[Jeff Wooldridge]

Santosh: With cross sectional data or panel data? And by "snp" you mean semi-nonparametric, and "sml" means simulated maximum likelihood? You need to show or better describe the response probabilities in the two approaches. Simulated ML is an estimation method, not a model. Maybe you mean something else.

[Santosh Pathak]

Santosh: With cross sectional data or panel data? And by "snp" you mean semi-nonparametric, and "sml" means simulated maximum likelihood? You need to show or better describe the response probabilities in the two approaches. Simulated ML is an estimation method, not a model. Maybe you mean something else.

Thank you Dr. Woolridge for the reply. I am using cross sectional data. SNP and SML refer to semi-nonparametric method and semiparametric maximum likelihood, respectively.

[Jeff Wooldridge]

Are you sure these models are appropriately nonnested? This can be tricky in semiparametric contexts. Can you say more about what exactly you're doing? Vuong's test has been worked out for the parametric case. If, say, you were using two different distributions but allowing, say, the means to be nonparametric, I could see it working. But one has to be careful.

[Santosh Pathak]

Professor Jeff Wooldridge:

I am trying to find the determinants of household adaptation against floods with univariate binary choice model. Following SNP and SML framework given by De Luca (2008), I found that Gaussianity does not hold for my dataset. Now, I wish to find which among SNP and SML best works to find the adaptation determinants.

I am sure that parametric model is not nested within semiparametric model but not sure if the variants of semiparametrics (SNP and SML) are nonnested.

[Jeff Wooldridge]

It's odd to think a parametric model is not, at least asymptotically, nested in a semiparametric version. If so, one needs to be careful in using the Vuong test. But assuming they are not nested, here is a set of Stata code that will work for comparing logit and probit. (I should have done this some time ago, but left statalist for a period.) For your setup, you need to change calculation of the log likelihood functions. I'm assuming you're using pooled MLE in both cases.The test statistic, robust to any kind of dependence over time, is the t statistic on the constant in the last regression. The coefficient is the difference in the average log-likelihoods between the probit and logit models.

probit y x1 x2 ... xK i.year
predict phat_probit
gen llf_probit = (1 - y)*log(1 - phat_probit) + y*log(phat_probit)
logit y x1 x2 ... xK i.year
predict phat_logit
gen llf_logit = (1 - y)*log(1 - phat_logit) + y*log(phat_logit)
gen diff_llf = llf_probit - llf_logit
reg diff_llf, cluster(csid)

[Santosh Pathak]

It's odd to think a parametric model is not, at least asymptotically, nested in a semiparametric version. If so, one needs to be careful in using the Vuong test. But assuming they are not nested, here is a set of Stata code that will work for comparing logit and probit. (I should have done this some time ago, but left statalist for a period.) For your setup, you need to change calculation of the log likelihood functions. I'm assuming you're using pooled MLE in both cases.The test statistic, robust to any kind of dependence over time, is the t statistic on the constant in the last regression. The coefficient is the difference in the average log-likelihoods between the probit and logit models.

probit y x1 x2 ... xK i.year
predict phat_probit
gen llf_probit = (1 - y)*log(1 - phat_probit) + y*log(phat_probit)
logit y x1 x2 ... xK i.year
predict phat_logit
gen llf_logit = (1 - y)*log(1 - phat_logit) + y*log(phat_logit)
gen diff_llf = llf_probit - llf_logit
reg diff_llf, cluster(csid)

Thank you Prof. Woolridge for these codes. I really appreciate your response along with the codes. It helped me a lot.

-Regards,
Santosh Pathak

[Steffen Guder]

Here is the Stata code. The following Vuong test for panel data can be reasoned from Section 13.11.2 in my 2010 MIT Press book, Econometric Analysis of Cross Section and Panel Data. In effect, you are comparing the sums of squared residuals from the two FE estimations. It is important that the dependent variable and the two samples of data used are the same.

The first model contains x1 ... xK and the second z1 ... zK. The cross sectional identifier is csid. The intercept in the final regression -- no other explanatory variables -- is the estimate of SSR(1)/NT - SSR(2)/NT. The clustering gives the proper standard error, and so the t statistics is the cluster-robust Vuong test.

xtreg y x1 x2 ... xK, fe
predict u1h, e
gen uh1sq = uh1^2
xtreg y z1 ... zM, fe
predict uh2, e
gen uh2sq = uh2^2
gen diff = uh1sq - uh2sq
reg diff, cluster(csid)

JW

Dear Professor Wooldridge,

what is the exact code for conducting the Vuong Test for two nonnested OLS regressions? Moreover, how do I interpret the results? If the t-statistics is positive and significant is the first model or the second model the better choice?

Thanks in advance and kind regards,
Steffen