Solved – Quadratic terms in regression with categorical variables

categorical datamultiple regressionregression

I am working my way for the first time through predicting a continuous dependent variable in a problem where all independent variables are categorical using python statsmodels. I would like to add to this model 'y ~ + C(x1) + C(x2) + C(x3)' all possible quadratic terms. What is the right notation for that?

EDIT: one of my categorical variables is age, which I binned in four different bins. All other are transformed into dummy. So the idea was to square age.

Best Answer

Quadratic terms for categorical variables are undefined because you cannot square a categorical variable. On the other hand, given that you have a continuous variable with nonlinear relationship to your outcome/dependent variable, categorization may help and be such that it is synonymous to introducing quadratic terms but with the added benefit of simpler model to build and explain.

Related Solutions

Solved – Multiple regression interaction with categorical IV with 3 levels

You can definitely do that. you can introduce your categorical variable as a factorial one. If you have decided to use R programming this following code would be fine:

new_categ<-factor(categ,labels=c(0:2))

Then, you can interact the new categorical variable with other independent ones. You also could find examples centered around your problem in Modern Applied Statistics with S-PLUS by Venables and Ripley. However, if you are not willing to use R, you can still read its examples about regression which are beneficial for figuring out how to solve your problem.

Model Selection – R: Using Leaps and Glmnet with Categorical Variables

regsubsets (a function in the leaps package that also performs exhaustive model searches) can accept categorical variables that are not split out into dummy variables and, thus, treats them as groups of variables that are either all part of a model or not.

For example, if Year has levels 2013, 2014 and Treatment has levels C,N,O I can run the following statement:

> search_output<-regsubsets(y~Year+Treatment,data=stats_df, method="exhaustive")

Output:

Subset selection object
Call: regsubsets.formula(mu_ln ~ Year + Treatment, data = SS_stats_df, 
    nbest = 1, method = "exhaustive")
3 Variables  (and intercept)
           Forced in Forced out
Year2014       FALSE      FALSE
TreatmentN     FALSE      FALSE
TreatmentO     FALSE      FALSE
1 subsets of each size up to 3
Selection Algorithm: exhaustive

> summary(search_output)$which
  (Intercept) Year2014 TreatmentN TreatmentO
1        TRUE    FALSE       TRUE      FALSE
2        TRUE    FALSE       TRUE       TRUE
3        TRUE     TRUE       TRUE       TRUE

When faced with this same problem I found this post very helpful (my answer here is essentially an abbreviated version of the pertinent portion): http://rstudio-pubs-static.s3.amazonaws.com/2897_9220b21cfc0c43a396ff9abf122bb351.html

And for recoding or converting to factors or renaming factors these posts are helpful: https://stackoverflow.com/questions/5372896/recoding-variables-with-r http://www.cookbook-r.com/Manipulating_data/Recoding_data/

Best Answer

Related Solutions

Solved – Multiple regression interaction with categorical IV with 3 levels

Model Selection – R: Using Leaps and Glmnet with Categorical Variables

Related Question