Package {cdlogit}

Information criteria for the cdlogit model

Description

Calculates the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) for an object of class cdlogit, based on the log-likelihood and the number of parameters.

Usage

## S3 method for class 'cdlogit'
AIC(object, ...)

## S3 method for class 'cdlogit'
BIC(object, ...)

Arguments

Value

For AIC.cdlogit, the AIC value. For BIC.cdlogit, the BIC value.

Likelihood ratio test for cdlogit models

Description

The LRtest function performs a likelihood ratio test for two nested cdlogit models, to check whether one model provides a significantly better fit to the data than the other model.

Usage

LRtest(model1, model2, boundary = FALSE)

Arguments

Value

Summary of the likelihood ratio test, showing degrees of freedom, log-likelihood values, test statistic, and p-value.

References

Self SG, Liang KY (1987). "Asymptotic Properties of Maximum Likelihood Estimators and Likelihood Ratio Tests Under Nonstandard Conditions." Journal of the American Statistical Association, 82(398), 605–610. doi:10.2307/2289471.

Examples

### Conduct a likelihood ratio test for nested models ###
data(invest, package = "cdlogit")
mnl_model  = cdlogit(
  formula = choice ~  return + pos - 1,
  data = invest,  model = "rum", index = c("id", "task", "alt"))
crum_model  = cdlogit(
  formula = choice ~  return + pos - 1,
  data = invest,  model = "crum", index = c("id", "task", "alt"),
  context_attr = c("return", "pos"),
  context_effect = c("compromise", "attraction", "similarity"))
LRtest(mnl_model, crum_model)

### Conduct a likelihood ratio test when the parameters
### are on the boundary of the parameter space
## GRRM model
grrm_model = cdlogit(
  formula = choice ~  return + pos - 1,
  data = invest,
  model = "grrm",
  index = c("id", "task", "alt"))
summary(grrm_model)
## CRRM model
crrm_model = cdlogit(
  formula = choice ~  return + pos - 1,
  data = invest,
  model = "crrm",
  index = c("id", "task", "alt"))
summary(crrm_model)
LRtest(grrm_model, crrm_model)

Synthetic stated preference data for camera choices

Description

A generated dataset camera containing simulated stated choice data for cameras with different attributes.

The synthetic data include three camera alternatives in each choice set, represented by the brands Sony, Nikon, and Canon. Each camera profile is described by three alternative-specific attributes: camera resolution, battery life, and price. Respondent characteristics age, gender, and income are also included as individual-specific variables. The data contain choices of 200 individuals, each of whom faced 9 choice tasks.

Usage

data("camera", package = "cdlogit")

Format

A data frame in long format with the following columns:

id

Individual ID.

set_id

Choice set ID.

alt_id

Alternative ID, corresponding to the camera brand (Sony, Nikon, or Canon).

Megapixel

Camera resolution measured in megapixels (MP).

Battery

Battery life of the camera, measured in minutes (Mins).

Price

Camera price in euros (EUR).

Age

Respondent age in years.

Gender

Respondent gender.

Income

Respondent income category (Low, Medium, or High).

choice

Choice indicator, where 1 indicates the selected alternative and 0 otherwise.

Fit context-dependent discrete choice models

Description

The cdlogit function estimates a class of context-dependent discrete choice models. The function supports several models, including the standard random utility maximization (RUM) model, the classical and generalized random regret minimization (RRM) model, the random advantage maximization (RAM) model, the emergent value (EV) model and contextual random utility maximization (CRUM) model that explicitly incorporate measures of context effects, as well as pairwise normalization (PN) and range normalization (RN) models.

The error term is assumed to follow an i.i.d. Gumbel distribution, leading to logit models. Both fixed and mixed (random) specifications are supported.

The function supports a three-part formula syntax similar to that of the mlogit package, which includes:

• alternative specific variables with generic coefficients

• choice set specific or individual specific variables with alternative specific coefficients

• alternative specific variables with alternative specific coefficients.

Usage

cdlogit(
  formula,
  data,
  index,
  model,
  context_attr,
  context_effect = c("compromise", "attraction", "similarity"),
  reflevel = NULL,
  rpar = NULL,
  ra_weight = 1,
  norm_attr = NULL,
  num_draws = 40,
  start = NULL,
  seed = NULL,
  optim_method = "L-BFGS-B",
  optim_control = list(maxit = 1e+08),
  ...
)

Arguments

Value

An object of class cdlogit containing model fit results including the estimated parameters, log-likelihood, the variance-covariance matrix of the estimated parameters, the convergence status, the estimated individual level parameters, and the fitted choice probabilities.

