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Type:

Package

Title:

Kuhn-Tucker and Multiple Discrete-Continuous Extreme Value Models

Version:

1.3.0

Maintainer:

Patrick Lloyd-Smith <patrick.lloydsmith@usask.ca>

Description:

Estimates and simulates Kuhn-Tucker demand models with individual heterogeneity. The package implements the multiple-discrete continuous extreme value (MDCEV) model and the Kuhn-Tucker specification common in the environmental economics literature on recreation demand. Latent class and random parameters specifications can be implemented and the models are fit using maximum likelihood estimation or Bayesian estimation. All models are implemented in 'Stan' (see Stan Development Team, 2019) https://mc-stan.org/. The package also implements demand forecasting (Pinjari and Bhat (2011) https://repositories.lib.utexas.edu/handle/2152/23880) and welfare calculation (Lloyd-Smith (2018) <doi:10.1016/j.jocm.2017.12.002>) for policy simulation. 'Stan' models can be estimated using either the 'cmdstanr' (default) or 'rstan' backend. If using 'cmdstanr', then user will need to install 'cmdstanr' manually https://mc-stan.org/cmdstanr/.

License:

MIT + file LICENSE

Depends:

R (≥ 4.1.0), Rcpp (≥ 1.0.5), methods

Imports:

rstan (≥ 2.29.0), posterior (≥ 1.0.0), rstantools (≥ 2.3.0), dplyr (≥ 1.0.0), purrr, tibble, tidyr, utils, stats, Formula

LinkingTo:

BH (≥ 1.72.0), Rcpp, RcppEigen (≥ 0.3.3.3.0), RcppParallel (≥ 5.0.1), rstan (≥ 2.29.0), StanHeaders (≥ 2.29.0)

Language:

en-US

Encoding:

UTF-8

LazyData:

true

SystemRequirements:

GNU make, CmdStan (>= 2.29.0)

NeedsCompilation:

yes

RoxygenNote:

7.3.3

Biarch:

true

Suggests:

bench, knitr, rmarkdown, testthat (≥ 3.0.0), cmdstanr

Additional_repositories:

https://stan-dev.r-universe.dev/

URL:

https://github.com/plloydsmith/rmdcev

BugReports:

https://github.com/plloydsmith/rmdcev/issues

Packaged:

2026-03-06 14:14:13 UTC; plloy

Author:

Patrick Lloyd-Smith [aut, cre], Trustees of Columbia University [cph]

Repository:

CRAN

Date/Publication:

2026-03-10 21:10:02 UTC

'rmdcev': Estimating and simulating Kuhn-Tucker and multiple discrete-continuous extreme value (MDCEV) demand models

Description

The 'rmdcev' R package estimates and simulates Kuhn-Tucker demand models with individual heterogeneity. The models supported by 'rmdcev' are the multiple-discrete continuous extreme value (MDCEV) model and Kuhn-Tucker specification common in the environmental economics literature on recreation demand. Latent class and random parameters specifications can be implemented and the models are fit using maximum likelihood estimation or Bayesian estimation. All models are implemented in 'Stan', which is a 'C++' package for performing full Bayesian inference (see Stan Development Team, 2019) <https://mc-stan.org/>. The 'rmdcev' package also implements demand forecasting (Pinjari and Bhat (2011) <https://repositories.lib.utexas.edu/handle/2152/23880>) and welfare calculation (Lloyd-Smith (2018) <doi:10.1016/j.jocm.2017.12.002>) for policy simulation.

Author(s)

Maintainer: Patrick Lloyd-Smith patrick.lloydsmith@usask.ca

Other contributors:

Trustees of Columbia University [copyright holder]

CreateBlankPolicies

Description

Create 'zero effect' policies that can then be modified by the user

Usage

CreateBlankPolicies(npols, model, price_change_only = TRUE)

Arguments

npols

Number of policies to simulate

model

Estimated model from mdcev

price_change_only

Logical value for whether to include policy changes to dat_psi. Defaults to TRUE. TRUE implies that only price changes are used in simulation.

