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
)
```

- profiles
A data frame in which each row is a possible profile. This can be generated using the

`cbc_profiles()`

function.- n_resp
Number of survey respondents.

- n_alts
Number of alternatives per choice question.

- n_q
Number of questions per respondent.

- n_blocks
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.- n_draws
Number of draws used in simulating the prior distribution used in Bayesian D-efficient designs. Defaults to

`50`

.- n_start
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.- no_choice
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.- label
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`

.- method
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.- priors
A list of one or more assumed prior parameters used to generate a Bayesian D-efficient design. Defaults to

`NULL`

- prior_no_choice
Prior utility value for the "no choice" alternative. Only required if

`no_choice = TRUE`

. Defaults to`NULL`

.- probs
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`

.'- keep_d_eff
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`

.- keep_db_error
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`

.- max_iter
A numeric value indicating the maximum number allowed iterations when searching for a Bayesian D-efficient design. The default is 50.

- parallel
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`0`

s 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 1.28407
```