This function creates a data frame containing a choice-based conjoint survey design where each row is an alternative. Generate a variety of survey designs, including full factorial designs, orthogonal designs, and Bayesian D-efficient designs as well as designs with "no choice" options and "labeled" (also known as "alternative specific") designs.
cbc_design(
profiles,
n_resp,
n_alts,
n_q,
n_blocks = 1,
n_draws = 50,
n_start = 5,
no_choice = FALSE,
label = NULL,
method = "random",
priors = NULL,
prior_no_choice = NULL,
probs = FALSE,
keep_d_eff = FALSE,
keep_db_error = FALSE,
max_iter = 50,
parallel = FALSE
)A data frame in which each row is a possible profile. This
can be generated using the cbc_profiles() function.
Number of survey respondents.
Number of alternatives per choice question.
Number of questions per respondent.
Number of blocks used in Orthogonal or Bayesian D-efficient
designs. Max allowable is one block per respondent. Defaults to 1,
meaning every respondent sees the same choice set.
Number of draws used in simulating the prior distribution used
in Bayesian D-efficient designs. Defaults to 50.
A numeric value indicating the number of random start designs
to use in obtaining a Bayesian D-efficient design. The default is 5.
Increasing n_start can result in a more efficient design at the expense
of increased computational time.
Include a "no choice" option in the choice sets? Defaults to
FALSE. If TRUE, the total number of alternatives per question will be
one more than the provided n_alts argument.
The name of the variable to use in a "labeled" design (also
called an "alternative-specific design") such that each set of alternatives
contains one of each of the levels in the label attribute. Currently not
compatible with Bayesian D-efficient designs. If used, the n_alts
argument will be ignored as its value is defined by the unique number of
levels in the label variable. Defaults to NULL.
Choose the design method to use: "random", "full",
"orthogonal", "dopt", "CEA", or "Modfed". Defaults to "random".
See details below for complete description of each method.
A list of one or more assumed prior parameters used to generate
a Bayesian D-efficient design. Defaults to NULL
Prior utility value for the "no choice" alternative.
Only required if no_choice = TRUE. Defaults to NULL.
If TRUE, for Bayesian D-efficient designs the resulting design
includes average predicted probabilities for each alternative in each
choice set given the sample from the prior preference distribution.
Defaults to FALSE.'
If TRUE, for D-optimal designs (method = "dopt") the
returned object will be a list containing the design and the D-efficiency
score. Defaults to FALSE.
If TRUE, for Bayesian D-efficient designs the
returned object will be a list containing the design and the DB-error
score. Defaults to FALSE.
A numeric value indicating the maximum number allowed iterations when searching for a Bayesian D-efficient design. The default is 50.
Logical value indicating whether computations should be done
over multiple cores. The default is FALSE.
The returned design data frame contains a choice-based conjoint
survey design where each row is an alternative. It includes the following
columns:
profileID: Identifies the profile in profiles.
respID: Identifies each survey respondent.
qID: Identifies the choice question answered by the respondent.
altID:Identifies the alternative in any one choice observation.
obsID: Identifies each unique choice observation across all respondents.
blockID: If blocking is used, identifies each unique block.
The method argument determines the design method used. Options
are:
"random"
"full"
"orthogonal"
"dopt"
"CEA"
"Modfed"
All methods ensure that the two following criteria are met:
No two profiles are the same within any one choice set.
No two choice sets are the same within any one respondent.
The table below summarizes method compatibility with other design options, including the ability to include a "no choice" option, the creation of a "labeled" design (also called a "alternative-specific" design), the use of restricted profile, and the use of blocking.
| Method | Include "no choice"? | Labeled designs? | Restricted profiles? | Blocking? |
"random" | Yes | Yes | Yes | No |
"full" | Yes | Yes | Yes | Yes |
"orthogonal" | Yes | No | No | Yes |
"dopt" | Yes | No | Yes | Yes |
"CEA" | Yes | No | No | Yes |
"Modfed" | Yes | No | Yes | Yes |
The "random" method (the default) creates a design where choice sets are
created by randomly sampling from the full set of profiles *with
*replacement. This means that few (if any) respondents will see the same
sets of choice sets. This method is less efficient than other approaches
and may lead to a deficient experiment in smaller sample sizes, though it
guarantees equal ability to estimate main and interaction effects.
The "full" method for ("full factorial") creates a design where choice
sets are created by randomly sampling from the full set of profiles
without replacement. The choice sets are then repeated to meet the
desired number of survey respondents (determined by n_resp). If blocking
is used, choice set blocks are created using mutually exclusive subsets of
profiles within each block. This method produces a design with similar
performance with that of the "random" method, except the choice sets are
repeated and thus there will be many more opportunities for different
respondents to see the same choice sets. This method is less efficient than
other approaches and may lead to a deficient experiment in smaller sample
sizes, though it guarantees equal ability to estimate main and interaction
effects. For more information about blocking with full factorial designs,
see ?DoE.base::fac.design as well as the JSS article on the DoE.base
package (Grömping, 2018).
