st: Different likelihood estimates from -mixlpred- and own calculations using -mixlbeta-

[HSUEH-HSIANG 28Cher29 LI <hli37@wisc.edu>]

I’m having a problem with -mixlpred- in the -mixlogit- package. I obtained this user written program -mixlogit- by Arne Risa Hole with the updates from the SSC archive (I typed -ssc install mixlogit, replace- to get the updates). I am running the program on StataMP 12 for Windows.

 

I run -mixlogit- on a panel data. After running -mixlogit-, I used the postestimation command -mixlpred- to get the likelihood of each option chosen by individuals in each period. In the meanwhile, I also obtained individual coefficient estimates using -mixlbeta-, and then calculate the likelihood using these inidvidual coefficients by individual and period:

L_nit(beta_n)=exp(beta_n*X_nit)/[sum_{j=1,...J} exp(beta_n * X_njt)]

(the equation is from Arne Risa Hole, 2007 "Fitting mixed logit models by using masimum simulated likelihood", The Stata Journal, 7, Number 3, pp.388)

 

The predicted probabilities from -mixpred- and my own calculation using -mixlbeta- and the equation above are quite different. I am wondering how -mixpred- calculates the likelihood. It appears to me that this -mixlpred- likelihood is averaged over simulated draws conditional on the coefficient distribution estimates, rather than individual-specific coefficient estimates. Please correct me if I am wrong! Since I am interested in "simulating" how likelihood changes when coefficient estimates change, is it reasonable that I calculate the likelihood the way I mentioned above? Any suggestions and advice are welcomed!

 

Sincerely,

Cher