Problem with accuracy of interaction term in the probit regression

[Hoa Ngo]

Hi, everyone,

I am new to this forum so I am sorry if I post in the wrong topic but as I read guidelines in FAQ, I should post in threads with the same issues? So, I decided to post here, if not, I could post in a new topic. My question is also regarding to my thesis. I am doing my master thesis, too. But I do not know whether my understanding is correct or not because I am wondering about the correlation. For my topic, I am examining the impacts of internationally recognized quality certificates on exporting firms towards energy management measures adoption. and I use probit model ). To choose exporting firms, I use binary numbers (1 = firm has export activities, 0 = otherwise), for owning international recognized quality certificates ( 1 = firm has this certificate, 0 = otherwise), and for energy management measure adoption ( 1 = firm adopts, 0 = otherwise). the description is as below:

summarize energymanagement employees EX interantionalcertificates

Variable | Obs Mean Std. dev. Min Max
-------------+---------------------------------------------------------
energymana~t | 997 .2577733 .4376281 0 1
employees | 1,028 164.8959 647.6998 3 11742
EX | 1,028 .2412451 .4280469 0 1
interantio~s | 999 .1861862 .3894518 0 1



This is correlation:

corr employees EX interantionalcertificates

I assume that there is difference in impact on energy management measures adoption between exporting firms and non exporting firms when they own international recognized quality certificates, So I create interaction terms between international recognized quality certificate variable and export variable as: international quality certificate variable * export variable -> (excertificates _ interaction term) and then I run probit model as below:

 probit energymanagement employees othermanufacturing garments otherservices metalproducts construction EX interantionalcertificate> s excertificates

As you can see, "export", "owning international recognized certificate" and their interaction term has meaning. But what I wonder is that "owning international certificates" also could promote enterprises to export ( the image is as below) but the correlation is weak as I think, so I can ignore its relationship among these independent variables ( I am so sorry, I am new with probit and read many different resources from not only this forum but also other academic papers so I am not sure I am correct).

probit EX interantionalcertificates

and the correlation between dependent variable and independent variables are weak also, as below:

corr energymanagement employees EX interantionalcertificates

Normally, as I understand, I just need to check relationship between independent variables to avoid the multicollinearity, but in this case, I do not know whether my idea that creating interaction terms is bad or not because "owning international certificates" variable has positively impacts to export as well. In addition to this, I read research papers, but they said that Export and energy management has muatual relationship in every case, it means that in some research papers, they said that Export promotes environment performance of firms, in other research papers, they said that environment performance could promotes firms to export. I wondering my orientation for this topic is ok or not, too?

This forum is so useful for me and I learned a lot from this forum,

Thank you

[Carlo Lazzaro]

Hoa:
what does -estat vce,corr- give you back after -probit-?

[Hoa Ngo]

Hoa:
what does -estat vce,corr- give you back after -probit-?

Thank you for your feedback, Professor. Normally, I just check corr- between independent variables before running probit-, but in this case, I doubt that" owning internationally recognized certificates" variable impacts positively to "export" variable as well. It means that if I add these 2 variables in the model to measure their impacts in the separated way to " adopting energy management measures " variable _independent variable, the result is not correct because these independent variables are correlated? So, that is why I showed corr- as well after running the probit for your clear understanding my case.

[Carlo Lazzaro]

Hoa:
I would say that when adjusted for the other predictors, the predictor -owning internationally recognized certificates- contribute to explain variations in the dependent variable.

[Hoa Ngo]

Hoa:
I would say that when adjusted for the other predictors, the predictor -owning internationally recognized certificates- contribute to explain variations in the dependent variable.

Thank you for your quick feedback, Professor. I know that when adjusting for other predictors, the predictor -owning internationally recognized certificates- contribute to explain variations in the dependent variable. It means that I have to check correlation of predictors and control variables together before I run probit model. and as you can see, the value of correlation matrix is weak among predictors and control variables as well, it means that I could create interaction terms between "owning internationally recognized certificates" and "export". But, under other perspective, "owning internationally recognized certificates" also could promote "export" although its correlation value is weak (p_value <0.05). So, it is not correct if I create interaction term between these predictors? because they are correlated together. in the normal way, they should be not corelated and impact to the dependent variable separately to create reasonable interaction term to add in the model? Thank you

[Carlo Lazzaro]

Hoa:
you can create an interaction and see what Stata gives you back.
More substantively, please call me Carlo, lke all on (and many more off) this list do. Thanks.

[Hoa Ngo]

Hoa:
you can create an interaction and see what Stata gives you back.
More substantively, please call me Carlo, lke all on (and many more off) this list do. Thanks.

This is the result, Carlo

probit energymanagement employees othermanufacturing garments otherservices metalproducts construction EX interantionalcertificates excertificates

as you can see, the interaction term "export" * "owning internationally recognized quality certificates" has statistically significance ( the magnitude is -0.6185) that p_value <0.05? the interaction term is excertificates. and according to some research papers that I read, owning internationally recognized quality certificates could promote export performance, and in this my case, the value of their correlation is so weak, so is it reasonable if I could say that although owning internationally recognized quality certificates could promote export performance according to some results showed in research papers, their correlation is so weak that they were independent in this research and impact separately to the dependent variable?

[Carlo Lazzaro]

Hoa:
when adjusted for the remaining predictors, the coefficients you mention contribute to explain variations in the regressand.
Their contributions can be teased out via their highly statistically significant p-values.

[Hoa Ngo]

Hoa:
when adjusted for the remaining predictors, the coefficients you mention contribute to explain variations in the regressand.
Their contributions can be teased out via their highly statistically significant p-values.

thank you for your support. It means that I could assume that "firms having export activities" is the fixed variable in the model ( for firms having export activities during the surveyed year). So I do not need to care about the relationship between owning internationally recognized quality certificates and export activities and the correlation between these 2 variables is so weak. So I could say that for this purpose of this research which is examining whether there is difference between "owning the internationally recognized quality certificates" in firms having export activities and "firms having export activities with no internationally recognized quality certificates" and the value of their correlation is so weak, hence, the correlation between 2 these predictors is not mentioned in this research?

[Carlo Lazzaro]

Hoa:
to get a more informative insight about the meaning of your coefficients, you should -test- them (or use -margins-).

[Hoa Ngo]

Hoa:
to get a more informative insight about the meaning of your coefficients, you should -test- them (or use -margins-).

Thank you so much for your strong support.