idefix (version 0.2.4)

Modfed: Modified Federov algorithm for MNL models.

Description

The algorithm swaps every profile of an initial design with candidate profiles. By doing this it tries to minimize the D(B)-error, based on a multinomial logit model.

Usage

Modfed(cand.set, n.sets, n.alts, alt.cte, par.draws, start.des = NULL,
  max.iter = Inf)

Arguments

cand.set

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

n.sets

Numeric value indicating the number of choice sets.

n.alts

Numeric value indicating the number of alternatives per choice set.

alt.cte

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

par.draws

A numeric vector containing the parameter values, or a numeric matrix in which each row is a draw from the multivariate prior parameter distribution.

start.des

A matrix in which each row is a profile. The number of rows equals n.sets * n.alts, and the number of columns equals the number of columns of cand.set. If not specified a random start design will be generated.

max.iter

A numeric value indicating the maximum number allowed iterations.

Value

design

A numeric matrix wich contains an efficient design.

error

Numeric value indicating the D(B)-error of the design.

inf.error

Numeric value indicating the percentage of draws for which the D-error was Inf.

prob.diff

Numeric value indicating the difference between the alternative with the highest and the one with the lowest probability for each choice set. If a sample matrix was provided this is based on the average over all draws.

Details

Each iteration will loop through all profiles from the initial design, evaluating the change in D(B)-error for every profile from cand.set. The algorithm stops when an iteration occured without replacing a profile or when max.iter is reached.

By specifying a numeric vector in par.draws, the D-error will be calculated and the design will be optimised locally. By specifying a matrix, in which each row is a draw from a multivariate distribution, the DB-error will be calculated, and the design will be optimised globally. The number of columns should equal the number of parameter in alt.cte + the number of parameters in cand.set. This is also the order in which they should be sorted (first alt.cte parameters).

The DB-error is calculated by taking the mean over D-errors. It could be that for some draws the design results in an infinite D-error. The percentage of draws for which this was true for the final design can be found in the output inf.error.

Alternative specific constants can be specified in alt.cte. The lenght of this binary vector should equal n.alts, were 0 indicates the absence of an alternative specific constant and 1 the opposite.

References

federovmnldes

Examples

# NOT RUN {
# D-efficient design
# 3 Attributes, 2 are dummy coded and 1 continuous (= 3 parameters).
cs <- Profiles(lvls = c(2, 3, 2), coding = c("D", "C", "D"), c.lvls = list(c(2, 4, 6)))
ps <- c(0.8, 0.2, -0.3) # Prior parameter vector
Modfed(cand.set = cs, n.sets = 8, n.alts = 2, alt.cte = c(0, 0), par.draws = ps)

# DB-efficient design. 
# 3 Attributes with 2, 3 and 2 levels, all effect coded (= 4 parameters).
cs <- Profiles(lvls = c(2, 3, 2), coding = c("E", "E", "E")) 
m <- c(0.8, 0.2, -0.3, -0.2, 0.7) # Prior mean (total = 5 parameters).
v <- diag(length(m)) # Prior variance.
set.seed(123) 
ps <- MASS::mvrnorm(n = 10, mu = m, Sigma = v) # 10 draws.
Modfed(cand.set = cs, n.sets = 8, n.alts = 2, alt.cte = c(1, 0), par.draws = ps)
# }