Testing for Non-linearity in Fixed Effects

[Mol Nic]

Hello,

I am running individual FE models where my dep variable (DV) is treated as continuous but it ranges from 0 to 4. The main models have an interaction of a continuous and categorical variable. But before including interactions, I need to test whether there is a linear or nonlinear effect of IV on DV. My IV ranges from 0 to 40. Specifically, I need to test whether there is the same effect when moving in IV from 0 to 5 and moving from 30 to 35. I would appreciate any suggestions on how to do this in fixed effects models and how to make graphs to indicate these relationships! I know that it is problematic that my DV is actually ordinal but in my field most people run linear FE models with such variables. Thanks!!

[Phil Bromiley]

There are many ways to handle this - let me give you two. First, if you really only want to know the difference in effect for 0 to 5 and 30 to 35, you could make up a dummy variable that has values of one if the IV is between zero and five, two between five and 30, three greater than 30 and less than 36, and for greater than 35. Use factor variable notation to interact this with your original IV and you will have separate parameters available for those three ranges. While you can easily calculate the total effects (the parameter on the make variable without any interactions will be the value for 0 to 5 and you simply add the others to that to get the value for a given range), you can also let margins to the work for you.

Another way to do this would be to include the IV and the IV squared (again using factor variable notation), and then look at dydx and differences in predicted values for values like one and five versus 30 and 35. This imposes a particular functional form so it is not quite as general as the other one.

[Joro Kolev]

Apart from what Phil proposes, you can also partial out the fixed effects from both the dependent and independent variable, and plot one against the other.

If I remember right this plot in Stata is called added variable plot. Or maybe not. You can do it manually as in the previous paragraph.

[Joro Kolev]

For example like this:

. clear

.  webuse nlswork
(National Longitudinal Survey.  Young Women 14-26 years of age in 1968)

.         . xtset idcode
       panel variable:  idcode (unbalanced)

. qui regress ln_w tenure grade age c.age#c.age ttl_exp c.ttl_exp#c.ttl_exp tenure 2.race not_smsa south, absorb(idcode)

. avplot tenure