Wald chi2 vs. Likelihood ratio test of ln sigma2 using heteroskedastic probit model

[Phillip Ballhaus]

Hi there,

I am conducting a research on the effectiveness of economic sanctions based on a heteroskedastic probit model and I have some questions concerning the output STATA generates.
First, for one of my models the Wald chi2 (df=7) = 10.49 with Prob > chi2 = 0.1627. Can I still use this model even though the model as a whole is not significant (the main independent variables are highly significant at the 99 percent level).
Second, the model tells me that the likelihood ratio test of ln sigma2=0: chi2 (1) = 10.74 with Prob > chi2 = 0.0010. Does that mean that the test for heteroskedasticity is significant so that I can reject the null of homoskedasticity in my model (the variance coefficient in the variance equation is statistically significant at p < 0.01)? I read something about a critical value that chi2 has to reach in order to assume heteroskedasticity based on the likelihood ratio test of ln sigma2. Or can I generally argue that if Prob > chi2 = 0.0010, the model shows evidence of heteroskedasticity.

I really appreciate your help!

Cheers,
Phillip

[Richard Williams]

It would help if you posted the actual output using code tags. See pt. 12 of the Forum FAQ.

It is quite possible for a model chi-square to be insignificant even though individual coefficients are. If you add a bunch of junk variables to the model (variables which have no effect) it will drag the overall significance of the model down.

What variables are in the hetero model? Sometimes there is a lot of multicollinearity between the hetero model and the choice model, making it difficult to estimate effects.

Again, seeing the actual code and output may help.

[Phillip Ballhaus]

Hi Richard,

thanks for your answer. This is the code I used and the output stata produced:

. hetprob sanctions_outcome_new1 lagW costs i.multilateral i.institution i.alliance i.issuesalient tradedep_target, het(lagW)

Fitting probit model:

Iteration 0: log likelihood = -387.44049
Iteration 1: log likelihood = -366.37127
Iteration 2: log likelihood = -366.33995
Iteration 3: log likelihood = -366.33994

Fitting full model:

Iteration 0: log likelihood = -366.33994
Iteration 1: log likelihood = -364.7469
Iteration 2: log likelihood = -364.0957
Iteration 3: log likelihood = -362.83076 (not concave)
Iteration 4: log likelihood = -361.06361
Iteration 5: log likelihood = -360.98207
Iteration 6: log likelihood = -360.96978
Iteration 7: log likelihood = -360.96965
Iteration 8: log likelihood = -360.96965

Heteroskedastic probit model Number of obs = 628
Zero outcomes = 435
Nonzero outcomes = 193

Wald chi2(7) = 10.49
Log likelihood = -360.9696 Prob > chi2 = 0.1627

----------------------------------------------------------------------------------------
sanctions_outcome_new1 | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-----------------------+----------------------------------------------------------------
sanctions_outcome_new1 |
lagW | .324361 .1085472 2.99 0.003 .1116123 .5371097
costs | .1132939 .0637601 1.78 0.076 -.0116735 .2382613
1.multilateral | .0451624 .0398772 1.13 0.257 -.0329955 .1233202
1.institution | .0064796 .0406538 0.16 0.873 -.0732004 .0861596
1.alliance | -.0256962 .0252463 -1.02 0.309 -.075178 .0237856
1.issuesalient | .0020089 .0255201 0.08 0.937 -.0480097 .0520274
tradedep_target | -.1651134 .2048593 -0.81 0.420 -.5666302 .2364034
_cons | -.5309978 .2193369 -2.42 0.015 -.9608902 -.1011055
-----------------------+----------------------------------------------------------------
lnsigma2 |
lagW | -1.983325 .6416745 -3.09 0.002 -3.240984 -.7256657
----------------------------------------------------------------------------------------
Likelihood-ratio test of lnsigma2=0: chi2(1) = 10.74 Prob > chi2 = 0.0010

where sanctions_outcome_new1 is a binary variable coded 1 if sanctions resulted in a policy change in the target state, and 0 otherwise; lagW measures the size of the winning coalition (from 0 to .25 to .5 to .75 to 1) in the target state.

So again, if the Prob > chi2 = 0.0010 from the likelihood ratio test of lnsigma2, does this show 'evidence' of heteroskedasticity?