The "orthogonal" method creates a design where an orthogonal array from
the full set of profiles is found and then choice sets are created by
randomly sampling from this orthogonal array without replacement. The
choice sets are then repeated to meet the desired number of survey
respondents (determined by n_resp). If blocking is used, choice set
blocks are created using mutually exclusive subsets of the orthogonal array
within each block. For cases where an orthogonal array cannot be found, a
full factorial design is used. This approach is also sometimes called a
"main effects" design since orthogonal arrays focus the information on the
main effects at the expense of information about interaction effects. For
more information about orthogonal designs, see ?DoE.base::oa.design as
well as the JSS article on the DoE.base package (Grömping, 2018).
The "dopt" method creates a "D-optimal" design where an array from
profiles is found that maximizes the D-efficiency of a linear model
using the Federov algorithm, with the total number of unique choice sets
determined by n_q*n_blocks. Choice sets are then created by randomly
sampling from this array without replacement. The choice sets are then
repeated to meet the desired number of survey respondents (determined by
n_resp). If blocking is used, choice set blocks are created from the
D-optimal array. For more information about the underlying algorithm
for this method, see ?AlgDesign::optFederov.
The "CEA" and "Modfed" methods use the specified priors to create a
Bayesian D-efficient design for the choice sets, with the total number of
unique choice sets determined by n_q*n_blocks. The choice sets are then
repeated to meet the desired number of survey respondents (determined by
n_resp). If "CEA" or "Modfed" is used without specifying priors, a
prior of all 0s will be used and a warning message stating this will be
shown. In the opposite case, if priors are specified but neither Bayesian
method is used, the "CEA" method will be used and a warning stating this
will be shown. Restricted sets of profiles can only be used with
"Modfed". For more details on Bayesian D-efficient designs, see
?idefix::CEA and ?idefix::Modfed as well as the JSS article on the
idefix package (Traets et al, 2020).
Grömping, U. (2018). R Package DoE.base for Factorial Experiments. Journal of Statistical Software, 85(5), 1–41 doi:10.18637/jss.v085.i05
Traets, F., Sanchez, D. G., & Vandebroek, M. (2020). Generating Optimal Designs for Discrete Choice Experiments in R: The idefix Package. Journal of Statistical Software, 96(3), 1–41, doi:10.18637/jss.v096.i03
Wheeler B (2022)._AlgDesign: Algorithmic Experimental Design. R package version 1.2.1, https://CRAN.R-project.org/package=AlgDesign.
library(cbcTools)
# A simple conjoint experiment about apples
# Generate all possible profiles
profiles <- cbc_profiles(
price = c(1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5),
type = c("Fuji", "Gala", "Honeycrisp"),
freshness = c('Poor', 'Average', 'Excellent')
)
# Make a survey by randomly sampling from all possible profiles
# (This is the default setting where method = 'random')
design_random <- cbc_design(
profiles = profiles,
n_resp = 100, # Number of respondents
n_alts = 3, # Number of alternatives per question
n_q = 6 # Number of questions per respondent
)
# Make a survey using a full factorial design and include a "no choice" option
design_full <- cbc_design(
profiles = profiles,
n_resp = 100, # Number of respondents
n_alts = 3, # Number of alternatives per question
n_q = 6, # Number of questions per respondent
method = 'full', # Change this to use a different method, e.g. 'orthogonal', or 'dopt'
no_choice = TRUE
)
# Make a survey by randomly sampling from all possible profiles
# with each level of the "type" attribute appearing as an alternative
design_random_labeled <- cbc_design(
profiles = profiles,
n_resp = 100, # Number of respondents
n_alts = 3, # Number of alternatives per question
n_q = 6, # Number of questions per respondent
label = "type"
)
# Make a Bayesian D-efficient design with a prior model specified
# Note that by speed can be improved by setting parallel = TRUE
design_bayesian <- cbc_design(
profiles = profiles,
n_resp = 100, # Number of respondents
n_alts = 3, # Number of alternatives per question
n_q = 6, # Number of questions per respondent
n_start = 1, # Defaults to 5, set to 1 here for a quick example
priors = list(
price = -0.1,
type = c(0.1, 0.2),
freshness = c(0.1, 0.2)
),
method = "CEA",
parallel = FALSE
)
#> Bayesian D-efficient design found with DB-error of 1.3571