# st: mlogit constraints and dropped variables

 From Timothy Dang <[email protected]> To [email protected] Subject st: mlogit constraints and dropped variables Date Thu, 13 Jan 2005 12:38:37 -0700 (MST)

```Hello-

I'm just getting started with Stata and trying to do a multinomial logit
regression. It's a product choice regression over 3 products [indexed
as 0, 1, 2] (plus the possibility of choosing none which is indexed as
-1).

I only want to consider product characteristics, not individual
characteristics (it's data from a laboratory experiment). Also, I want the
structure of the "utility" for each of the three products to be the same.

So, I'm running mlogit with a lot of constraints, forcing some
coefficients to zero and others to be equal.

However, I'm getting some unexpectedly dropped variables. If I include the
constants in the regression and try to set them to be equal
(using constraint define 1 [0]_cons = [1]_cons
constraint define 2 [0]_cons = [2]_cons)
then one of the constants is estimated, but the other two are dropped.

If I leave the constant out of the regression with noconstant, then other
variables are dropped.

My data is highly colinear, but not perfectly so. Most particularly, I
have three variables (minprice0, minprice1, minprice2) where minpriceX is
a flag which is 1 if productX has strictlty the lowest price and 0
otherwise. Since sometimes prices are equal, sometimes all three
variables are zero.

If I do the regression without the constant, it is the coefficients on
these minpriceX variables which are dropped in two of the equations.

I hope this is clear. I'll include actual sample code below. I'd be

***********************************************
set matsize 60

constraint define 1 [0]_cons = [1]_cons
constraint define 2 [0]_cons = [2]_cons

constraint define 3 [0]base0 = [1]base1
constraint define 4 [0]base0 = [2]base2

constraint define 5 [0]price0 = [1]price1
constraint define 6 [0]price0 = [2]price2

constraint define 7 [0]price0lag = [1]price1lag
constraint define 8 [0]price0lag = [2]price2lag

constraint define 9 [0]count0lag = [1]count1lag
constraint define 10 [0]count0lag = [2]count2lag

constraint define 11 [0]minprice0 = [1]minprice1
constraint define 12 [0]minprice0 = [2]minprice2

constraint define 13 [0]base1 = 0
constraint define 14 [0]base2 = 0
constraint define 15 [1]base0 = 0
constraint define 16 [1]base2 = 0
constraint define 17 [2]base0 = 0
constraint define 18 [2]base1 = 0

constraint define 19 [0]price1 = 0
constraint define 20 [0]price2 = 0
constraint define 21 [1]price0 = 0
constraint define 22 [1]price2 = 0
constraint define 23 [2]price0 = 0
constraint define 24 [2]price1 = 0

constraint define 25 [0]price1lag = 0
constraint define 26 [0]price2lag = 0
constraint define 27 [1]price0lag = 0
constraint define 28 [1]price2lag = 0
constraint define 29 [2]price0lag = 0
constraint define 30 [2]price1lag = 0

constraint define 31 [0]count1lag = 0
constraint define 32 [0]count2lag = 0
constraint define 33 [1]count0lag = 0
constraint define 34 [1]count2lag = 0
constraint define 35 [2]count0lag = 0
constraint define 36 [2]count1lag = 0

constraint define 37 [0]minprice1 = 0
constraint define 38 [0]minprice2 = 0
constraint define 39 [1]minprice0 = 0
constraint define 40 [1]minprice2 = 0
constraint define 41 [2]minprice0 = 0
constraint define 42 [2]minprice1 = 0

mlogit choice base0 base1 base2 price0 price0lag price1 price1lag price2 price2lag ///
count0lag count1lag count2lag minprice0 minprice1 minprice2, base(-1) cons(1-42)
***********************************************

------------------------------
Timothy O'Neill Dang / Cretog8
520-884-7261
One monkey don't stop no show.
------------------------------
The opinions or statements expressed herein are my own and should not be
taken as a position, opinion, or endorsement of the University of Arizona.
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```