38   0.000     .6194521     .757403
              Hispanic  |   .4443583    .026571   -13.56   0.000      .395216     .499611
       Asian and other  |    .569761   .0447787    -7.16   0.000     .4884218    .6646459
                        |
              logincome |   1.842902    .045284    24.88   0.000      1.75625    1.933829
              logwealth |   1.538464   .0185232    35.78   0.000     1.502584      1.5752
               1.crisis |    .918001   .0296298    -2.65   0.008     .8617264    .9779505
                  _cons |   4.74e-06   1.32e-06   -43.94   0.000     2.74e-06    8.18e-06

These are my results for my logistic regression with the "i" command, however, I am still wondering about the meaning of my Wald test

[Luke Brown]

Or in other words, which is the best post estimation command to use if i want gain more information about the effect of my variable "crisis" on my dependent variable?
Thank you for you time

[Maarten Buis]

A test tests a null hypothesis. test reported the null hypothesis in the output, that is the line ( 1) [hequity]crisis = 0, which means that the coefficient of crisis equals 0, or equivalently, that the odds ratio equals 1. In words that means that the variable crisis has no effect on hequity. Relying on the output of a program to determine your null-hypothesis is obviously the wrong way around: You should determine the hypothesis you want to test, turn that into a null-hypothesis suitable for statistical testing, and find a way to make your software test that hypothesis.

If you chose a significance level of 5%, then the result of your test is that you can reject that hypothesis at that chosen significance level (the p-value 0.008 is less than our significance level 0.05).

[Maarten Buis]

The effect of crisis can be seen by looking at your odds ratios: the odds of being hequity (whatever that may mean, that is up to you) decreases by a factor 0.92 when a crisis occurs, i.e. the odds decreases by (0.92-1)*100%=-8%