Built using Zelig version 5.1.4.90000

Ecological Inference Model by Maximum Likelihood with eiml in ZeligEI.

## Syntax

The EI models accept several different formula syntaxes. If $$C1$$ and $$C2$$ are the column totals, and $$R1$$ and $$R2$$ are the row totals, and $$N=R1_i + R2_i = C1_i + C2_i$$ is the total in unit $$i$$, then the formula can be expressed with just one row and one column, with the totals provided separately as:

z.out <- zelig(C1 ~ R1, N = N, data = data)

The argument N can be either a numeric vector of the total in each i-th unit, or the character name of a variable in the dataset that contains these values.

Or with both rows and columns coupled together, and omitting the totals:

z.out <- zelig(cbind(C1,C2) ~ cbind(R1,R2), data = data)

Additionally, if C1, C2, R1, R2 are percentages rather than counts, then either formula method above is acceptable, however, N must always be provided.

library(zeligverse)

Here is an example of all the syntax for the analysis using the first syntax method, and the direct use of the reference classes:

z5 <- zeiml$new() z5$zelig(C1 ~ R1, N = myN, weights = w, data = myData)

With the Zelig 4 compatibility wrappers this looks like:

z.out <- zelig(C1 ~ R1, N=N, model = "eiml", weights = w, data = myData)

## Examples

We’ll use a dataset from the ei package, of black and non-black turnout in 141 precincts.

library("ei", quietly=TRUE)
data(sample)

Here is the model estimated in Zelig.

z.out <- zeiml$new() z.out$zelig(t ~ x, N = "n", data = sample)
## [1] "Running 2x2 ei"
## Maximizing likelihood
## Importance Sampling..
summary(z.out)
## Model:
## $Erho ## [1] 0.5 ## ##$Esigma
## [1] 0.5
##
## $Ebeta ## [1] 0.5 ## ##$N
## [1] 75
##
## $Resamp ## [1] 21 ## ##$Maximum likelihood results in scale of estimation (and se's)
##         Bb0       Bw0       sigB       sigW       rho Zb Zw
##  -1.1533874 0.8214529 -2.2860101 -1.8816375 0.4128279  0  0
##   0.1018115 0.1017286  0.2494434  0.1572393 0.3651596  0  0
##
## $Untruncated psi's ## BB BW SB SW RHO ## 0.1955265 0.7227119 0.1069191 0.1531497 0.3520577 ## ##$Truncated psi's (ultimate scale)
##         BB        BW         SB        SW       RHO
##  0.2031422 0.7139941 0.09837747 0.1418888 0.2960979
##
## $Aggregate Bounds ## betab betaw ## lower 0.09549504 0.3979843 ## upper 0.60893461 0.8031228 ## ##$Estimates of Aggregate Quantities of Interest
##         mean          sd
## Bb 0.2028756 0.012304964
## Bw 0.7183923 0.009709447
##
## \$precision
## [1] 4
##
## attr(,"class")
## [1] "summary"

This model is part of the ei package by Gary King and Molly Roberts. Advanced users may wish to refer to help(ei) in the ei package.