SeqCEA {idefix}

Sequential Coordinate Exchange algorithm for MNL model.

Description

Selects the choice set that minimizes the DB-error when added to an initial design, given (updated) parameter values.

Usage

SeqCEA(
  des = NULL,
  lvls,
  coding,
  c.lvls = NULL,
  n.alts,
  par.draws,
  prior.covar,
  alt.cte = NULL,
  no.choice = NULL,
  weights = NULL,
  parallel = TRUE,
  reduce = TRUE,
  n.cs = NULL
)

Arguments

des

A design matrix in which each row is a profile. If alternative specific constants are present, those should be included as the first column(s) of the design. Can be generated with Modfed or CEA

lvls

A numeric vector which contains for each attribute the number of levels.

coding

Type of coding that needs to be used for each attribute.

c.lvls

A list containing numeric vectors with the attribute levels for each continuous attribute. The default is NULL.

n.alts

Numeric value indicating the number of alternatives per choice set.

par.draws

A matrix or a list, depending on alt.cte.

prior.covar

Covariance matrix of the prior distribution.

alt.cte

A binary vector indicating for each alternative whether an alternative specific constant is desired. The default is NULL.

no.choice

An integer indicating the no choice alternative. The default is NULL.

weights

A vector containing the weights of the draws. Default is NULL. See also ImpsampMNL.

parallel

Logical value indicating whether computations should be done over multiple cores.

reduce

Logical value indicating whether the candidate set should be reduced or not.

n.cs

An integer indicating the number of possible random choice sets to consider in the search for the next best choice set possible. The default is NULL.

Details

This algorithm is ideally used in an adaptive context. The algorithm will select the next DB-efficient choice set given parameter values and possible previously generated choice sets. In an adaptive context these parameter values are updated after each observed response.

Previously generated choice sets, which together form an initial design, can be provided in des. When no design is provided, the algorithm will select the most efficient choice set based on the fisher information of the prior covariance matrix prior.covar.

If alt.cte = NULL, par.draws should be a matrix in which each row is a sample from the multivariate parameter distribution. In case that alt.cte is not NULL, a list containing two matrices should be provided to par.draws. The first matrix containing the parameter draws for the alternative specific parameters. The second matrix containing the draws for the rest of the parameters.

The list of potential choice sets is created by selecting randomly a level for each attribute in an alternative/profile. n.cs controls the number of potential choice sets to consider. The default is NULL, which means that the number of possible choice sets is the product of attribute levels considered in the experiment. For instance, an experiment with 3 attribute and 3 levels each will consider 3^3 = 27 possible choice sets.

The weights argument can be used when the par.draws have weights. This is for example the case when parameter values are updated using ImpsampMNL.

When parallel is TRUE, detectCores will be used to decide upon the number of available cores. That number minus 1 cores will be used to search for the optimal choice set. For small problems (6 parameters), parallel = TRUE can be slower. For larger problems the computation time will decrease significantly.

Note: this function is faster than SeqMOD, but the output is not as stable. This happens because this function makes a random search to get the choice set, whereas SeqMOD makes an exhaustive search.

Value

set

A matrix representing a DB efficient choice set.

error

A numeric value indicating the DB-error of the whole design.

References

Traets F, Sanchez G, Vandebroek M (2020). “Generating Optimal Designs for Discrete Choice Experiments in R: The idefix Package.” Journal of Statistical Software, 96(3).

Yu J, Goos P, Vandebroek M (2011). “Individually adapted sequential Bayesian conjoint-choice designs in the presence of consumer heterogeneity.” https://www.sciencedirect.com/science/article/pii/S0167811611000668.

Meyer RK, Nachtsheim CJ (1995). “The Coordinate-Exchange Algorithm for Constructing Exact Optimal Experimental Designs.” Technometrics, 37(1), 60–69. ISSN 00401706, https://www.jstor.org/stable/1269153.

Kessels R, Jones B, Goos P, Vandebroek M (2009). “An Efficient Algorithm for Constructing Bayesian Optimal Choice Designs.” Journal of Business & Economic Statistics, 27(2), 279–291. ISSN 07350015.

Examples

# DB efficient choice set, given a design and parameter draws. 
# 3 attributes with 3 levels each
m <- c(0.3, 0.2, -0.3, -0.2, 1.1, 2.4) # mean (total = 6 parameters).
pc <- diag(length(m)) # covariance matrix
set.seed(123)
sample <- MASS::mvrnorm(n = 10, mu = m, Sigma = pc)
# Initial design.
des <- example_design
# Efficient choice set to add.
SeqCEA(des = des, lvls = c(3, 3, 3), coding = c("D", "D", "D"), n.alts = 2,
       par.draws = sample, prior.covar = pc, parallel = FALSE)

# DB efficient choice set, given parameter draws. 
# with alternative specific constants 
des <- example_design2
ac <- c(1, 1, 0) # Alternative specific constants.
m <- c(0.3, 0.2, -0.3, -0.2, 1.1, 2.4, 1.8, 1.2) # mean
pc <- diag(length(m)) # covariance matrix
pos <- MASS::mvrnorm(n = 10, mu = m, Sigma = pc)
sample <- list(pos[ , 1:2], pos[ , 3:8])
# Efficient choice set.
SeqCEA(des = des, lvls = c(3, 3, 3), coding = c("D", "D", "D"), n.alts = 3, 
      par.draws = sample, alt.cte = ac, prior.covar = pc, parallel = FALSE)