ei.reg {eiPack}

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,\ldots,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, \ldots, R and i = 1, \ldots, n

• –T_{ci} = \sum_{r=1}^R \beta_{rci}X_{ri} for c = 1,\ldots,C and i = 1\ldots,n

Then regressing

T_{ci} = \beta_{rc} X_{ri} + \epsilon_{ci}

for c = 1,\dots,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 \times C matrix of estimated population cell fractions

se

an R \times 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.