ei.reg.bayes {eiPack}

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

Details

For i \in 1,\ldots,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)\propto \sigma^{-2}.

The proper prior is p(\beta, \sigma^2|x) \propto I(\beta \in [0,1])\times \sigma^{-2}.

Value

A list containing

call

the call to ei.reg.bayes

draws

A, R \times C \times sample array containing posterior draws for each population cell fraction

Author(s)

Olivia Lau <[e-mail]> and Ryan T. Moore <[e-mail]>

References

Leo Goodman. 1953. “Ecological Regressions and the Behavior of Individuals.” American Sociological Review 18:663–664.