Can I use the numerical integration and Monte-Carlo integration together in panel data

[jianbiao wang]

Dear Prof. Michel Bierlaire,

Is the following specification right?

This is the specification of random parameter of travel time:

B_TIME = Beta('B_TIME', 0, None, None, 0)   # the mean of parameter

B_TIME_S_o = Beta('B_TIME_S', 1, None, None, 0) # the s.t.d of parameter (varies across observation)

B_TIME_S_i = Beta('B_TIME_S', 1, None, None, 0) # the s.t.d of parameter (varies across individual)

omega = RandomVariable('omega') # variable for numerical integration 

density = dist.normalpdf(omega)

B_TIME_RND = B_TIME + B_TIME_S_o * omega + B_TIME_S_i * bioDraws('B_TIME_RND', 'NORMAL'))

The reason why I use this specification is that, I think the random parameter will not only varies across individual, but also will varies across observation, even though in the panel data. Then,  to obtain the probability (where B_TIME_S_o varies across observation, B_TIME_S_i  varies across individual)

condprob = models.logit(V, av, CHOICE)   # the chosen probability 

prob = Integrate(condprob * density, 'omega')  # integrate the probability with respect to 'omega' (across observation)

condprobIndiv = PanelLikelihoodTrajectory(prob)  #get the trajectory of each person

logprob = log(MonteCarlo(condprobIndiv))  #simulate the probability, the random parameter varies across individual

Is it correct in this way? If not, could you please tell me how to fix it? 

Thank you very much!

Best Regards,

WANG

 

[Bierlaire Michel]

It looks correct. The best way to know is to try...

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