ei.reg: Ecological regression

In eiPack: Ecological Inference and Higher-Dimension Data Management

Ecological regression

Description

Estimate an ecological regression using least squares.

Usage

ei.reg(formula, data, ...)

Arguments

formula	An R formula object of the form cbind(c1, c2, ...) ~ cbind(r1, r2, ...)
data	data frame containing the variables specified in formula
...	Additional arguments passed to lm.

Details

For i in 1,...,C, C regressions of the form c_i ~ cbind(r1, r2, ...) are performed.

These regressions make use of the accounting identities and the constancy assumption, that beta_rci = beta_rc for all i.

The accounting identities include

• –defining the population cell fractions beta_rc such that sum_{c=1}^{C} beta_rc = 1 for every r

• –sum_{c=1}^{C} beta_rci = 1 for r = 1,...,R and i = 1,...,n

• –T_ci = sum_{r=1}^R beta_rci X_ri for c = 1,...,C and i = 1,...,n

Then regressing

T_ci = beta_rc X_ri + epsilon_ci

for c = 1,...C recovers the population parameters beta_rc when the standard linear regression assumptions apply, including E[epsilon_ci] = 0 and Var[epsilon_ci] = sigma_c^2 for all i.

Value

A list containing

call	the call to ei.reg
coefficients	an R x C matrix of estimated population cell fractions
se	an R x C matrix of standard errors for coefficients.
cov.matrices	A list of the C scaled variance-covariance matrices for each of the ecological regressions

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.

eiPack documentation built on March 7, 2023, 7:04 p.m.