Value

A named list with four elements:

price_p: A list of npols numeric vectors, each of length J+1 (number of non-numeraire alternatives plus the numeraire), initialised to zero. Modify these vectors to specify proportional price changes for each policy.
dat_psi_p: If price_change_only = FALSE and the model has psi variables, a list of npols matrices copied from the estimated model's psi covariate data (one row per individual-alternative combination). NULL otherwise.
dat_phi_p: If price_change_only = FALSE and the model is a kt_ee specification with phi variables, a list of npols matrices copied from the estimated model's phi covariate data. NULL otherwise.
price_change_only: Logical; the value of the price_change_only argument, retained for use by mdcev.sim().

Examples


data_rec <- mdcev.data(data_rec, subset = id <= 500, id.var = "id",
                alt.var = "alt", choice = "quant")

mdcev_est <- mdcev( ~ 0, data = data_rec,
               model = "hybrid0", algorithm = "MLE",
               std_errors = "mvn", backend = "rstan")
CreateBlankPolicies(npols = 2, mdcev_est)

GenerateMDCEVData

Description

Simulate data for KT models

Usage

GenerateMDCEVData(
  model,
  nobs = 1000,
  nalts = 10,
  income = stats::runif(nobs, 1e+05, 150000),
  price = matrix(stats::runif(nobs * nalts, 100, 500), nobs, nalts),
  alpha_parms = 0.5,
  scale_parms = 1,
  gamma_parms = stats::runif(nalts, 1, 10),
  psi_i_parms = c(-1.5, 2, -1),
  psi_j_parms = c(-5, 0.5, 2),
  phi_parms = c(-5, 0.5, 2),
  dat_psi_i = matrix(2 * stats::runif(nobs * length(psi_i_parms)), nobs,
    length(psi_i_parms)),
  dat_psi_j = cbind(matrix(stats::runif(nalts * (length(psi_j_parms)), 0, 1), nrow =
    nalts)),
  dat_phi = cbind(matrix(stats::runif(nalts * (length(phi_parms)), 0, 1), nrow = nalts)),
  nerrs = 1,
  tol = 1e-20,
  max_loop = 999
)

Arguments

model

A string indicating which model specification is estimated. The options are "alpha", "gamma", "hybrid" and "hybrid0" for the MDCEV model and "kt_ee" for the environmental economics Kuhn-Tucker specification.

nobs

Number of individuals

nalts

Number of non-numeraire alts

income

Vector of individual income

price

Matrix of prices for non-numeraire alternatives.

alpha_parms

Parameter value for alpha term

scale_parms

Parameter value for scale term

gamma_parms

Parameter value for gamma terms

psi_i_parms

Parameter value for psi terms that vary by individual

psi_j_parms

Parameter value for psi terms that vary by alt (all models except kt_ee)

phi_parms

Parameter value for phi terms that vary by alt (kt_ee model only)

dat_psi_i

(nobs X # psi_i_parms) matrix with individual-specific characteristics

dat_psi_j

(nalts X # psi_j_parms) matrix with alternative-specific variables (all models except kt_ee)

dat_phi

(nalts X # phi_parms) matrix with alternative-specific variables (kt_ee model only)

nerrs

Number of error draws for demand simulation

tol

Tolerance level for simulations if using general approach

max_loop

maximum number of loops for simulations if using general approach

Value

A 'mdcev.data' object, which is a 'data.frame' in long format. Also includes parms_true with parameter values

Examples


data <- GenerateMDCEVData(model = "gamma")

PrepareSimulationData

Description

Prepare data for WTP/demand simulation from a fitted mdcev object.

Usage

PrepareSimulationData(object, policies, nsims = 30, class = "class1")

Arguments

object

An object of class mdcev.

policies

A list produced by CreateBlankPolicies containing price_p (additive price changes) and optionally dat_psi_p / dat_phi_p (alternative-attribute changes).

nsims

Number of parameter draws to use for uncertainty quantification.

class

Class label for Latent Class models (e.g. "class1").

Value

A list with df_indiv (individual-level data), df_common (shared simulation inputs), and sim_options (model metadata).