References

Chorus CG, van Cranenburgh S, Dekker T (2014). "Random Regret Minimization for Consumer Choice Modeling: Assessment of Empirical Evidence." Journal of Business Research, 67(11), 2428–2436. doi:10.1016/j.jbusres.2014.02.010.

Coorevits H, Mulder LD (2023). Context Effects in an Investment Setting: A RUM vs RRM Approach. Master's thesis, KU Leuven, Faculty of Economics and Business.

Daviet R, Webb R (2023). "A Test of Attribute Normalization via a Double Decoy Effect." Journal of Mathematical Psychology, 113, 102741. doi:10.1016/j.jmp.2022.102741.

Guevara CA, Fukushi M (2016). "Modeling the Decoy Effect with Context-RUM Models: Diagrammatic Analysis and Empirical Evidence from Route Choice SP and Mode Choice RP Case Studies." Transportation Research Part B: Methodological, 93, 318–337. doi:10.1016/j.trb.2016.07.012.

Landry P, Webb R (2021). "Pairwise Normalization: A Neuroeconomic Theory of Multi-attribute Choice." Journal of Economic Theory, 193, 105221. doi:10.1016/j.jet.2021.105221.

McFadden D (1974). Conditional Logit Analysis of Qualitative Choice Behavior. Academic Press, New York.

Rooderkerk RP, Van Heerde HJ, Bijmolt THA (2011). "Incorporating Context Effects into a Choice Model." Journal of Marketing Research, 48(4), 767–780. doi:10.1509/jmkr.48.4.767.

Tversky A, Simonson I (1993). "Context-Dependent Preferences." Management Science, 39(10), 1179–1189. doi:10.1287/mnsc.39.10.1179.

Xi Y, Meulders M, Vandebroek M (2026). "Context Dependence in Discrete Choice Models." Submitted.

Examples

data(invest, package = "cdlogit")
######## MNL model ########
mnl_model = cdlogit(
  formula = choice ~  return + pos - 1,
  data = invest, model = "rum",
  index = c("id", "task", "alt"))
summary(mnl_model)

######## EV model #########
ev_invest_model = cdlogit(
  formula = choice ~  return + pos - 1,
  data = invest, model = "ev", index = c("id", "task", "alt"),
  context_attr = c("return", "pos"),
  context_effect = c("compromise", "attraction"))
summary(ev_invest_model)
predict(ev_invest_model, invest[1:3, 2:5])
ev_invest_model$cdmeasure

######## PN model ########
pn_model = cdlogit(
  formula = choice ~  return + pos - 1,
  data = invest,  model = "pn1",
  index = c("id", "task", "alt"),
  norm_attr = c("return", "pos"))
summary(pn_model)

Context Effect Measures

Description

Computes context effect measures for each alternative within a choice set, including compromise, attraction (decoy), and similarity measures used in context-dependent discrete choice models. The function operates directly on choice-set designs and can be used without estimating a model. It can be used to check the presence and magnitude of context effects in the design of a choice experiment.

Measures are only available for models of type "crum" or "ev".

Usage

cdmeasure(
  data,
  index,
  model,
  context_attr,
  context_effect = c("compromise", "attraction", "similarity"),
  ...
)

Arguments

Value

A data frame equal to data with additional columns containing the context effect measures. Only relevant for models of type "crum" or "ev". For the CRUM model, the appended columns CRUM_compromise, CRUM_attraction, and CRUM_dissimilarity correspond to measures of the compromise, attraction (decoy), and similarity effects, respectively. For the EV model, the appended columns EV_compromise and EV_attraction are measure of the compromise and attraction effects.

