ei {ei}

Ecological Inference Estimation

Description

ei is the main command in the package EI. It gives observation-level estimates (and various related statistics) of \beta_i^b and \beta_i^w given variables T_i and X_i (i=1,...,n) in this accounting identity: T_i=\beta_i^b*X_i + \beta_i^w*(1-X_i). Results are stored in an ei object, that can be read with summary() or eiread() and graphed in plot().

Usage

ei(formula, total = NULL, Zb = 1, Zw = 1, id = NA, data =NA, erho = 0.5, 
esigma = 0.5, ebeta = 0.5, ealphab = NA, ealphaw = NA, truth = NA, 
simulate = TRUE, covariate = NULL, lambda1 = 4, lambda2 = 2, 
covariate.prior.list = NULL, tune.list = NULL, start.list = NULL, 
sample = 1000, thin = 1, burnin = 1000, verbose = 0, ret.beta = "r", 
ret.mcmc = TRUE, usrfun = NULL)

Arguments

formula

A formula of the form t ~x in the 2x2 case and cbind(col1,col2,...) ~ cbind(row1,row2,...) in the RxC case.

total

‘total’ is the name of the variable in the dataset that contains the number of individuals in each unit

Zb

p x k^b matrix of covariates or the name of covariates in the dataset

Zw

p x k^w matrix of covariates or the name of covariates in the dataset

id

‘id’ is the nae of the variable in the dataset that identifies the precinct. Used for ‘movie’ and ‘movieD’ plot functions.

data

data frame that contains the variables that correspond to formula. If using covariates and data is specified, data should also contain Zb and Zw.

erho

The standard deviation of the normal prior on \phi_5 for the correlation. Default =0.5.

esigma

The standard deviation of an underlying normal distribution, from which a half normal is constructed as a prior for both \breve{\sigma}_b and \breve{\sigma}_w. Default = 0.5

ebeta

Standard deviation of the "flat normal" prior on \breve{B}^b and \breve{B}^w. The flat normal prior is uniform within the unit square and dropping outside the square according to the normal distribution. Set to zero for no prior. Setting to positive values probabilistically keeps the estimated mode within the unit square. Default=0.5

ealphab

cols(Zb) x 2 matrix of means (in the first column) and standard deviations (in the second) of an independent normal prior distribution on elements of \alpha^b. If you specify Zb, you should probably specify a prior, at least with mean zero and some variance (default is no prior). (See Equation 9.2, page 170, to interpret \alpha^b).

ealphaw

cols(Zw) x 2 matrix of means (in the first column) and standard deviations (in the second) of an independent normal prior distribution on elements of \alpha^w. If you specify Zw, you should probably specify a prior, at least with mean zero and some variance (default is no prior). (See Equation 9.2, page 170, to interpret \alpha^w).

truth

A length(t) x 2 matrix of the true values of the quantities of interest.

simulate

default = TRUE:see documentation in eiPack for options for RxC ei.

covariate

see documentation in eiPack for options for RxC ei.

lambda1

default = 4:see documentation in eiPack for options for RxC ei.

lambda2

default = 2:see documentation in eiPack for options for RxC ei.

covariate.prior.list

see documentation in eiPack for options for RxC ei.

tune.list

see documentation in eiPack for options for RxC ei.

start.list

see documentation in eiPack for options for RxC ei.

sample

default = 1000

thin

default = 1

burnin

default = 1000

verbose

default = 0:see documentation in eiPack for options for RxC ei.

ret.beta

default = "r": see documentation in eiPack for options for RxC ei.

ret.mcmc

default = TRUE: see documentation in eiPack for options for RxC ei.

usrfun

see documentation in eiPack for options for RxC ei.

Details

The EI algorithm is run using the ei command. A summary of the results can be seen graphically using plot(ei.object) or numerically using summary(ei.object). Quantities of interest can be calculated using eiread(ei.object).

Author(s)

Gary King <<email: [e-mail]>> and Molly Roberts <<email: [e-mail]>>

References

Gary King (1997). A Solution to the Ecological Inference Problem. Princeton: Princeton University Press.

Examples

data(sample)
form <- t ~ x
dbuf <- ei(form,total="n",data=sample)
summary(dbuf)