sahpmlm {sahpm}

This implements the stochastic search based on Simulated Anneling strategy.

Description

Highest posterior model is widely accepted as a good model among available models. In terms of variable selection highest posterior model is often the true model. Our stochastic search process SAHPM based on simulated annealing maximization method tries to find the highest posterior model by maximizing the model space with respect to the posterior probabilities of the models. This function currently contains the SAHPM method only for linear models. The codes for GLM will be added in future.

Usage

sahpmlm(formula, data, na.action, g = n, nstep = 200, abstol = 1e-07,
  replace = FALSE, burnin = FALSE, nburnin = 50)

Arguments

formula

an object of class formula (or one that can be coerced to that class): a symbolic description of the model to be fitted.

data

an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which lm is called.

na.action

a function which indicates what should happen when the data contain NAs. The default is set by the na.action setting of options, and is na.fail if that is unset. The “factory-fresh” default is na.omit. Another possible value is NULL, no action. Value na.exclude can be useful.

g

value of g for g prior. Default is sample size n.

nstep

maximum number of steps for simulated annealing search.

abstol

desired level of difference of marginal likelihoods between two steps.

replace

logical. If TRUE the replce step is considered in the search. Default is FALSE.

burnin

logical. If TRUE the burnin is added. Default is FALSE. Number of burnin is specified by the next input.

nburnin

Number of burnin (required if burnin = TRUE). Default is 50.

Details

The model is:

y= \alpha + X\beta+\epsilon, \epsilon \sim N(0,\sigma^2)

The Zellner's g prior is used with default g = n.

Value

final.model

A column vector which corresponds to the original variable indices.

history

A history of the search process. By columns: Step number, temperature, current objective function value, current minimal objective function value, current model, posterior probability of current model.

References

Maity, A., K., and Basu, S. Highest Posterior Model Computation and Variable Selection via the Simulated Annealing

Examples

require(mvtnorm)     # for multivariate normal distribution
n <- 100             # sample size
k <- 40              # number of variables
z <- as.vector(rmvnorm(1, mean = rep(0, n), sigma = diag(n)))
x <- matrix(NA, nrow = n, ncol = k)
for(i in 1:k)
{
x[, i] <- as.vector(rmvnorm(1, mean = rep(0, n), sigma = diag(n))) + z
}                    # this induce 0.5 correlation among the variables
beta <- c(rep(0, 10), rep(2, 10), rep(0, 10), rep(2, 10))
                     # vector of coefficients
sigma <- 1
sigma.square <- sigma^2
linear.pred <- x %*% beta
y <- as.numeric(t(rmvnorm(1, mean = linear.pred, sigma = diag(sigma.square, n))))
                     # response
answer <- sahpmlm(formula = y ~ x)
answer$final.model
answer$history


## Not run: 
# With small effect size
beta <- c(rep(0, 10), rep(1, 10), rep(0, 10), rep(1, 10))
                     # vector of coefficients

linear.pred <- x %*% beta
y <- as.numeric(t(rmvnorm(1, mean = linear.pred, sigma = diag(sigma.square, n))))
                     # response
answer <- sahpmlm(formula = y ~ x)
answer$final.model  # Might miss some of the true predictors
answer$history

# Able to recover all the predictors with 50 burnin
answer <- sahpmlm(formula = y ~ x, burnin = TRUE, nburnin = 50)
answer$final.model  # Misses some of the true predictors
answer$history

## End(Not run)