Examples


data(data_rec, package = "rmdcev")

data_rec <- mdcev.data(data_rec, subset = id <= 500, id.var = "id",
                alt.var = "alt", choice = "quant")

mdcev_est <- mdcev( ~ 0, data = data_rec,
               model = "hybrid0", algorithm = "MLE",
               std_errors = "mvn", backend = "rstan")

policies <- CreateBlankPolicies(npols = 2, mdcev_est,
             price_change_only = TRUE)

df_sim <- PrepareSimulationData(mdcev_est, policies)

Recreation data from Value of Nature to Canadians Survey

Description

Data from 2000 individuals from the Value of Nature to Canadians (VNC) survey. The travel costs are calculated using the approach described in Lloyd-Smith (2020)

Usage

data(data_rec)

Format

A tibble with 34000 rows and 8 variables

Source

Canadian Nature Survey 2012

References

Federal, Provincial, and Territorial Governments of Canada. 2014. “2012 Canadian Nature Survey: Awareness, Participation, and Expenditures in Nature-Based Recreation, Conservation, and Subsistence Activities.” Ottawa, ON: Canadian Councils of Resource Ministers. (catalogue no. B64-513/1-2012E-PDF)

Lloyd-Smith, P (2022). “The Economic Benefits of Recreation in Canada”. Canadian Journal of Economics. doi:10.1111/caje.12560

mdcev

Description

Fit a MDCEV model using MLE or Bayes

Usage

mdcev(
  formula = NULL,
  data,
  weights = NULL,
  model = c("alpha", "gamma", "hybrid", "hybrid0", "kt_ee"),
  n_classes = 1,
  fixed_scale1 = 0,
  single_scale = 0,
  trunc_data = 0,
  psi_ascs = NULL,
  gamma_ascs = 1,
  seed = "123",
  max_iterations = 2000,
  jacobian_analytical_grad = 1,
  initial.parameters = "random",
  hessian = TRUE,
  algorithm = c("MLE", "Bayes"),
  flat_priors = NULL,
  print_iterations = TRUE,
  prior_psi_sd = 10,
  prior_gamma_sd = 10,
  prior_phi_sd = 10,
  prior_alpha_shape = 1,
  prior_scale_sd = 1,
  prior_delta_sd = 10,
  gamma_nonrandom = 0,
  alpha_nonrandom = 0,
  std_errors = "deltamethod",
  n_draws = 50,
  keep_loglik = 0,
  random_parameters = "fixed",
  show_stan_warnings = TRUE,
  n_iterations = 200,
  n_chains = 4,
  n_cores = 4,
  max_tree_depth = 10,
  adapt_delta = 0.8,
  lkj_shape_prior = 4,
  ...
)

## S3 method for class 'mdcev'
print(
  x,
  digits = max(3, getOption("digits") - 3),
  width = getOption("width"),
  ...
)

## S3 method for class 'mdcev'
summary(object, printCI = FALSE, ...)

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

Arguments

formula

Formula for the model to be estimated. The formula is divided in three parts, separated by the symbol |. The first part is reserved for alternative-specific and individual-specific variables in the psi parameters. Note that alternative-specific constants are handled by the psi_ascs argument. The second part corresponds for individual-specific variables that enter in the probability assignment in models with latent classes. The third part is reserved for the $q_k$ variables included in the $phi_k$ parameters in the KT model specification used in environmental economics model = "kt_ee".

data

The (IxJ) data to be passed to Stan of class mdcev.data including 1) id, 2) alt, 3) choice, 4) price, 5) income, and columns for alternative-specific and individual specific variables. Note: I is number of individuals and J is number of non-numeraire alternatives.

weights

an optional vector of weights. Default to 1.

model

n_classes

The number of latent classes. Note that the LC model is automatically estimated as long as the prespecified number of classes is set greater than 1.

fixed_scale1

Whether to fix scale at 1.

single_scale

For lc models, whether to estimate a single scale parameter

trunc_data

Whether the estimation should be adjusted for truncation of non-numeraire alternatives. This option is useful if the data only includes individuals with positive non-numeraire consumption levels such as recreation data collected on-site. To account for the truncation of consumption, the likelihood is normalized by one minus the likelihood of observing zero consumption for all non-numeraire alternatives (i.e. likelihood of positive consumption) following Englin, Boxall and Watson (1998) and von Haefen (2003).

psi_ascs

Whether to include alternative-specific psi parameters. The first alternative is used as the reference category. Only specify to 1 for MDCEV models.

gamma_ascs

Indicator to include alternative-specific gammas parameters.

seed

Random seed.

max_iterations

Maximum number of iterations in MLE.

