BayesLogit (version 0.3)

mlogit: Bayesian Multinomial Logistic Regression

Description

Run a Bayesian multinomial logistic regression.

Usage

mlogit(y, X, n=rep(1,nrow(as.matrix(y))),
       m.0=array(0, dim=c(ncol(X), ncol(y))),
       P.0=array(0, dim=c(ncol(X), ncol(X), ncol(y))),
       samp=1000, burn=500)

Arguments

y

An N x J-1 dimensional matrix; $y_{ij}$ is the average response for category j at $x_i$.

X

An N x P dimensional design matrix; $x_i$ is the ith row.

n

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.

Value

• mlogit returns a list.
• beta
  A samp x P x J-1 array; the posterior sample of the regression coefficients.
• w
  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.
• y
  The response matrix--different than input if data is combined.
• X
  The design matrix--different than input if data is combined.
• n
  The number of samples at each observation--different than input if data is combined.

Details

Multinomial logistic regression is a classifiction mechanism. Given the multinomial data ${y_i}$ with J categories and the p-dimensional predictor variables ${x_i}$, one wants to forecast whether a future data point y* at the predictor x*. Multinomial Logistic regression stiuplates that the statistical model for observing a draw category j after rolling the multinomial die $n^*=1$ time is governed by

$$P(y^* = j | x^*, \beta, n^*=1) = e^{x^* \beta_j} / \sum_{k=1}^J e^{x^* \beta_k}.$$

Instead of representing data as the total number of responses in each category, one may record the average number of responses in each category and the total number of responses $n_i$ at $x_i$. We follow this method of encoding data.

We assume that $\beta_J = 0$ for purposes of identification!

You may use mlogit for binary logistic regression with a normal prior.

References

Nicholas G. Polson, James G. Scott, and Jesse Windle. Bayesian inference for logistic models using Polya-Gamma latent variables. http://arxiv.org/abs/1205.0310

See Also

rpg, logit.EM, logit

Examples

## 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 = mlogit(y, X, samp=1000, burn=100);