mlr: Bayesian Multinomial Logistic Regression

Description

Inference for Bayesian multinomial logistic regression models by Gibbs sampling from the Bayesian posterior distribution.

Usage

mlr(y, X, n=rep(1,nrow(as.matrix(y))),
                   m.0=array(0, dim=c(ncol(X), ncol(y))),
                   P.0=array(diag(0, ncol(X)), dim=c(ncol(X),ncol(X),ncol(y))),
                   samp=1000, burn=500, float=0, device=0, parameters=NULL)

Arguments

an N x J-1 dimensional matrix; \(y_{ij}\) is the average response for category j at \(x_i\).

an N x P dimensional design matrix; \(x_i\) is the ith row.

an N dimensional vector; \(n_i\) is the total number of observations at each \(x_i\).

m.0

a P x J-1 matrix with the \(\beta_j\)'s prior means.

P.0

a P x P x J-1 array of matrices with the \(\beta_j\)'s prior precisions.

samp

the number of MCMC iterations saved.

burn

the number of MCMC iterations discarded.

float

a number representing the degree of precision to use: for single-precision floating point use 0, for or double-precision floating point use 1.

device

if no external pointer is provided to function, we can provide the ID of the device to use.

parameters

a 9 dimensional vector of parameters to tune the GPU implementation.

Value

mlr returns a list.

beta

a samp x P x J-1 array; the posterior sample of the regression coefficients.

a samp x N' x J-1 array; the posterior sample of the latent variable. WARNING: N' may be less than N if data is combined.

the response matrix--different than input if data is combined.

the design matrix--different than input if data is combined.

the number of samples at each observation--different than input if data is combined.

Details

Classic multinomial logistic regression for classifiction. We assume that \(\beta_J = 0\) for purposes of identification.

Examples

Run this code


## Use the iris dataset.
data(iris)
N <- nrow(iris)
P <- ncol(iris)
J <- nlevels(iris$Species)

X     <- model.matrix(Species ~ ., data=iris);
y.all <- model.matrix(~ Species - 1, data=iris);
y     <- y.all[,-J];

out <- mlr(y, X, samp=1000, burn=100, device=0);