jacobian_analytical_grad

indicator whether to use analytical gradient method for Jacobian (=1) or numerical gradient method (=0). For "kt_ee" model only,

initial.parameters

The default for fixed and random parameter specifications is to use random starting values. (except for the scale parameter with a starting value set to 1). For LC models, the default is to use slightly adjusted MLE point estimates from the single class model. Initial parameter values should be included in a named list. For example, the LC "hybrid" specification initial parameters can be specified as: initial.parameters = list(psi = array(0, dim = c(K, num_psi)), gamma = array(1, dim = c(K, num_alt)), alpha = array(0.5, dim = c(K, 0)), scale = array(1, dim = c(K))) where K is the number of classes (i.e. K = 1 is used for single class models), num_psi is number of psi parameters, and num_alt is number of non-numeraire alternatives.

hessian

Whether to keep the Hessian matrix

algorithm

Either "Bayes" for Bayes or "MLE" for maximum likelihood estimation.

flat_priors

indicator if completely uninformative priors should be specified. Defaults to 1 if MLE used and 0 if Bayes used. If using MLE and set flat_priors = 0, penalized MLE is used and the optimizing objective is augmented with the priors.

print_iterations

Whether to print iteration information

prior_psi_sd

standard deviation for normal prior with mean 0.

prior_gamma_sd

standard deviation for half-normal prior with mean 1.

prior_phi_sd

standard deviation for normal prior with mean 0.

prior_alpha_shape

shape parameter for beta distribution.

prior_scale_sd

standard deviation for half-normal prior with mean 0.

prior_delta_sd

standard deviation for normal prior with mean 0.

gamma_nonrandom

indicator set to 1 if gamma parameters should not be random (i.e. no standard deviation).

alpha_nonrandom

indicator set to 1 if alpha parameters should not be random (i.e. no standard deviation).

std_errors

Compute standard errors using the delta method ("deltamethod") or multivariate normal draws ("mvn"). The default is "deltamethod". Note that mvn parameter draws should be used to incorporate parameter uncertainty for demand and welfare simulation. For maximum likelihood estimation only.

n_draws

The number of multivariate normal draws for standard error calculations if "mvn" is specified.

keep_loglik

Whether to keep the log_lik calculations

random_parameters

The form of the covariance matrix for Bayes. Can be 'fixed' for no random parameters, 'uncorr' for uncorrelated random parameters, or 'corr' for correlated random parameters.

show_stan_warnings

Whether to show warnings from Stan.

n_iterations

The number of iterations to use in Bayesian estimation. The default is for the number of iterations to be split evenly between warmup and posterior draws. The number of warmup draws can be directly controlled using the warmup argument (see rstan::sampling).

n_chains

The number of independent Markov chains in Bayesian estimation.

n_cores

The number of cores used to execute the Markov chains in parallel in Bayesian estimation. Can set using options(mc.cores = parallel::detectCores()).

max_tree_depth

https://mc-stan.org/misc/warnings.html#maximum-treedepth-exceeded

adapt_delta

https://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup

lkj_shape_prior

Prior for Cholesky matrix

...

Additional parameters to pass on to rstan::stan and rstan::sampling.

x, object

an object of class 'mdcev'

digits

the number of digits,

width

the width of the printing,

printCI

set to TRUE to print 95% confidence intervals

Value

A object of class mdcev

Examples


data(data_rec, package = "rmdcev")

data_rec <- mdcev.data(data_rec, subset = id <= 500, id.var = "id",
                alt.var = "alt", choice = "quant")

mdcev_est <- mdcev( ~ 0,
data = data_rec,
model = "hybrid0",
algorithm = "MLE",
backend = "rstan")

data.frame for mdcev model

Description

shape a 'data.frame' in a suitable form for the use of the 'mdcev' function and complete some data checks

Usage

mdcev.data(
  data,
  id.var = "id",
  alt.var = NULL,
  choice = "choice",
  price = "price",
  income = "income",
  alt.levels = NULL,
  drop.index = FALSE,
  subset = NULL,
  ...
)

Arguments

data

a 'data.frame',

id.var

the name of the variable that contains the individual index.

alt.var

the name of the variable that contains the alternative index or the name under which the alternative index will be stored (the default name is 'alt'),

choice

the variable indicating the consumption of non-numeraire alternatives that is made: it has to be a numerical vector. Default is "choice".

price

the variable indicating the price of the non-numeraire alternatives. Default is "price"

income

the variable indicating the income of the individual. Default is "income".

alt.levels

the name of the alternatives: if null, they are guessed from the 'alt.var' argument,

drop.index

should the index variables be dropped from the 'data.frame',

subset

a logical expression which defines the subset of observations to be selected,

...

further arguments.