Examples

## Compute context effect measures for a single block of choice sets
## from the invest dataset.
## The resulting measures can be inspected before model estimation
## to evaluate the context-effect structure of the design.

crum_measures_invest <- cdmeasure(
  data = invest[1:33, c("id", "task", "alt", "return", "pos")],
  index = c("id", "task", "alt"),
  model = "crum",
  context_attr = c("return", "pos"),
  context_effect = c("compromise", "attraction", "similarity")
)
print(crum_measures_invest)

ev_measures_invest <- cdmeasure(
  data = invest[1:33, c("id", "task", "alt", "return", "pos")],
  index = c("id", "task", "alt"),
  model = "ev",
  context_attr = c("return", "pos"),
  context_effect = c("compromise", "attraction")
)
print(ev_measures_invest)

Individual-level parameter estimates for mixed cdlogit models

Description

Returns the individual-specific parameter estimates for mixed cdlogit models. These correspond to the posterior means (i.e., empirical Bayes estimates or conditional mean estimates) and posterior standard deviations of the random parameters for each individual.

Usage

indvpar(object, ...)

Arguments

Value

A data frame containing the individual-level estimates of the random parameters. Each row corresponds to an individual in the estimation sample. The first column is the individual id. Subsequent columns contain the posterior mean and posterior standard deviation of each random parameter.

Examples

######### Mixed CRUM model ########
mixed_crum_model = cdlogit(
  formula = choice ~  return + pos - 1,
  data = invest,  model = "crum",
  index = c("id", "task", "alt"),
  rpar = c(pos = 'normal', return = "normal"),
  context_attr =c("return", "pos"),
  context_effect = c("compromise", "attraction", "similarity"))
summary(mixed_crum_model)
indvpar(mixed_crum_model)
predict(object = mixed_crum_model,
  newdata = invest[1:3, c("task", "alt", "return", "pos")])

Investment choice data

Description

A stated preference dataset from the investment choice experiment of Coorevits and Mulder (2023). The dataset contains choices among investment alternatives designed to investigate context effects in decision making.

Respondents were presented with hypothetical investment scenarios in which they had to allocate a fixed amount of EUR 1000 to one of three investment options. Each option was characterized by its expected return and probability of success. If the selected investment was successful, the respondent received EUR 1000 plus the stated return; otherwise, the respondent retained the original EUR 1000.

The dataset contains 174 respondents, each completing 11 choice tasks. Each task consists of three unlabelled investment alternatives.

Usage

data("invest", package = "cdlogit")

Format

A data frame in long format with the following columns:

id

Respondent ID.

task

Choice set ID.

alt

Alternative ID.

return

Potential return from a successful investment (EUR).

pos

Probability of investment success (percentage).

choice

Choice indicator, where 1 indicates the selected alternative and 0 otherwise.

gender

Respondent gender.

age

Respondent age in years.

finknow

Self-reported financial knowledge level (Basic, Intermediate, or Advanced).

References

Coorevits, H. and Mulder, L. D. (2023). Context Effects in an Investment Setting: A RUM vs RRM Approach. Master's thesis, KU Leuven, Faculty of Economics and Business.

Predict choice probabilities from a cdlogit model

Description

Computes predicted choice probabilities for each alternative in (new) choice sets using a fitted cdlogit model.

Usage

## S3 method for class 'cdlogit'
predict(object, newdata, ...)

Arguments

Value

A data frame equal to newdata with additional columns containing predicted choice probabilities. For models with fixed parameters, probabilities are computed directly from the estimated parameters. For mixed models, the function provides:

• population_pred: Population-level predicted probabilities obtained by integrating over the estimated distribution of the random coefficients, conditional on the observed characteristics included in the model. These predictions are particularly relevant for new individuals for whom no choice history is available;

• posterior_pred: Individual-specific predicted probabilities obtained by conditioning on the observed choices of each individual and integrating over the corresponding posterior distribution of the random coefficients. For a new choice set, this yields predicted probabilities for each individual in the estimation sample;

• plugin_pred: Individual-specific predicted probabilities computed by evaluating the choice probabilities at the mean of the individual-specific posterior distribution. This provides a computationally convenient approximation to posterior prediction.

Summary method for cdlogit model objects.

Description

Provides a summary of the estimation results of the fitted cdlogit model.

Usage

## S3 method for class 'cdlogit'
summary(object, ...)

Arguments

Value

Estimation results of the fitted cdlogit model, including:

• The model call, showing how the cdlogit model was specified.

• A table that includes the estimates of the coefficients, and the corresponding standard errors, z-values, p-values, and significance codes.

• The log-likelihood of the fitted model.