How to define a constraint on all parameters of all levels of a factor variable in a restricted regression

[Jiahao Chen]

I want to run a constrained regression where there is factor variable (with a lot of levels). I want to add the constraint that the sum of the parameters of all levels of this factor variable is 1. How should I do this? Ideally, I want to do something like

constraint 1 sum(i.group)=1
cnsreg y x1 x2 x3 x4 i.group, constraints(1)

But this syntax obviously does not work. I searched for a while but did not find the right code to use. I am wondering if you are so kind to share with me some sample code that does this task. Thanks!

[Clyde Schechter]

So, if the variable group has, say, 5 levels, 1, 2, 3, 4, 5 you would write it as:

constraint def 1 1.group + 2.group + 3.group + 4.group + 5.group = 1
cnsreg y x1 x2 x3 x4 i.group, constraints(1)

Added: If group has too many levels for this to be practical:

levelsof group, local(c1)
local c1: subinstr local c1 " " ".group+", all
local c1 `c1'.group = 1
constraint def 1 `c1'
cnsreg y x1 x2 x3 x4 i.group, constraints(1)

[Jiahao Chen]

Thanks!

[Davide Pietrobon]

Thank you, Clyde Schechter.

I have a similar problem. I want to add the constraint that all the parameters of all levels of a factor variable are negative. Hence, something like:

constraint 1 i.group < 0
cnsreg y x1 x2 x3 x4 i.group, constraints(1)

I have many levels, so your first solution is, unfortunately, not practical. I have been trying to adapt your second solution to my problem without success. I would be very grateful if you could give me a hand.

[Clyde Schechter]

You cannot, in Stata, constrain the coefficient of a regression to be negative. The only constraints that are supported are constraints that can be written as linear equations; no inequalities are supported.

What you can do, though it will be very tedious to set up, is use the -nl- command for the regression, and designate the coefficients in that model to be the negative exponentials of parameters you estimate. That would guarantee that the coefficients themselves are always negative.

[Davide Pietrobon]

Thank you, Clyde Schechter.