Package 'ei'

Convert to ei_tbl objects

Description

Convert to ei_tbl objects

Usage

as_ei_tbl(x)

ei_as_ei_tbl(ei.object)

Arguments

x	an object to be coerced
ei.object	list-based ei object to convert to tibble-based object

Value

ei_tbl object

Examples

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

---

Black Literacy in 1910

Description

A dataset of aggregate literacy rates (t) and fraction of the population that is black (x), from the 1910 US Census. Each observation represents one county.

Format

A data frame containing 1030 observations.

Source

Gary King, 1997, "Replication data for: A Solution to the Ecological Inference Problem: Reconstructing Individual Behavior from Aggregate Data", http://hdl.handle.net/1902.1/LWMMKUTYXS UNF:3:DRWozWd89+vNLO7lY2AHbg== IQSS Dataverse Network Distributor V3 Version

References

Gary King. (1997). A Solution to the Ecological Inference Problem. Princeton: Princeton University Press. Section 13.2:241-5.

Robinson, William S. (1950). “Ecological Correlation and the Behavior of Individuals.” American Sociological Review 15:351-357.

---

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,
  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 Zb and Zw.
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 eiPack for 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 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).

Value

ei object

Author(s)

Gary King <<email: [email protected]>> and Molly Roberts <<email: [email protected]>>

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)
summary(dbuf)

---

Run (tidy) Ecological Inference Estimation and Simulation

Description

Run (tidy) Ecological Inference Estimation and Simulation

Usage

ei_(
  data,
  x,
  t,
  n,
  Zb = NULL,
  Zw = NULL,
  id = NA,
  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

data	data where x, t, total, Zb, Zw are found
x	<data-masking> column of subgroup proportions in data
t	<data-masking> column of turnout in data
n	<data-masking> column of total in data
Zb	<data-masking> columns of covariates in data
Zw	<data-masking> columns of covariates in data
id	<data-masking> column of unique ids in data
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 eiPack for 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 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.

Value

an ei_tbl

Examples

data(sample_ei)
dbuf <- ei_(sample_ei, x, t, n)

---

Run (tidy) Ecological Inference Estimation

Description

Run (tidy) Ecological Inference Estimation

Usage

ei_est(
  data,
  t,
  x,
  n,
  id = seq_len(nrow(data)),
  Zb = NULL,
  Zw = NULL,
  erho = 0.5,
  esigma = 0.5,
  ebeta = 0.5,
  ealphab = NA,
  ealphaw = NA,
  truth = NA
)

Arguments

data	data where x, t, total, Zb, Zw are found
t	<data-masking> column of turnout in data
x	<data-masking> column of subgroup proportions in data
n	<data-masking> column of total in data
id	<data-masking> column of unique ids in data
Zb	<data-masking> columns of covariates in data
Zw	<data-masking> columns of covariates in data
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).
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.

Value

ei_tbl

Examples

data(sample_ei)
dbuf <- ei_est(sample_ei, x, t, n)

---

Run Ecological Inference Simulation

Description

Run Ecological Inference Simulation

Usage

ei_sim(data, ndraws = 99, nsims = 100)

Arguments

data	an ei_tbl object from ei_est()
ndraws	integer, default 99. The number of draws.
nsims	integer, default 10. The number of simulations with each draw.

Value

ei_tbl

Examples

data(sample_ei)
dbuf <- ei_est(sample_ei, x, t, n) %>% ei_sim()

---

Computes Analytical Bounds from Accounting Identity

Description

Returns analytical bounds from accounting identity on unknown table relationships beta_b, beta_w, from known, observed, table marginals, x, t (and sample size n).

Usage

ei.bounds(x, t, n)

Arguments

x	vector of characteristics, e.g. percentage of blacks in each district
t	vector of characteristics, e.g. percentage of people that voted in each district
n	size of each observation, e.g. number of voters in each district

Value

a numeric matrix

Author(s)

Gary King <<email: [email protected]>> and Molly Roberts <<email: [email protected]>>

References

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

Examples

data(census1910)
output <- ei.bounds(x = census1910$x, t = census1910$t, n = census1910$n)

---

Simulate EI Solution via Importance Sampling

Description

Simulate EI Solution via Importance Sampling

Usage

ei.sim(ei.object, ndraws = 99, nsims = 100)

Arguments

ei.object	ei object
ndraws	integer. The number of draws. Default is 99.
nsims	integer. The number of simulations within each draw. Default is 100.

Value

ei.sim object

Author(s)

Gary King <<email: [email protected]>> and Molly Roberts <<email: [email protected]>>

References

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

Examples

data(sample_ei)
form <- t ~ x
ei_obj <- ei(form, total = "n", data = sample_ei, simulate = FALSE)
sims <- ei.sim(ei_obj)

---

Quantities of Interest from Ecological Inference Estimation

Description

eiread is the command that pulls quantities of interest from the ei object. The command returns a list of quantities of interest requested by the user.

