ApolloChoiceModelling forum

Dear David and Stephane,

Thank you for your marvelous work with Apollo.

I'm interested in estimating a joint model for ownership and use preference of motorcycle, using latent variables. I have a dataset from a survey where each responder answer the number of motorcycles owned and the frequency of use. I would like to make a binomial model for ownership (0 = none, 1 = own at least one motorcycle), and a MNL for use preference (where the dependent variable takes the value of 1, if the individual uses the motorcycle less days than the days he/she commutes; 2, if both numbers are equal; and 3, if the individual uses the motorcycle more days than the days he/she commutes.

It would be expected that both decisions are related, as an individual may value the number of days he/she would use the vehicle vs. the days of commuting, and then decide to acquire the motorcycle. Hence, the interest to model both decisions in a joint model. I want to ask you if defining both models (binomial and MNL), and then using the function apollo_combineModels would be enough to "join" both decisions, or if it would be necessary to develop further steps to achieve this using Apollo.

Thank you in advance,

Santiago Mesa

Santiago

using apollo_combineModels will mean that both models contribute to the likelihood of the model. But the actual link between the two requires some parameters to be shared. If both models use completely separate sets of parameters, then the joint LL is simply the sum of the the LLs for two separate models

Stephane

Stephan, thank you for your answer.

May I ask if the parameters to be shared must be the betas of the regression, or there is another way to join both decisions (like using a random coefficient or a latent variable) while keeping independent/separate betas for every choice (ownership, preference of use 1, and preference of use 3).

Santiago

Santiago

if you include a random coefficient, that would still use parameters too, same for a latent variable.

Stephane