Interaction effects indicate that a third variable influences the relationship between an independent and dependent variable. In this situation, statisticians say that these variables interact because the relationship between an independent and dependent variable changes depending on the value of a third variable.

Thank you for your answer Abdullah. However, I still am not sure if the direction and significance of the interaction term of 3 categorical variables can be determined in the same way as normally. I have not found any research that does the same. Do you by any chance know?

Two questions. Have you done an interaction plot? the second one is are you using logistic regression? Best wishes David Booth

Yes, I did both.

This does not answer your question directly but should give you some ideas - this is for the situation when there are many categorical variables involved and they have several categories:

Article Uncovering interactions in multivariate contingency tables: ...

Article Age, sex, qualifications and voting at recent English genera...

In general I find the easiest way to understand the results is to do some marginal predictions and plot the results - in our software MLwiN we have built tools to do this easily see bespoke prediction in; you can do this on the logit, odd or probability scale: Article Manual supplement for MLwiN Version 2.14

i am not interested in such stupid stuff. To the hell!

"I haven't found any literature on the interaction effect between 3 categorical variables." Your interaction effect appears to be between two (independent) variables, Family Ownership x Host-Country Network, not three.

Martin Willis correct, but the dependent variable is also categorical (entry mode). This case, I haven't found in any literature

You might find this helpful: https://stats.oarc.ucla.edu/stata/seminars/deciphering-interactions-in-logistic-regression/

If you are using a logit model, the underlying response is the log -odds of the outcome. Consequently the modelled latent variable is not categorical but continuous even if the observed variable is.

Rafael Roders Almeida I would never use a variable with three categories as a dependent variable. That is just me. Are you using logistic regression or what? I would recommend you pick ONE outcome that you want to look at the data with. Whatever you mean as far as entry mode, pick one-- You say equity vs nonequity but what does that mean or what indicators are you using?

For me, I am looking at the odds a student is successful. It is 1 for successful and 0 for failure. Then I have my variables including interaction of interventionXrace. In my case I modeled race by multiple dummy variables to see each differently. Still trying to sort out my analysis.

Martin Willis can appreciate the link but the article is horrible. Not helpful in understanding.