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,
erho = c(0.5, 3, 5, 0.1, 10),
esigma = 0.5,
ebeta = 0.5,
ealphab = NA,
ealphaw = NA,
truth = NA,
simulate = TRUE,
ndraws = 99,
nsims = 100,
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 name 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
ZbandZw.- erho
The standard deviation of the normal prior on \(\phi_5\) for the correlation. Numeric vector, used one at a time, in order. Default `c(.5, 3, 5, .1, 10)`.
- 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
eiPackfor options for RxC ei.- ndraws
integer. The number of draws. Default is 99.
- nsims
integer. The number of simulations within each draw. Default is 100.
- covariate
see documentation in
eiPackfor options for RxC ei.- lambda1
default = 4:see documentation in
eiPackfor options for RxC ei.- lambda2
default = 2:see documentation in
eiPackfor options for RxC ei.- covariate.prior.list
see documentation in
eiPackfor options for RxC ei.- tune.list
see documentation in
eiPackfor options for RxC ei.- start.list
see documentation in
eiPackfor options for RxC ei.- sample
default = 1000
- thin
default = 1
- burnin
default = 1000
- verbose
default = 0:see documentation in
eiPackfor options for RxC ei.- ret.beta
default = "r": see documentation in
eiPackfor options for RxC ei.- ret.mcmc
default = TRUE: see documentation in
eiPackfor options for RxC ei.- usrfun
see documentation in
eiPackfor 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).
References
Gary King (1997). A Solution to the Ecological Inference Problem. Princeton: Princeton University Press.
Examples
data(sample_ei)
form <- t ~ x
dbuf <- ei(form, total = "n", data = sample_ei)
#> ℹ Running 2x2 ei
#> ℹ Maximizing likelihood for `erho` = 0.5.
#> ℹ Running 2x2 ei
#> ℹ Maximizing likelihood for `erho` = 3.
#> ℹ Running 2x2 ei
#> ℹ Maximizing likelihood for `erho` = 5.
#> ℹ Running 2x2 ei
#> ℹ Maximizing likelihood for `erho` = 0.1.
#> ℹ Running 2x2 ei
#> ✔ Running 2x2 ei [4ms]
#>
#> ⠙ Beginning importance sampling.
#> ✔ Beginning importance sampling. [2.9s]
#>
summary(dbuf)
#>
#> ── Summary ─────────────────────────────────────────────────────────────────────
#>
#> ── Erho ──
#>
#> 0.1
#>
#>
#> ── Esigma ──
#>
#> 0.5
#>
#>
#> ── Ebeta ──
#>
#> 0.5
#>
#>
#> ── N ──
#>
#> 75
#>
#>
#> ── Resamp ──
#>
#> 30
#>
#>
#> ── Maximum likelihood results in scale of estimation (and se's) ──
#>
#> Bb0 Bw0 sigB sigW rho Zb0 Zw0
#> -1.1605918 0.8264157 -2.1410777 -1.8073480 0.03161319 0 0
#> 0.1175759 0.1130699 0.2519238 0.1606003 0.09794052 0 0
#>
#>
#> ── Untruncated psi's ──
#>
#> BB BW SB SW RHO
#> 0.1865717 0.732367 0.1260613 0.1664071 0.023376
#>
#>
#> ── Truncated psi's (ultimate scale) ──
#>
#> BB BW SB SW RHO
#> 0.2055475 0.712404 0.1102888 0.1489791 0.05493517
#>
#>
#> ── Aggregate Bounds ──
#>
#> betab betaw
#> lower 0.09549504 0.3979843
#> upper 0.60893461 0.8031228
#>
#>
#> ── Estimates of Aggregate Quantities of Interest ──
#>
#> mean sd
#> Bb 0.2051746 0.01457635
#> Bw 0.7165782 0.01150172
#>
#>
#> ── Precision ──
#>
#> 4
#>