Usage

eiread(ei.object, ...)

Arguments

ei.object	An ei object from the function ei.
...	A list of quantities of interest for eiread() to return. See values below.

Value

betab	$p$ x $1$ point estimate of $\beta_i^b$ based on its mean posterior. See section 8.2
betaw	$p$ x $1$ point estimate of $\beta_i^w$ based on its mean posterior. See section 8.2
sbetab	$p$ x $1$ standard error for the estimate of $\beta_i^b$, based on the standard deviation of its posterior. See section 8.2
sbetaw	$p$ x $1$ standard error for the estimate of $\beta_i^w$, based on the standard deviation of its posterior. See section 8.2
phi	Maximum posterior estimates of the CML
psisims	Matrix of random simulations of $\psi$. See section 8.2
bounds	$p$ x $4$: bounds on $\beta_i^b$ and $\beta_i^w$, lowerB ~ upperB ~ lowerW ~ upperW. See Chapter 5.
abounds	$2$ x $2$: aggregate bounds rows:lower, upper; columns: betab, betaw. See Chapter 5.
aggs	Simulations of district-level quantities of interest $\hat{B^b}$ and $\hat{B^w}$. See Section 8.3.
maggs	Point estimate of 2 district-level parameters, $\hat{B^b}$ and $\hat{B^w}$ based on the mean of aggs. See Section 8.3.
VCaggs	Variance matrix of 2 district-level parameters, $\hat{B^b}$ and $\hat{B^w}$. See Section 8.3.
CI80b	$p$ x $2$: lower~upper $80\%$ confidence intervals for $\beta_i^b$. See section 8.2.
CI80w	$p$ x $2$: lower~upper $80\%$ confidence intervals for $\beta_i^w$. See section 8.2.
eaggbias	Regressions of estimated $\beta_i^b$ and $\beta_i^w$ on a constant term and $X_i$.
goodman	Goodman's Regression. See Section 3.1

numeric values

Author(s)

Gary King <<email: [email protected]>> and Molly Roberts <<email: [email protected]>>

References

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

Examples

data(sample_ei)
formula <- t ~ x
dbuf <- ei(formula = formula, total = "n", data = sample_ei)
eiread(dbuf, "phi")
eiread(dbuf, "betab", "betaw")

---

RxC Sample Dataset

Description

Sample EI data for RxC with estimates for White, Black, and Hispanic groups.

Format

A data frame containing 93 observations.

Source

Sample data

References

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

---

Voter Transitions

Description

Aggregated data from 289 precincts in Fulton County, Georgia. The variable t represents the fraction voting in 1994 and x the fraction in 1992. Beta_b is then the fraction who vote in both elections, and Beta_w the fraction of nonvoters in 1992 who vote in the midterm election of 1994.

Format

A data frame containing 289 observations.

Source

Gary King, 1997, "Replication data for: A Solution to the Ecological Inference Problem: Reconstructing Individual Behavior from Aggregate Data", http://hdl.handle.net/1902.1/LWMMKUTYXS UNF:3:DRWozWd89+vNLO7lY2AHbg== IQSS Dataverse Network Distributor V3 Version

References

Gary King (1997). A Solution to the Ecological Inference Problem. Princeton: Princeton University Press. Section 13.1:235-41.

---

Turnout by Race in Louisiana

Description

The fraction of blacks registered voters (x) and fraction of voter turnout (t) in each Louisiana precinct, along with the true fraction of black turnout (tb) and non-black turnout (tw).

Format

A data frame containing 3262 observations.

Source

Gary King, 1997, "Replication data for: A Solution to the Ecological Inference Problem: Reconstructing Individual Behavior from Aggregate Data", http://hdl.handle.net/1902.1/LWMMKUTYXS UNF:3:DRWozWd89+vNLO7lY2AHbg== IQSS Dataverse Network Distributor V3 Version

References

Gary King (1997). A Solution to the Ecological Inference Problem. Princeton: Princeton University Press. Section 1.4:22-4.

---

Voter Registration by Race in Southern States

Description

Aggregate voter registration and fraction black, in counties in Florida, Louisiana, North Carolina and South Carolina

Format

A data frame containing 268 observations.

Source

Gary King, 1997, "Replication data for: A Solution to the Ecological Inference Problem: Reconstructing Individual Behavior from Aggregate Data", http://hdl.handle.net/1902.1/LWMMKUTYXS UNF:3:DRWozWd89+vNLO7lY2AHbg== IQSS Dataverse Network Distributor V3 Version

References

Gary King (1997). A Solution to the Ecological Inference Problem. Princeton: Princeton University Press. Chapter 10.

---

Nonminority Turnout in New Jersey

Description

New Jersey turnout and counts for White and non-white voters.

