What specific type of math model helps predict if people will choose to drive, ride a bus, or walk for their trip?

The specific type of math model that helps predict if people will choose to drive, ride a bus, or walk for their trip is known as a Discrete Choice Model. These models are fundamentally based on the principle of Random Utility Maximization (RUM). In simple terms, Random Utility Maximization posits that individuals will choose the option from a set of available alternatives that provides them with the highest utility. Utility is a numerical representation of the satisfaction or preference an individual derives from choosing a specific alternative, such as driving, taking a bus, or walking. This utility is composed of two parts: a deterministic component and a random component. The deterministic component is based on observable characteristics of the travel alternatives (like travel time, travel cost, convenience, reliability) and observable characteristics of the decision-maker (like income, car ownership, or age). The random component accounts for unobservable factors that influence choice, variations in individual preferences not captured by observed attributes, and measurement errors. Because of this random component, the models predict the *probabilityof an individual choosing each option, rather than a certain outcome. The most common Discrete Choice Models used for mode choice – which refers to the specific decision of which transportation method to use for a trip – include Logit Models (such as Multinomial Logit or Nested Logit) and more advanced Mixed Logit Models. These models are developed by specifying a mathematical utility function for each available travel mode. This function expresses utility as a combination of relevant attributes weighted by coefficients. These coefficients are numerical values, estimated through statistical methods like Maximum Likelihood Estimation using observed travel behavior data, which quantify the impact of each attribute on a mode's utility. For example, a negative coefficient for travel time indicates that longer travel times reduce a mode's utility. The models also include Alternative Specific Constants (ASCs), which are terms unique to each mode that capture the average unobserved utility or inherent attractiveness of that mode relative to a baseline mode, not accounted for by other specified variables. Once these coefficients are estimated, the model can calculate the probability of an individual choosing each mode given a specific set of conditions, allowing planners to predict how changes in travel times, costs, or service levels might affect people's choices.