ei.reg {eiPack} | R Documentation

## 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 <olivia.lau@post.harvard.edu> and Ryan T. Moore <rtm@wustl.edu>

### References

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

[Package eiPack version 0.1-6 Index]