Dear Statlist community,

I have a question regarding the complete precedere of a probit analysis.
I conducted a probit regression analysis if a HH sends a migrant based on HH characteristics such as HH_Size, Agricultural Income, Education and so on. I cleaned my data, run the probit regression and have my outputs.

I am wondering if (or which) tests or check ups I need to conduct to achieve a robust output. I read through some post online and I found some options I can do but they dont seem compulsory to me.

What i found is:

Interaction effects: check for interaction effects between the variables. If the interaction effect is significant I should incorporate it in my model. But this results just in a another model spezification I guess.

Linktest: Checks if model is correctly spezified. If i run the linktest and the result shows its not correct specified, I should use these model outputs?

Distribution: my metric variables are not normaly but chi2 distributed. Is this a problem?

Edogeneity: I would guess Agr_Income is influenced by HH_Size. Do i control for this by the interaction effect? Or how can i check for this relation?

Homoscedasticity: Do i need to check for this?

Are there other tests, characteristics I need to check?

Thank you in advance!