How to equality test for multnomial logit model with two differen groups?

[Daffa Harafandi]

Hello everyone, I would like to ask related with equality test in multinomial logit. Here is my two model of mlogit:

mlogit formal_trans i.training1 age sq_age i.educ i.marstat child i.cities i.pulau if gender==0, base (0) robust

mlogit formal_trans i.training1 age sq_age i.educ i.marstat child i.cities i.pulau if gender==1, base (0) robust

I separate the model by gender, where gender==0 is for male and gender==1 is for female. So I would like to do equality test to make sure that I can disaggregation my sample based on gender. Is there any equality test that I can perform for my mlogit models? Thank you.

[Carlo Lazzaro]

Daffa:
welcome to this forum.
As far as your query is concerned:
1) see -help suest-;
2) why not creating interactions via -fvvarlist- notation?

c.age##c.age

[Daffa Harafandi]

Thanks Carlo for your suggestion. However, I would like to have two types of mlogit model in my research. The first one is the regression of whole sample and second one is the regression that separated by gender. Also, I do not considering to using interaction terms between variables. Actually I decided to run the first model such as:

mlogit formal_trans i.training1 gender age sq_age i.educ i.marstat child i.cities i.pulau, base (0) robust

After that, I perform postestimation to know whether there is significance difference between gender on working transition. Here is the syntax and results:

test ([Formal_Formal = Formal_TB = Formal_Informal]: gender)

 ( 1)  [Formal_Formal]o.gender - [Formal_TB]gender = 0
 ( 2)  [Formal_Formal]o.gender - [Formal_Informal]gender = 0

           chi2(  2) = 1273.88
         Prob > chi2 =    0.0000

The results explain that we reject the null hypothesis, therefore there are differences in coefficient of gender for outcome variables. Because of that, I could perform the next model of mlogit where I could run the model separately for male and female. What I would like to ask, is my postestimation correct? Thanks.

[Carlo Lazzaro]

Daffa:
1) when referring to interactions, I meant that linear and squared terms (an interaction of -age- with itself) can be written more efficiently;
2) while your -test- procedure seems correcti, I'd probably interact -gender- with working transition in a single -mlogit-.

[Daffa Harafandi]

Carlo:
1) So, would it be better for me to do single mlogit with interaction terms between training and gender?
2) If I also want to run the model separately by gender, is that appropriate?

Thank you.

[Richard Williams]

I suggest you look at this article by Mize, Doan, & Long, "A General Framework for Comparing Predictions and Marginal Effects across Models". Even if it isn't exactly what you want is very useful to know about it.

https://journals.sagepub.com/doi/10....81175019852763


Abstract
Many research questions involve comparing predictions or effects across multiple models. For example, it may be of interest whether an independent variable’s effect changes after adding variables to a model. Or, it could be important to compare a variable’s effect on different outcomes or across different types of models. When doing this, marginal effects are a useful method for quantifying effects because they are in the natural metric of the dependent variable and they avoid identification problems when comparing regression coefficients across logit and probit models. Despite advances that make it possible to compute marginal effects for almost any model, there is no general method for comparing these effects across models. In this article, the authors provide a general framework for comparing predictions and marginal effects across models using seemingly unrelated estimation to combine estimates from multiple models, which allows tests of the equality of predictions and effects across models. The authors illustrate their method to compare nested models, to compare effects on different dependent or independent variables, to compare results from different samples or groups within one sample, and to assess results from different types of models.

[Daffa Harafandi]

Dear Richard,

Thanks for your information. Perhaps I would like to read the references first.

Best regards,
Daffa