Traffic Studies and Mobility

Introduction Transport researchers frequently face the challenge of modelling human decision-making when multiple transport alternatives are available. Discrete choice models (DCMs) have long been a powerful tool in transport economics, yet capturing individual heterogeneity has remained a methodological challenge. The Mixed Logit model (also known as the random parameters logit) offers a solution by allowing coefficients to vary across individuals.

The Challenge of Closed-Form Solutions Unlike simple multinomial logit models, Mixed Logit models do not have closed-form solutions due to the integral over the distribution of random coefficients. This is especially true in transport applications where user preferences vary by income, travel time sensitivity, and environmental concern.

Simulation-Based Estimation: The Role of MSL To overcome this, estimation is performed using Maximum Simulated Likelihood (MSL). The simulation approximates the integral using random or quasi-random draws. In practical terms, more draws improve estimation accuracy but also increase computational time. Stata’s cmmixlogit command automates this, and allows control over integration method (e.g., Hammersley, Halton) and number of draws (e.g., intpoints(1000)).

Application to Transport Let us assume a case study in urban Brisbane, where individuals choose between five modes of public transport: Bus, Metro, Ferry, Tram, and Carpool. Each alternative has specific attributes (fare, travel time, frequency), and individuals have personal characteristics (e.g., income). Using cmmixlogit, we can:

1. Estimate the impact of fare and travel time on transport choice.
2. Introduce random coefficients for travel time to capture preference heterogeneity.
3. Include case-specific variables like income using the casevars() option.
4. Simulate changes (e.g., a 10% fare increase) and use margins to forecast shifts in modal share.

Example Output Interpretation If the coefficient on fare is negative and significant, it indicates fare increases reduce the probability of choosing that mode. A large standard deviation in the random parameter for travel time suggests diverse sensitivity among the population.

Advanced Extensions

• Use of lognormal distribution to ensure coefficients (e.g., on fare) are always negative.
• Modelling correlated random coefficients for variables like fare and frequency.
• Adding random intercepts for transport modes to control for unobserved utility.

Conclusion Mixed Logit models bridge the gap between theoretical transport models and observed behaviour by accommodating individual-level variation. This is critical in modern transport planning, especially in cities like Brisbane where inclusiveness, affordability, and service variety are central to mobility policies.

Keywords: discrete choice, transport modelling, mixed logit, simulation, maximum simulated likelihood, Brisbane, fare elasticity, public transport, heterogeneity, income effects