Hello Marian. I think you mean that the model would have 3-4 explanatory variables and all two-way interactions. Is that right? If all explanatory variables are quantitative, a model with 4 variables and all two-way interactions (linear components only) would have 10 terms:

x1 x2 x3 x4

x1*x2 x1*x3 x1*x4

x2*x3 x2*x4

x3*x4

If you are asking whether n=220 is large enough to avoid over-fitting, most rules of thumb would suggest that yes, it is. See Mike Babyak's nice article for more info.

• https://people.duke.edu/~mababyak/papers/babyakregression.pdf

HTH.

Hello Marian. I think you mean that the model would have 3-4 explanatory variables and all two-way interactions. Is that right? If all explanatory variables are quantitative, a model with 4 variables and all two-way interactions (linear components only) would have 10 terms:

x1 x2 x3 x4

x1*x2 x1*x3 x1*x4

x2*x3 x2*x4

x3*x4

If you are asking whether n=220 is large enough to avoid over-fitting, most rules of thumb would suggest that yes, it is. See Mike Babyak's nice article for more info.

• https://people.duke.edu/~mababyak/papers/babyakregression.pdf

HTH.

Thank you Bruce

If you are asking if some of the interaction terms modify other interaction terms then things are a bit more complicated but all of Bruce's suggestion are still quite correct. You If you just build terms like: let I1=x1* X2, I2 =X3*X4 then look at things like I1*I2. You need to worry about model assumptions here esp colinearity and the number of observations in your data set. Lasso regression might be helpful to you if this is a predictive model. In that case, see the attached. You might find my comments here helpful:

https://www.researchgate.net/post/How_do_I_assess_moderation_among_a_mixed_between-group_and_repeated_measures_experimen. If you are interested in moderation and mediation together, see this link:

https://www.google.com/search?q=moderation+and+mediation+in+linear+regression+models&rlz=1C1CHBF_enUS847US847&oq=moderation+and+mediation+in+linear+regression+models&aqs=chrome..69i57.42133j1j8&sourceid=chrome&ie=UTF-8

Best, D. Booth

If the two factor interactions should not disturb the main effects, I suggest you to look into resolution IV experiments. The main effects are not aliased with two factor interactions. Initially, it is required to have basic background on DOE. Please study the DOE book by D C Montgomery and proceed

If you have continuous predictors then generally statistical power to detect interactions is very low so you'll struggle to detect interactions with 220 observations.

This is because statistical power for the interaction depends on the co-occurence of extreme values of both var 1 and var 2. If most observations are average - as say if data are approximately normal - on var 1 and var 2 these values (low-low, low-high, high-low and high-high) are are rare and statistical power is consequently poor.

Find a lengthy chapter on interaction effects in my online book (chapter 5.5):

https://www.researchgate.net/project/Book-New-statistics-for-the-design-researcher