Predicted probabilities after mi estimate: mlogit

[Katya Baldina]

Hello!

I am estimating multinomial logistic regression using mi estimate: mlogit. I need to get predicted probabilities for all outcome categories.
For example, if I use regular dataset without multiple imputations I would do this (I used simulated data):

clear all
set obs 1000

g x1 = invnorm(runiform())
g x2 = invnorm(runiform())
g x3 = invnorm(runiform())

gen byte y=1
forval i=1/3 {
    replace y=y+1 if runiform()<.3+.1*x1+.2*x2-.3*(!x3)
}

tab y

foreach var of varlist x1-x3 {
    replace `var' = . if runiform()<.2
    }

mlogit y x1 x2 x3

predict pr1 pr2 pr3 pr4, pr

This will give me predicted probabilities for each of the outcome categories. However, I cannot do the same with mi data.
My code is:

mi set flong
mi reg imp x1 x2 x3

mi impute chained (pmm, knn(10)) x1 x2 x3 = y, add(10)

mi estimate, saving(simulation.ster, replace): mlogit y x1 x2 x3

mi predict nxb1 using simulation.ster, storecompleted equation(#1)
mi predict nxb2 using simulation.ster, storecompleted equation(#2)
mi predict nxb3 using simulation.ster, storecompleted equation(#3)
mi predict nxb4 using simulation.ster, storecompleted equation(#4)

sum nxb*
mi xeq: generate nps1 = invlogit(nxb1)
mi xeq: generate nps2 = invlogit(nxb2)
mi xeq: generate nps3 = invlogit(nxb3)
mi xeq: generate nps4 = invlogit(nxb4)


sum nps*

This gives me a constant probability for category 4 (0.5), which is because the linear prediction for this category is 0 (since it is base outcome). Is there any way to do something similar that predict command after mlogit do in the regular settings?

Thank you in advance!

[Rich Goldstein]

h mi predict

[Katya Baldina]

h mi predict

Thank you for your reply! I've already went through all help file for "mi predict" that's why I came here If you know the solution, could you please share it with me?

[daniel klein]

(code omitted)
mi xeq: generate nps1 = invlogit(nxb1)
mi xeq: generate nps2 = invlogit(nxb2)
mi xeq: generate nps3 = invlogit(nxb3)
mi xeq: generate nps4 = invlogit(nxb4)

I don't think this code is correct. The predicted probababilty for category \(i\) in a multinomial logit is given by

\[
\frac{exp(xb_i)}{1+\sum_j{exp(xb_j)}}
\]

where \(i \neq j\).

Thus, the code should be along the lines:

mi xeq: generate nps1 = exp(nxb1) / ( exp(nxb2) + exp(nxb3) + exp(nxb4) )

[daniel klein]

mi xeq: generate nps1 = exp(nxb1) / ( exp(nxb2) + exp(nxb3) + exp(nxb4) )

should be

mi xeq: generate nps1 = exp(nxb1) / ( 1 + (exp(nxb2) + exp(nxb3) + exp(nxb4)) )