choice_formula: Define choice model formula

In choicedata: Working with Choice Data

Define choice model formula

Description

The choice_formula object defines the choice model equation.

Usage

choice_formula(formula, error_term = "probit", random_effects = character())

## S3 method for class 'choice_formula'
print(x, ...)

Arguments

formula	[formula] A symbolic description of the choice model, see details.
error_term	[character(1)] Defines the model's error term. Current options are: "probit" (default): errors are multivariate normally distributed "logit": errors follow a type-I extreme value distribution
random_effects	[character()] Defines the random effects in the model. The expected format of elements in random_effects is "<covariate>" = "<distribution>", where "<covariate>" is the name of a variable on the formula right-hand side. Every random effect must reference an explicit covariate (or "ASC" for alternative-specific constants) that appears in the supplied model formula. Current options for "<distribution>" are: "cn": correlated (with other "cn" random effects) normal distribution To have random effects for the ASCs, use "ASC" for "<covariate>".
x	[choice_formula] A choice_formula object.
...	Currently not used.

Value

An object of class choice_formula, which is a list of the elements:

formula

The model formula.

error_term

The name of the model's error term specification.

choice

The name of the response variable.

covariate_types

The (up to) three different types of covariates.

ASC

Does the model have ASCs?

random_effects

The names of covariates with random effects.

Specifying the model formula

The structure of formula is choice ~ A | B | C, i.e., a standard formula object but with three parts on the right-hand side, separated by |, where

• choice is the name of the discrete response variable,

• A are names of alternative-specific covariates with a coefficient that is constant across alternatives,

• B are names of covariates that are constant across alternatives,

• and C are names of alternative-specific covariates with alternative-specific coefficients.

The following rules apply:

1. By default, intercepts (referred to as alternative-specific constants, ASCs) are added to the model. They can be removed by adding + 0 in the second part, e.g., choice ~ A | B + 0 | C. To not include any covariates of the second type but to estimate ASCs, add 1 in the second part, e.g., choice ~ A | 1 | C. The expression choice ~ A | 0 | C is interpreted as no covariates of the second type and no ASCs.

2. To not include covariates of any type, add 0 in the respective part, e.g., choice ~ 0 | B | C.

3. Some parts of the formula can be omitted when there is no ambiguity. For example, choice ~ A is equivalent to choice ~ A | 1 | 0.

4. Multiple covariates in one part are separated by a + sign, e.g., choice ~ A1 + A2.

5. Arithmetic transformations of covariates in all three parts of the right-hand side are possible via the function I(), e.g., choice ~ I(A1^2 + A2 * 2). In this case, a random effect can be defined for the transformed covariate, e.g., random_effects = c("I(A1^2 + A2 * 2)" = "cn").

Examples

choice_formula(
  formula = choice ~ I(A^2 + 1) | B | I(log(C)),
  error_term = "probit",
  random_effects = c("I(A^2+1)" = "cn", "B" = "cn")
)

choicedata documentation built on Nov. 5, 2025, 5:46 p.m.