Value

A 'mdcev.data' object, which is a 'data.frame' in long format, *i.e.* one line for each alternative. It has a 'index' attribute, which is a 'data.frame' that contains the index of the individual ('id') and the index of the alternative ('alt').

mdcev.sim

Description

Simulate welfare or demand for MDCEV model

Usage

mdcev.sim(
  df_indiv,
  df_common,
  sim_options,
  sim_type = c("welfare", "demand"),
  nerrs = 30,
  cond_error = 1,
  draw_mlhs = 1,
  algo_gen = NULL,
  tol = 1e-20,
  max_loop = 999,
  suppressTime = FALSE,
  stan_seed = 3,
  ...
)

## S3 method for class 'mdcev.sim'
print(
  x,
  digits = max(3, getOption("digits") - 3),
  width = getOption("width"),
  ...
)

## S3 method for class 'mdcev.sim'
summary(object, ci = 0.95, ...)

## S3 method for class 'summary.mdcev.sim'
print(
  x,
  digits = max(3, getOption("digits") - 2),
  width = getOption("width"),
  ...
)

Arguments

df_indiv

Prepared individual level data from PrepareSimulationData

df_common

Prepared common data from PrepareSimulationData

sim_options

Prepared simulation options from PrepareSimulationData

sim_type

Either "welfare" or "demand"

nerrs

Number of error draws for welfare analysis

cond_error

Choose whether to draw errors conditional on actual demand or not. Conditional error draws (=1) or unconditional error draws.

draw_mlhs

Generate draws using Modified Latin Hypercube Sampling algorithm (=1) or uniform (=0)

algo_gen

Type of algorithm for simulation. algo_gen = 0 for Hybrid Approach (i.e. constant alphas, only hybrid models) algo_gen = 1 for General approach (i.e. heterogeneous alpha's, all models)

tol

Tolerance level for simulations if using general approach

max_loop

maximum number of loops for simulations if using general approach

suppressTime

Suppress simulation time calculation

stan_seed

Seed for pseudo-random number generator get_rng see help(get_rng, package = "rstan")

...

Additional parameters to pass to mdcev.sim

x, object

an object of class 'mdcev.sim'

digits

the number of digits,

width

the width of the printing,

ci

choose confidence interval for simulations. Default is 95 percent.

Value

a object of class mdcev.sim which contains a list for each individual holding either 1) nsims x npols matrix of welfare changes if welfare is being simulated or 2) nsims number of lists of npols x # alternatives matrix of Marshallian demands is demand is being simulated.

Examples


data(data_rec, package = "rmdcev")

data_rec <- mdcev.data(data_rec, subset = id <= 500, id.var = "id",
                alt.var = "alt", choice = "quant")

mdcev_est <- mdcev( ~ 0, data = data_rec,
               model = "hybrid0", algorithm = "MLE",
               std_errors = "mvn", backend = "rstan")

policies <- CreateBlankPolicies(npols = 2,
             mdcev_est,
             price_change_only = TRUE)

df_sim <- PrepareSimulationData(mdcev_est, policies)

wtp <- mdcev.sim(df_sim$df_indiv,
                 df_common = df_sim$df_common,
                 sim_options = df_sim$sim_options,
                 cond_err = 1, nerrs = 5, sim_type = "welfare")

'rmdcev': Estimating and simulating Kuhn-Tucker and multiple discrete-continuous extreme value (MDCEV) demand models

Description

Author(s)

See Also

CreateBlankPolicies

Description

Usage

Arguments

Value

Examples

GenerateMDCEVData

Description

Usage

Arguments

Value

Examples

PrepareSimulationData

Description

Usage

Arguments

Value

Examples

Recreation data from Value of Nature to Canadians Survey

Description

Usage

Format

Source

References

mdcev

Description

Usage

Arguments

Value

Examples

data.frame for mdcev model

Description

Usage

Arguments

Value

mdcev.sim

Description

Usage

Arguments

Value

See Also

Examples