idefix (version 0.2.4)

ImpsampMNL: Importance sampling MNL

Description

This function samples from the posterior distribution using importance sampling, assuming a multivariate normal prior distribution and a MNL likelihood.

Usage

ImpsampMNL(prior.mean, prior.covar, des, n.alts, y, m, b = 2)

Arguments

prior.mean

Numeric vector indicating the mean of the multivariate normal distribution (prior).

prior.covar

Covariance matrix of the prior distribution.

des

A design matrix in which each row is a profile. Can be generated with Modfed

n.alts

Numeric value indicating the number of alternatives per choice set.

y

A binary response vector. RespondMNL can be used to simulate respons data.

m

Numeric value. Number of draws = base^m.

b

Numeric value indicating the base. The default = 2.

Value

sample

Numeric vector with the (unweigthted) draws from the posterior distribution.

weights

Numeric vector with the associated weights of the draws.

max

Numeric vector with the estimated mode of the posterior distribution.

covar

Matrix representing the estimated variance covariance matrix.

Examples

# NOT RUN {
# Importance sampling MNL 
pm <- c(0.8, 0.3, 0.2, -0.3, -0.2) # Prior mean (4 parameters).
pc <- diag(length(pm)) # Prior variance
cs <- Profiles(lvls = c(3, 3), coding = c("E", "E"))
ps <- MASS::mvrnorm(n = 10, mu = pm, Sigma = pc) # 10 draws.
# Efficient design. 
design <- Modfed(cand.set = cs, n.sets = 8, n.alts = 2, alt.cte = c(1,0), par.draws = ps)$design
# Respons.
resp <- RespondMNL(par = c(0.7, 0.6, 0.5, -0.5, -0.7), des = design, n.alts = 2)
# Parameters draws from posterior.
ImpsampMNL(prior.mean =  pm, prior.covar = pc, des = design, n.alts = 2, y = resp, m = 6)

# Importance sampling MNL
pm <- c(0.3, 0.2, -0.3, -0.2) # Prior mean (4 parameters).
pc <- diag(length(pm)) # Prior variance
cs <- Profiles(lvls = c(3, 3, 2), coding = c("D", "C", "D"), c.lvls = list(c(2,4,6)))
ac <- c(0, 0) # No alternative specific constants. 
ps <- MASS::mvrnorm(n = 10, mu = pm, Sigma = pc) # 10 draws.
# Efficient design. 
design <- Modfed(cand.set = cs, n.sets = 8, n.alts = 2, alt.cte = c(0,0), par.draws = ps)$design
# Respons
resp <- RespondMNL(par = c(0.6, 0.5, -0.5, -0.7), des = design, n.alts = 2)
# Parameters draws from posterior.
ImpsampMNL(prior.mean =  pm, prior.covar = pc, des = design, n.alts = 2, y = resp, m = 6)
# }