Thanks for your help!

[Richard Williams]

Thanks. But note my recommendation to use code tags, which is also in the FAQ. You output is very hard to read

[Phillip Ballhaus]

Oh, you're right, I'm sorry. Finally, this looks much nicer:

hetprob sanctions_outcome_new1 lagW costs i.multilateral i.institution i.alliance i.issuesalient tradedep_target, het(lagW)

Fitting probit model:

Iteration 0:   log likelihood = -387.44049  
Iteration 1:   log likelihood = -366.37127  
Iteration 2:   log likelihood = -366.33995  
Iteration 3:   log likelihood = -366.33994  

Fitting full model:

Iteration 0:   log likelihood = -366.33994  
Iteration 1:   log likelihood =  -364.7469  
Iteration 2:   log likelihood =  -364.0957  
Iteration 3:   log likelihood = -362.83076  (not concave)
Iteration 4:   log likelihood = -361.06361  
Iteration 5:   log likelihood = -360.98207  
Iteration 6:   log likelihood = -360.96978  
Iteration 7:   log likelihood = -360.96965  
Iteration 8:   log likelihood = -360.96965  

Heteroskedastic probit model                    Number of obs     =        628
                                                Zero outcomes     =        435
                                                Nonzero outcomes  =        193

                                                Wald chi2(7)      =      10.49
Log likelihood = -360.9696                      Prob > chi2       =     0.1627

----------------------------------------------------------------------------------------
sanctions_outcome_new1 |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-----------------------+----------------------------------------------------------------
sanctions_outcome_new1 |
                  lagW |    .324361   .1085472     2.99   0.003     .1116123    .5371097
                 costs |   .1132939   .0637601     1.78   0.076    -.0116735    .2382613
        1.multilateral |   .0451624   .0398772     1.13   0.257    -.0329955    .1233202
         1.institution |   .0064796   .0406538     0.16   0.873    -.0732004    .0861596
            1.alliance |  -.0256962   .0252463    -1.02   0.309     -.075178    .0237856
        1.issuesalient |   .0020089   .0255201     0.08   0.937    -.0480097    .0520274
       tradedep_target |  -.1651134   .2048593    -0.81   0.420    -.5666302    .2364034
                 _cons |  -.5309978   .2193369    -2.42   0.015    -.9608902   -.1011055
-----------------------+----------------------------------------------------------------
lnsigma2               |
                  lagW |  -1.983325   .6416745    -3.09   0.002    -3.240984   -.7256657
----------------------------------------------------------------------------------------
Likelihood-ratio test of lnsigma2=0: chi2(1) =    10.74   Prob > chi2 = 0.0010

I appreciate your help!

[Richard Williams]

It worries me that lagW is the only significant var in either equation. What happens if you run a regular probit with no het equation?

[Phillip Ballhaus]

prob sanctions_outcome_new1 lagW costs i.multilateral i.institution i.alliance i.issuesalient tradedep_target

Iteration 0:   log likelihood = -387.44049  
Iteration 1:   log likelihood = -366.37127  
Iteration 2:   log likelihood = -366.33995  
Iteration 3:   log likelihood = -366.33994  

Probit regression                               Number of obs     =        628
                                                LR chi2(7)        =      42.20
                                                Prob > chi2       =     0.0000
Log likelihood = -366.33994                     Pseudo R2         =     0.0545

----------------------------------------------------------------------------------------
sanctions_outcome_new1 |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-----------------------+----------------------------------------------------------------
                  lagW |   .2741529   .1890783     1.45   0.147    -.0964338    .6447395
                 costs |   .4401754   .0943568     4.67   0.000     .2552395    .6251113
        1.multilateral |   .2775133   .1257059     2.21   0.027     .0311343    .5238923
         1.institution |    .110759   .1968226     0.56   0.574    -.2750062    .4965243
            1.alliance |  -.0920984   .1127182    -0.82   0.414    -.3130221    .1288253
        1.issuesalient |   .0526722   .1241251     0.42   0.671    -.1906085    .2959529
       tradedep_target |  -.6594622   1.033271    -0.64   0.523    -2.684636    1.365712
                 _cons |   -1.39645   .2220078    -6.29   0.000    -1.831577   -.9613227
----------------------------------------------------------------------------------------