reglogit (version 1.2-5)

predict.reglogit: Prediction for regularized (polychotomous) logistic regression models

Description

Sampling from the posterior predictive distribution of a regularized (multinomial) logistic regression fit, including entropy information for variability assessment

Usage

# S3 method for reglogit
predict(object, XX, burnin = round(0.1 * nrow(object$beta)), ...)
# S3 method for regmlogit
predict(object, XX, burnin = round(0.1 * dim(object$beta)[1]), ...)

Arguments

object

a "reglogit"-class object or a "regmlogit"-class object, depending on whether binary or polychotomous methods were used for fitting

XX

a matrix of predictive locations where ncol(XX) == object$ncol(XX).

burnin

a scalar positive integer indicate the number of samples of object$beta to discard as burn-in; the default is 10% of the number of samples

...

For compatibility with generic predict method; not used

Value

The output is a list with components explained below. For predict.regmlogit everyhing (except entropy) is expanded by one dimension into an array or matrix as appropriate.

p

a nrow(XX) x (T-burnin) sized matrix of probabilities (of class 1) from the posterior predictive distribution.

mp

a vector of average probablities calculated over the rows of p

pc

class labels formed by rouding (or arg max for predict.regmlogit) the values in mp

ent

The posterior mean entropy given the probabilities in mp

Details

Applies the logit transformation (reglogit) or multinomial logit (regmlogit) to convert samples of the linear predictor at XX into a samples from a predictive posterior probability distribution. The raw probabilties, averages (posterior means), entropies, and posterior mean casses (arg-max of the average probabilities) are returned.

References

R.B. Gramacy, N.G. Polson. “Simulation-based regularized logistic regression”. (2012) Bayesian Analysis, 7(3), p567-590; arXiv:1005.3430; http://arxiv.org/abs/1005.3430

C. Holmes, K. Held (2006). “Bayesian Auxilliary Variable Models for Binary and Multinomial Regression”. Bayesian Analysis, 1(1), p145-168.

See Also

reglogit and regmlogit

Examples

# NOT RUN {
## see reglogit for a full example of binary classifiction complete with
## sampling from the posterior predictive distribution.  

## the example here is for polychotomous classification and prediction

# }
# NOT RUN {
library(plgp)
x <- seq(-2, 2, length=40)
X <- expand.grid(x, x)
C <- exp2d.C(X)
xx <- seq(-2, 2, length=100)
XX <- expand.grid(xx, xx)
CC <- exp2d.C(XX)

## build cubically-expanded design matrix (with interactions)
Xe <- cbind(X, X[,1]^2, X[,2]^2, X[,1]*X[,2],
            X[,1]^3, X[,2]^3, X[,1]^2*X[,2], X[,2]^2*X[,1],
            (X[,1]*X[,2])^2)

## perform MCMC
T <- 1000
out <- regmlogit(T, C, Xe, nu=6, normalize=TRUE)

## create predictive (cubically-expanded) design matrix
XX <- as.matrix(XX)
XXe <- cbind(XX, XX[,1]^2, XX[,2]^2, XX[,1]*XX[,2],
             XX[,1]^3, XX[,2]^3, XX[,1]^2*XX[,2], XX[,2]^2*XX[,1],
             (XX[,1]*XX[,2])^2)

## predict class labels
p <- predict(out, XXe)

## make an image of the predictive surface
cols <- c(gray(0.85), gray(0.625), gray(0.4))
par(mfrow=c(1,3))
image(xx, xx, matrix(CC, ncol=length(xx)), col=cols, main="truth")
image(xx, xx, matrix(p$c, ncol=length(xx)), col=cols, main="predicted")
image(xx, xx, matrix(p$ent, ncol=length(xx)), col=heat.colors(128),
      main="entropy")
# }