ApolloChoiceModelling forum

Posted: **06 Jun 2020, 13:32**

I am rather new to choice modeling and Apollo. Trying to run a mixed multinomial logit model with heterogeneity in means and variances on a large sample of vehicle crash data. I can estimate the model with NLogit, but it runs very slowly (I gave up after it ran for 48 hours on a fast AWS cluster). Apollo's multi-threading capability could make this task more practical, given that we need to compare results from dozens of specifications. However, I cannot find reference to mean/variance heterogeneity in the random parameters model in the Apollo documentation.

Is it possible to run such a model in Apollo? If so, can someone please boost me up the learning curve?

For those familiar with NLogit, the following code is a reduced form of what we want to achieve in Apollo:

RPLOGIT;
LHS=DAMAGE;
CHOICES = C1, C2, C3;
MODEL:
U(C1)= C1*ONE + C1*X1 + C1*X2 /
U(C2) = C2*X3 + C2*X4 + C2*X5 +C2*X6 /
U(C3)= C3*ONE + C3*X7 + C3*X8 + C3*X9 + C3*X10 + C3*X11 ;
PTS=1000; HALTON;
RPL = X2, X5;
HFR = X2, X5, X6;
FCN = X12(N|#11!111), X13(N|#11!010), X14(N|#11!010) $

The LHS "choices" (C1, C2, C3) are levels of damage to vehicles and the independent variables (X1-X14) are mostly 0/1 dummies describing the crash and contributing factors (e.g. head on collision, driver age, type of vehicle, speeding). Hence, the independent variables are not choice-specific.

A paper that estimates a similar model is Seraneeprakarn, P., Huang, S., Shankar, V., Mannering, F., Venkataraman, N., Milton, J., 2017. Occupant injury severities in hybrid-vehicle involved crashes: A random parameters approach with heterogeneity in means and variances. Analytic Methods in Accident Research 15, 41-55. Available from
https://www.dropbox.com/s/am3v78i8q4tpy ... e.pdf?dl=0

Thank you.

Posted: **06 Jun 2020, 16:43**

Hi

yes, this is very straightforward to do.

Let's use a simple example where you have that beta_cost follows a negative lognormal distribution, where we then estimate the parameters (mean and sd) of the Normal distribution of log(-beta_cost). Let's call these mu and sig and assume that mu is different for men and women, while sig is interacted continuously with income.

We could specify this as follows. Where I put ... is to add other things for your model. Here, I assume that you have variables in your data called male, female and income, and that the cost for the first alternative is cost_1:

Code: Select all

apollo_beta = c(mu_male    = 0,
                        mu_female = 0,
                        sig              = 0.1,
                        lambda_inc_sig = 0,
                        ...)

apollo_draws = list(
...
  interNormDraws = c("draws_beta_cost"...),
...
)

apollo_randCoeff = function(apollo_beta, apollo_inputs){
  randcoeff = list()

  randcoeff[["beta_cost"]] = -exp( mu_male * male + mu_female * female + sig * income ^ lambda_inc_sig * draws_beta_cost)
...

  return(randcoeff)
}

apollo_probabilities=function(apollo_beta, apollo_inputs, functionality="estimate"){

...
  V[['alt1']] = b_cost * cost_1 
...

Posted: **06 Jun 2020, 19:11**

This is very helpful. Thank you for the fast reply.

ApolloChoiceModelling forum

Mixed Multinomial Logit with heterogeneity in means and variances

Mixed Multinomial Logit with heterogeneity in means and variances

Re: Mixed Multinomial Logit with heterogeneity in means and variances

Re: Mixed Multinomial Logit with heterogeneity in means and variances