Bug in margins with factor variable notation for quadratic term

[Ariel Karlinsky]

Description:

I think I found a bug with margins. specifically with the atmeans option. If the model is estimated with factor variable notation for a squared term, atmeans uses the square of the mean of the independent variable instead of the mean of the squared variable.

Simple code to replicate issue:

clear all
sysuse auto
gen weight2 = c.weight#c.weight
summ weight c.weight#c.weight weight2
reg price c.weight##c.weight
margins, atmeans
reg price weight weight2
margins, atmeans

The output, where the first "margins" output is incorrect (it uses the square of the mean of weight) and the second one is correct (it uses the mean of weight²):

Adjusted predictions                            Number of obs     =         74
Model VCE    : OLS

Expression   : Linear prediction, predict()
at           : weight          =    3019.459 (mean)

------------------------------------------------------------------------------
             |            Delta-method
             |     Margin   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       _cons |   5263.004   374.2033    14.06   0.000     4516.864    6009.144
------------------------------------------------------------------------------

Adjusted predictions                            Number of obs     =         74
Model VCE    : OLS

Expression   : Linear prediction, predict()
at           : weight          =    3019.459 (mean)
               weight2         =     9713003 (mean)

------------------------------------------------------------------------------
             |            Delta-method
             |     Margin   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       _cons |   6165.257   270.6208    22.78   0.000     5625.655     6704.86
------------------------------------------------------------------------------

Technical details:

Stata/SE 14.2 for Windows (64-bit x86-64)
Revision 13 Jul 2017

[daniel klein]

Description:
If the model is estimated with factor variable notation for a squared term, atmeans uses the square of the mean of the independent variable instead of the mean of the squared variable.

I would argue that what margins does is correct. Because there is only one variable, weight, the predicted value when that variable is set to its mean should indeed be based on the square of the mean, not the mean of the square. Using the mean of the square implies that there are two separate variables that can change values independently from each other, which clearly is not the case.

Best
Daniel

[Richard Williams]

I agree with Daniel. For more, see

https://www3.nd.edu/~rwilliam/xsoc73994/Margins01.pdf

See especially slides 11-14.

Incidentally, as the handout also explains, I personally prefer the default asobserved behavior over atmeans.