Discrete Choice Models

Overview

Discrete Choice Models describe, explain, and predict choices between two or more discrete alternatives. Unlike standard regression where the dependent variable is continuous (e.g., income, temperature), here the target is categorical (e.g., “Buy Product A, B, or C”, “Commute by Car, Bus, or Train”).

These models are fundamental in Econometrics, Marketing (consumer choice), and Transportation Planning.

Binary Choice

When there are only two alternatives (0 or 1):

LOGIT_MODEL: Uses the Logistic distribution for the error term. The coefficients represent the change in the log-odds of the outcome.
PROBIT_MODEL: Uses the Normal distribution (CDF) for the link function. Often preferred in econometrics when error terms are assumed to be normally distributed.

Multiple Choice

When there are more than two alternatives:

MULTINOMIAL_LOGIT: Also known as MNL. The standard model for choosing more than two unordered items. It assumes “Independence of Irrelevant Alternatives” (IIA).
ORDERED_LOGIT (and Ordered Probit): Used when the alternatives have a natural ordering (e.g., Survey ratings: “Strongly Disagree”, “Neutral”, “Strongly Agree”). It calculates cut-points (thresholds) along a latent continuous scale.

Figure 1: Multinomial Probabilities: In a discrete choice model with 3 alternatives (A, B, C), the probabilities sum to 1. As the value of a predictor changes (x-axis), the probability of choosing each option shifts.

Native Excel Capabilities

Excel is not designed for discrete choice analysis: - No Native Functions: It lacks functions for Logit, Probit, or MNL estimation. - Workarounds: Users can implement simple Binary Logit using Solver to maximize likelihood, but Multinomial Logit is extremely difficult to set up manually due to the complex structure of the probability formulas and gradients. - Third-Party: Most serious choice modeling in Excel is done via expensive proprietary add-ins (like XLSTAT or specialized marketing tools).

The functions in this section allow you to estimate these complex econometric models directly from your data range.

Tools

Tool	Description
LOGIT_MODEL	Fits a binary logistic regression model to predict binary outcomes using maximum likelihood estimation.
MULTINOMIAL_LOGIT	Fits a multinomial logistic regression model for multi-category outcomes.
ORDERED_LOGIT	Fits an ordered logistic regression model for ordinal outcomes.
PROBIT_MODEL	Fits a binary probit regression model using maximum likelihood estimation.