Problem with linearity and transformation in xtreg

[Mike Rouven]

Dear all,

I am using STATA 14.2 and would like to use xtreg,fe since the Hausman test recommended me to use fixed effects.

First I tested my variables for linearity with -nlcheck-. Here, one moderator (VOR) and two of my control variables (HGS and BFFA) were significant, indicating a violation of the linearity assumption.

quietly xtreg c.TER c.ARMQ c.VOR c.REVEN SUER c.HGS c.AVGG c.BFFA c.RIST,fe


nlcheck VOR

Nonlinearity test:

       F(  9,   818) =    3.59
            Prob > F =    0.0002



nlcheck HGS

Nonlinearity test:

       F(  9,   818) =    5.86
            Prob > F =    0.0000



nlcheck BFFA

Nonlinearity test:

       F(  9,   818) =    1.96
            Prob > F =    0.0406

Additionally, I plotted the linearity assumption to check the p-values of the previous test.

acprplot VOR, lowess

acprplot HGS, lowess

acprplot BFFA , lowess

The control variable BFFA is already log-transformed.


From my point of view, there is definitely a violation of the linearity assumption for these three variables. Now to my questions:

1) I have read here in the forum that one can get around the violation of the linearity assumption by integrating an additional squared term of the corresponding variable. Is this possible even though this is a moderator? Would the following regressions be properly formulated in that case?

quietly xtreg c.TER c.ARMQ c.VOR c.VOR^2 c.REVEN SUER c.HGS c.AVGG c.BFFA c.RIST,fe

quietly xtreg c.TER c.ARMQ##c.VOR c.ARMQ##c.VOR^2 c.REVEN SUER c.HGS c.AVGG c.BFFA c.RIST,fe

2) Does the violation of the linearity assumption by control variables matter at all or does the linearity assumption only matter for predictor variables.


Thanks a lot for your help!