Regression for a parabolic continuous outcome

[Thuva]

Hello,

I am looking for suggestions on how to model a dichotomous independent variable 'treatment' (intervention vs. control) with the following outcome that takes the shape of a parabola. Ln and different 'root (e.g. square root, cube root, etc) transformations don't allow for linear regression.  Any recommendations? I am using SAS 9.4.

[Reeza]

It looks like you have a categorical variable and a dichotomous outcome? What does a chisquare with the treatment look like. You wouldn't be running a linear regression you would be running either PROC FREQ or possible LOGISTIC or CATMOD with this type of data IMO.

[Thuva]

Thanks Reeza. There are seven levels to the outcome/dependent variable, so I am treating it as a continuous outcome. The independent variable is binary: treatment group. I need to also adjust for another categorical variable so I won't be able to run PROC FREQ. 

Thuva 

[Reeza · Accepted solution]

Then that's looking a lot like a logistic regression model or CATMOD type analysis.

[Thuva]

Thanks Reeza and everyone else for your help! I decided to use an ordinal logistic regression model for this outcome with PROC LOGISTIC. 

[PaigeMiller]

I like the CATMOD idea.

Binary X, 7 levels ordinal Y, you could fit some sort of polynomial or other curve to the 7 levels of Y, and then do ANOVA.

Another alternative, you have 7 levels of Y, create 7 dummy variables for each, then MANOVA.

But there's no way I would call this a regression.