bayesm (version 3.1-6)

rhierBinLogit: MCMC Algorithm for Hierarchical Binary Logit

Description

This function has been deprecated. Please use rhierMnlRwMixture instead.

rhierBinLogit implements an MCMC algorithm for hierarchical binary logits with a normal heterogeneity distribution. This is a hybrid sampler with a RW Metropolis step for unit-level logit parameters.

rhierBinLogit is designed for use on choice-based conjoint data with partial profiles. The Design matrix is based on differences of characteristics between two alternatives. See Appendix A of Bayesian Statistics and Marketing for details.

Usage

rhierBinLogit(Data, Prior, Mcmc)

Value

A list containing:

Deltadraw

\(R/keep x nz*nvar\) matrix of draws of Delta

betadraw

\(nlgt x nvar x R/keep\) array of draws of betas

Vbetadraw

\(R/keep x nvar*nvar\) matrix of draws of Vbeta

llike

\(R/keep x 1\) vector of log-like values

reject

\(R/keep x 1\) vector of reject rates over nlgt units

Arguments

Data

list(lgtdata, Z)

Prior

list(Deltabar, ADelta, nu, V)

Mcmc

list(R, keep, sbeta)

Author

Peter Rossi, Anderson School, UCLA, .

Details

Model and Priors

\(y_{hi} = 1\) with \(Pr = exp(x_{hi}'\beta_h) / (1+exp(x_{hi}'\beta_h)\) and \(\beta_h\) is \(nvar x 1\)
\(h = 1, \ldots, length(lgtdata)\) units (or "respondents" for survey data)

\(\beta_h\) = ZDelta[h,] + \(u_h\)
Note: here ZDelta refers to Z%*%Delta with ZDelta[h,] the \(h\)th row of this product
Delta is an \(nz x nvar\) array

\(u_h\) \(\sim\) \(N(0, V_{beta})\).

\(delta = vec(Delta)\) \(\sim\) \(N(vec(Deltabar), V_{beta}(x) ADelta^{-1})\)
\(V_{beta}\) \(\sim\) \(IW(nu, V)\)

Argument Details

Data = list(lgtdata, Z) [Z optional]

lgtdata:	list of lists with each cross-section unit MNL data
lgtdata[[h]]$y:	\(n_h x 1\) vector of binary outcomes (0,1)
lgtdata[[h]]$X:	\(n_h x nvar\) design matrix for h'th unit
Z:	\(nreg x nz\) mat of unit chars (def: vector of ones)

Prior = list(Deltabar, ADelta, nu, V) [optional]

Deltabar:	\(nz x nvar\) matrix of prior means (def: 0)
ADelta:	prior precision matrix (def: 0.01I)
nu:	d.f. parameter for IW prior on normal component Sigma (def: nvar+3)
V:	pds location parm for IW prior on normal component Sigma (def: nuI)

Mcmc = list(R, keep, sbeta) [only R required]

R:	number of MCMC draws
keep:	MCMC thinning parm -- keep every keepth draw (def: 1)
sbeta:	scaling parm for RW Metropolis (def: 0.2)

References

For further discussion, see Chapter 5, Bayesian Statistics and Marketing by Rossi, Allenby, and McCulloch.

See Also

rhierMnlRwMixture

Examples

if(nchar(Sys.getenv("LONG_TEST")) != 0) {R=10000} else {R=10}
set.seed(66)

nvar = 5              ## number of coefficients
nlgt = 1000           ## number of cross-sectional units
nobs = 10             ## number of observations per unit
nz = 2                ## number of regressors in mixing distribution

Z = matrix(c(rep(1,nlgt),runif(nlgt,min=-1,max=1)), nrow=nlgt, ncol=nz)
Delta = matrix(c(-2, -1, 0, 1, 2, -1, 1, -0.5, 0.5, 0), nrow=nz, ncol=nvar)
iota = matrix(1, nrow=nvar, ncol=1)
Vbeta = diag(nvar) + 0.5*iota%*%t(iota)

lgtdata=NULL
for (i in 1:nlgt) { 
  beta = t(Delta)%*%Z[i,] + as.vector(t(chol(Vbeta))%*%rnorm(nvar))
  X = matrix(runif(nobs*nvar), nrow=nobs, ncol=nvar)
  prob = exp(X%*%beta) / (1+exp(X%*%beta)) 
  unif = runif(nobs, 0, 1)
  y = ifelse(unif