Request for Guidance on Hybrid Choice Model Implementation in Python Biogeme

[Ali Karami]

Dear Prof. Bierlaire,

I hope this email finds you well.

First of all, I would like to sincerely thank you for developing the comprehensive and powerful Python Biogeme package. It has been an invaluable tool in my research.

I am currently working on a hybrid choice model that includes two latent variables. However, I’ve encountered a persistent issue during estimation:

Final log likelihood: nan  
McFadden's rho-squared: 0.0  
Despite reviewing the documentation and examples, I have not been able to resolve the problem. I would be very grateful if you could kindly help me identify any potential issues in my implementation.

Below, I’ve outlined the key components of my model:

Structural Equations for Latent Variables

γe_age    = Beta('γe_age',    0, None, None, 0)
γe_gender = Beta('γe_gender', 0, None, None, 0)
γe_inc    = Beta('γe_inc',    0, None, None, 0)
η_env     = bioDraws('ETA_ENV', 'NORMAL')
sigma_s_Env = Beta('sigma_s_Env', 1, None, None, 0)

LV_env = γe_age * Age \
       + γe_gender * Gender \
       + γe_inc * Income \
       + sigma_s_Env * η_env

Measurement Equations (Example)

INTER_alfa_Enviro1 = Beta('INTER_alfa_Enviro1', 0, -10000, 10000, 1)
B_Enviro_Loading1 = Beta('B_Enviro_Loading1', -1, -10000, 10000, 1)
MODEL_Enviro1 = INTER_alfa_Enviro1 + B_Enviro_Loading1 * LV_env
SIGMA_STAR_Enviro1 = Beta('SIGMA_STAR_Enviro1', 1, 1e-6, None, 1)

tau_1_Enviro1 = -delta_1_Enviro1 - delta_2_Enviro1
tau_2_Enviro1 = -delta_1_Enviro1
tau_3_Enviro1 = delta_1_Enviro1
tau_4_Enviro1 = delta_1_Enviro1 + delta_2_Enviro1

Enviro1_tau_1 = (tau_1_Enviro1 - MODEL_Enviro1) / SIGMA_STAR_Enviro1
Enviro1_tau_2 = (tau_2_Enviro1 - MODEL_Enviro1) / SIGMA_STAR_Enviro1
Enviro1_tau_3 = (tau_3_Enviro1 - MODEL_Enviro1) / SIGMA_STAR_Enviro1
Enviro1_tau_4 = (tau_4_Enviro1 - MODEL_Enviro1) / SIGMA_STAR_Enviro1

Ind_Enviro1 = {
    1: Φ(Enviro1_tau_1),
    2: Φ(Enviro1_tau_2) - Φ(Enviro1_tau_1),
    3: Φ(Enviro1_tau_3) - Φ(Enviro1_tau_2),
    4: Φ(Enviro1_tau_4) - Φ(Enviro1_tau_3),
    5: 1 - Φ(Enviro1_tau_4),
    6: 1.0
}
P_Enviro1 = Elem(Ind_Enviro1, Envir01)

This process is repeated for all indicators.

Choice Model Specification

ASC_car  = Beta('ASC_car', 0, None, None, 0)
ASC_pt   = Beta('ASC_pt', 0, None, None, 0)
ASC_oth  = Beta('ASC_oth', 0, None, None, 0)

β_time = Beta('β_time', 0, None, None, 0)
β_cost = Beta('β_cost', 0, None, None, 0)

δ_env = Beta('δ_env', 0, None, None, 0)
δ_mob = Beta('δ_mob', 0, None, None, 0)

V = {
    0: β_time * TimeCar + β_cost * CostCar + δ_env * LV_env + δ_mob * LV_mob,
    1: ASC_pt  + β_time * TimePT  + β_cost * CostPT  + δ_env * LV_env + δ_mob * LV_mob,
    2: ASC_oth + δ_env * LV_env + δ_mob * LV_mob
}
avail = {0: 1, 1: 1, 2: 1}
prob_choice = loglogit(V, avail, Choice)

Joint Likelihood and Monte Carlo Integration

cond_prob = log(prob_choice) \
          + log(P_Enviro1) + log(P_Enviro2) + log(P_Enviro3) \
          + log(P_Mobil1) + log(P_Mobil2)

loglike = MonteCarlo(cond_prob)

biogeme_obj = BIOGEME(database, loglike, numberOfDraws=100)

biogeme_obj.modelName = "OPT_HCM_SigmaEnhanced"

# Estimate and grab results
results = biogeme_obj.estimate()



Despite following the recommended structure, the estimation returns nan for the log-likelihood and 0.0 for McFadden’s rho-squared. I suspect the issue may lie in the integration or the measurement equations, but I would deeply appreciate your expert insight.

Thank you very much for your time and consideration. I look forward to any guidance you may be able to offer.

Warm regards,

Ali