I am trying to analyze the determinants of the intention to grow an a certain variety of maize in Zambia. The data has decision variable, whether to choose to grow the variety in the coming season (1 if they grow, 0 otherwise), and if they decide the area of land they would dedicate to that specific variety. Ideally, my understanding is to use double hurdle model to investigate this. However, I believe I need to justify why I chose this model over Tobit model. While I read articles, they mention that they used Likelihood Ratio Test to see which model is appropriate.

My understanding was that we use Likelihood Ratio Test to compare nested models. In this case, the models are not nested. Rather the estimators are different with the same number of variables. And that is what STATA has been confirming to me. Therefore, I was wondering how they did it. I tried to email some of the authors, but could not get responses so far.

Using STATA 16, I tried to run the following commands to do the LR Test to see if it works. I used "churdle" model to estimate the double hurdle model.

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tobit depvar var1 var2 var 3, ll(0)
est store tobit1

churdle linear depvar var1 var2 var 3, select (var1 var2 var 3) ll(0)
est store churdle1

lrtest tobit1 craggit1

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*Result*

. lrtest tobit1 craggit1
test involves different estimators: craggit vs. tobit

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I even tried to calculate the LR manually, but it cannot do the significance test as there is no difference in degrees of freedom because the two models have the same number of variables unlike nested modes.

My question is, is LR Test the right method to compare the two models? If so, what is the command that would get me results. If not, what is the appropriate test?

Thank you.