What would be the justification for not including higher order interaction terms in the model ? Is it just the interpretation of the model becomes complicated with higher order interaction ?

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    $\begingroup$ This question has been asked many times before on this site. Perform a simple search for the word "interaction" and you'll find many explanations why it can be important to include interactions. See for example, stats.stackexchange.com/questions/143798/… stats.stackexchange.com/questions/178592/… stats.stackexchange.com/questions/19903/… $\endgroup$ Mar 29 '16 at 0:55
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    $\begingroup$ My question is why do not we add 5th or 90th order interaction in the model ? Every body stops at 3 or 4th order interaction in the analysis. $\endgroup$
    – user35571
    Mar 29 '16 at 1:02
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    $\begingroup$ Well, not everyone stops at the 3rd or 4th interaction. Where you stops depends on your needs. Most models are simplifications of a real world phenomena. In general, no more than 3rd or 4th order interactions are needed to approximate most phenomena. Plus as you use terms, you consume degrees of freedom. At some point you'd have more terms than observations and would you wouldn't be able to estimate from the data. Also, not all models could get as large as 90 interactions. If you had a model with only 3 variables, you could only get each of 3 variables, plus the 3 second order (con't) $\endgroup$ Mar 29 '16 at 3:44
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    $\begingroup$ interactions and the 1 3 order interactions. You could only form 3+3+1=7 terms in your model. $\endgroup$ Mar 29 '16 at 3:44

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