SeqKL {idefix}

Sequential Kullback-Leibler based algorithm for the MNL model.

Description

Selects the choice set that maximizes the Kullback-Leibler divergence between the prior parameter values and the expected posterior, assuming a MNL model.

Usage

SeqKL(
  des = NULL,
  cand.set,
  n.alts,
  par.draws,
  alt.cte = NULL,
  no.choice = NULL,
  weights = NULL,
  allow.rep = FALSE
)

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.

cand.set

A numeric matrix in which each row is a possible profile. The Profiles function can be used to generate this matrix.

n.alts

Numeric value indicating the number of alternatives per choice set.

par.draws

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

alt.cte

A binary vector indicating for each alternative if an alternative specific constant is desired.

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.

allow.rep

Logical value indicating whether repeated choice sets are allowed in the design.

Details

This algorithm is ideally used in an adaptive context. The algorithm selects the choice set that maximizes the Kullback-Leibler divergence between prior and expected posterior. Otherwisely framed the algorithm selects the choice set that maximizes the expected information gain.

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 are created using combn. 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.

Value

set

Numeric matrix containing the choice set that maximizes the expected KL divergence.

kl

Numeric value which is the Kullback leibler divergence.

References

Crabbe M, Akinc D, Vandebroek M (2014). “Fast algorithms to generate individualized designs for the mixed logit choice model.” https://www.sciencedirect.com/science/article/pii/S0191261513002178.

Examples

# KL efficient choice set, given parameter draws. 
# Candidate profiles 
cs <- Profiles(lvls = c(3, 3), coding = c("E", "E"))
m <- c(0.3, 0.2, -0.3, -0.2) # Prior mean (4 parameters).
pc <- diag(length(m)) # Prior variance
set.seed(123)
ps <- MASS::mvrnorm(n = 10, mu = m, Sigma = pc) # 10 draws.
# Efficient choice set to add. 
SeqKL(cand.set = cs, n.alts = 2, alt.cte = NULL, par.draws = ps, weights = NULL)

# KL efficient choice set, given parameter draws. 
# Candidate profiles 
cs <- Profiles(lvls = c(3, 3), coding = c("C", "E"), c.lvls = list(c(5,3,1)))
m <- c(0.7, 0.3, -0.3, -0.2) # Prior mean (4 parameters).
pc <- diag(length(m)) # Prior variance
set.seed(123)
ps <- MASS::mvrnorm(n = 10, mu = m, Sigma = pc) # 10 draws.
sample <- list(ps[ , 1], ps[ , 2:4])
ac <- c(1, 0) # Alternative specific constant. 
# Efficient choice set to add. 
SeqKL(cand.set = cs, n.alts = 2, alt.cte = ac, par.draws = sample, weights = NULL)