ApolloChoiceModelling forum

Dear Apollo Team,

I am estimating a Hybrid Choice Model (HCM) and have a brief technical question regarding the use of apollo_combineModels for a mediated choice structure.

My Model Structure:

Latent Variable (LV) with ordered logit measurement equations and structural effects from observed characteristics

Choice 1 (Medium-term, binary logit): Car Ownership (Yes, No), where the utility is driven by the LV and observed characteristics

Choice 2 (Short-term, Ordered Logit): Car Use Frequency, where the utility is driven by the LV, the observed choice outcome of Choice 1 (Car Ownership) and observed characteristics

My Question:
Is it technically correct in Apollo to include the observed choice variable from Component 1 as a direct covariate in the utility function of Component 2, and then simply multiply all probability lists (Measurement + Choice 1 + Choice 2) using apollo_combineModels(P, apollo_inputs, functionality)?

I want to ensure this standard approach correctly captures the joint likelihood when one choice component directly depends on the observed outcome of the other.

Thank you very much for your time and guidance!

Best regards,

Matthias

Matthias

would people without a car still have non-zero use frequency though? If not, then you wouldn't use the choice 2 at all. If yes, then you could use different thresholds for such people. I wouldn't directly include car ownership in the utiity

Stephane

Hi Stephane,

Thank you for your quick reply and for pointing this out! You are completely right regarding the structural zero issue for people without a car.

I actually need to clarify my variable definition: I am not modeling car ownership, but rather car availability.

To resolve the issue you mentioned, my approach is as follows:

The Choice 1 Variable: It is a binary indicator for high availability (1 = "always available", 0 = "sometimes available").

The Sample Restriction: I have completely excluded individuals who never have access to a car from the estimation sample. Therefore, everyone in the dataset can have a non-zero car use frequency for Choice 2.

Given this setup (where the structural zero issue is eliminated), I would like to re-ask my initial question:

Is it technically correct in Apollo to include the observed choice variable from Component 1 (Car availability) as a direct covariate in the utility function of Component 2 (Car use frequency), and then simply multiply all probability lists (Measurement + Choice 1 + Choice 2) using apollo_combineModels(P, apollo_inputs, functionality)? Or is it standard practice to not include the outcome of Choice 1 into the utility of Choice 2?

I have to say that I successfully ran this model with 5000 Draws and the coefficients make sense (significant effects from LVs to Car availability and use and significant positive effect from car availability to use as well), but I want to ensure that it is also correct from a methodological standpoint.

Matthias

I would potentially interact it with the thresholds in your ordered model for car use

regarding the joint model, what is shared between the models?

1. Regarding the thresholds:
I am actually already doing exactly this. A violated Brant test led me to specify a Partial Proportional Odds Model (HPOM) for the ordered choice component. Car availability does not just enter as a simple linear shift but interacts with the specific thresholds (yielding distinct, threshold-specific parameters for the transitions).

2. Regarding the shared components:
To account for endogeneity and to justify the joint estimation, both choice models (Car availability and Car use frequency) share the same Latent Variable. The LV enters the utility functions of both components significantly. The likelihoods are combined conditionally on this shared latent construct and integrated over the random draws.

Does this structure fully resolve the methodological concerns regarding the joint estimation?

Hi

yes, this clarifies things, though adding an LV does not necessarily solve endogeneity issues of course

Stephane