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Define choice model formula

Source: R/choice_formula.R
choice_formula.Rd

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()]
Named vector defining random effects, see details.

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").

Specifying random effects

Specify random effects as "<covariate>" = "<distribution>". Each covariate must appear explicitly on the right-hand side of formula; use "ASC" for alternative-specific constants.

Available distributions are:

  • "cn": correlated normal

  • "n": uncorrelated normal

  • "cln": positively signed correlated log-normal

  • "ln": positively signed uncorrelated log-normal

  • "cln-": negatively signed correlated log-normal

  • "ln-": negatively signed uncorrelated log-normal

Examples

### specify a choice formula
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")
)
#> 
#> ── Choice formula 
#> • choice ~ I(A^2 + 1) | B | I(log(C))
#> • error term: probit
#> • random effects:
#>   • I(A^2+1): cn
#>   • B: cn