eiPack (version 0.1-7)

ei.reg.bayes: Ecological regression using Bayesian Normal regression

Description

Estimate an ecological regression using Bayesian normal regression.

Usage

ei.reg.bayes(formula, data, sample = 1000, weights = NULL, truncate=FALSE)

Arguments

formula

An R formula object of the form cbind(c1, c2, ...) ~ cbind(r1, r2, ...)

data

data frame containing the variables specified in formula

sample

number of draws from the posterior

weights

a vector of weights

truncate

if TRUE, imposes a proper uniform prior on the unit hypercube for the coefficients; if FALSE, an improper uniform prior is assumed

Value

call

the call to ei.reg.bayes

draws

A, $R x C x$ sample array containing posterior draws for each population cell fraction

Details

For $i in 1,...,C$, $C$ Bayesian regressions of the form c_i ~ cbind(r1, r2, ...) are performed. See the documentation for ei.reg for the accounting identities and constancy assumption underlying this Bayesian linear model.

The sampling density is given by $$y|\beta, \sigma^2, X \sim N(X\beta, \sigma^2 I)$$

The improper prior is $p(beta,sigma^2|X) proportional to 1/sigma^2$.

The proper prior is $p(beta, sigma^2|x) proportional to I(beta in [0,1])* 1/sigma^2$.

References

Leo Goodman. 1953. ``Ecological Regressions and the Behavior of Individuals.'' American Sociological Review 18:663--664.