Squared Terms

[Jake Naismith]

Dear Statalist members,

I have a panel dataset where my dependent variable is a dummy = 1 if the client switches to using self-directed investing, 0 otherwise. My independent variables are performance ratio and the cumulative percentage of using automation.

g PercentAutoBid_2= PercentAutoBid*PercentAutoBid

        eststo: reghdfe Auto2Man l.performance_ratio l.PercentAutoBid l.PercentAutoBid_2 ///
            ,a(`fe') cluster(interaction)

I want to check whether to include squared term in my regression so I run nlcom

        nlcom -_b[l.PercentAutoBid]/(2*_b[l.PercentAutoBid_2])

------------------------------------------------------------------------------
    Auto2Man | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
       _nl_1 |   .4370262   .0009158   477.22   0.000     .4352314    .4388211
------------------------------------------------------------------------------

The results show me that the coefficient (0.43) lies between the range of PercentAuto. Percent auto is from 0 to 1. which means that I have an inverted U shape right?

then I run the margins command

        margins, at(l.PercentAutoBid = (0(0.2)1))
        marginsplot

And I get this result



Can someone help me whether I should include a squared term or not?

Thanks

[Rich Goldstein]

1. the -nl- command you used tells you where the vertex (local min or max) is but does not tell you whether you should include a squared term

2. since you formed the squared term yourself, rather than using factor variable notation, margins will not help here; see

help fvvarlist
help margins

3. otherwise you have not given enough info (note that contextual knowledge here is very important - is there any reason to expect a non-linearity and, in particular, is there reason to expect a parabola?)

[Carlo Lazzaro]

Jake:
1) why not using -fvvarlist- notation (supported by the community-contributed module -reghdfe-) to create squared terms (assuming that a squared term makes sense given your predictors)?

reghdfe Auto2Man i.performance_ratio c.PercentAutoBid##c.PercentAutoBid_2  ,a(`fe') cluster(interaction)

2) in addition, if you create another variable with the squared term outside the -fvvarlist- notation framework, -margns- and -marginspot- cannot track down the link between linear and squared terms variables, that they consider as uncorrelated.