Format

A data frame containing 493 observations.

Source

Gary King, 1997, "Replication data for: A Solution to the Ecological Inference Problem: Reconstructing Individual Behavior from Aggregate Data", http://hdl.handle.net/1902.1/LWMMKUTYXS UNF:3:DRWozWd89+vNLO7lY2AHbg== IQSS Dataverse Network Distributor V3 Version

References

Gary King (1997). A Solution to the Ecological Inference Problem. Princeton: Princeton University Press. Section 1.4:24-5.

---

Visualizing EI (bound)

Description

Visualizing EI (bound)

Usage

plot_bound(ei.object, options = list())

Arguments

ei.object	The output of ei() (it should be used with the truth argument)
options	The list of options parameter: A parameter to plot. It takes either betab or betaw. This option is only for the 2x2 case.

Value

a ggplot object

Examples

# 2x2
data(matproii)
truth <- cbind(matproii$tb, matproii$tw)
suppressMessages({
  ei_res <- ei(formula = t ~ x, total = "n", truth = truth, data = matproii)
})
plot_bound(ei_res, options = list(parameter = "betab"))
plot_bound(ei_res, options = list(parameter = "betaw"))
# RxC
data(RxCdata)
formula <- cbind(turnout, noturnout) ~ cbind(white, black, hisp)
suppressMessages({
  ei_resRxC <- ei(formula, data = RxCdata)
})
plot_bound(ei_resRxC)

---

Get data used to create a plot

Description

Get data used to create a plot

Usage

plot_data(x)

Arguments

x	a plot object.

Value

a data.frame

---

Visualizing EI (density)

Description

Visualizing EI (density)

Usage

plot_density(ei.object, options = list(parameter = "betab"))

Arguments

ei.object	The output of ei()
options	The list of options parameter: A parameter to plot. It takes either betab or betaw.

Value

a ggplot object

Examples

data(matproii)
suppressMessages({
  ei_res <- ei(formula = t ~ x, total = "n", data = matproii)
})
plot_density(ei_res, options = list(parameter = "betab"))
plot_density(ei_res, options = list(parameter = "betaw"))

---

Visualizing EI (Shiny visualization)

Description

Visualizing EI (Shiny visualization)

Usage

plot_movie(ei.object)

Arguments

ei.object

The output of ei()

---

Visualizing EI (simulation)

Description

Visualizing EI (simulation)

Usage

plot_sims(ei.object)

Arguments

ei.object

The output of ei()

Value

a ggplot object

Examples

data(matproii)
suppressMessages({
  ei_res <- ei(formula = t ~ x, total = "n", data = matproii)
})
plot_sims(ei_res)

---

Visualizing EI (tomography plot)

Description

Tomography plot with various options.

Usage

plot_tomog(
  ei.object,
  options = list(color = TRUE, linecolor = "length", category = 0, breaks = "even", CI =
    NULL, points = FALSE, contour_ML = FALSE, contour_posterior = FALSE)
)

Arguments

ei.object

The output of ei()

options

The list of options color: Change the line color by linecolor option. linecolor: Focus of the line color, options are length, betab, and betaw. category: Categorize values to color lines. The default value 0 means that it does not categorize values. When creating categories, it uses the option breaks. breaks: How to create categories. Options are even and quantile. CI: Tomography plot with confidence intervals. The default value is 0.8 (80% CI). If it is NULL, CI will not be shown. points: Tomography plot with estimated mean posterior $\beta_i^b$ and $\beta_i^w$ points. contour_ML: Tomography plot with ML contours. contour_posterior: Tomography plot with mean posterior contours.

Value

a ggplot object

Examples

data(matproii)
suppressMessages({
  ei_res <- ei(formula = t ~ x, total = "n", data = matproii)
})
plot_tomog(ei_res)
plot_tomog(ei_res, options = list(linecolor = "betab"))
plot_tomog(ei_res, options = list(linecolor = "betaw", category = 5))
plot_tomog(ei_res, options = list(CI = 0.8))
plot_tomog(ei_res, options = list(points = TRUE, contour_ML = TRUE))

---

Visualizing EI (tomography plot for RxC)

Description

A tomography plot for an estimated Ecological Inference model in RxC data. This function supports the 2x3 case.

Usage

plot_tomogRxC(formula, data, total = NULL)

Arguments

formula	A formula of the form cbind(col1, col2,...)~cbind(row1,row2,...)
data	data that contains the data that corresponds to the formula
total	‘total’ is the name of the variable in the dataset that contains the number of individuals in each unit

Value

a ggplot object

Examples

data(RxCdata)
formula <- cbind(turnout, noturnout) ~ cbind(white, black, hisp)
plot_tomogRxC(formula, RxCdata)

---

Visualizing EI (with truth)

Description

Compares truth to estimates at the district and precinct-level. Requires the truth argument in the ei object.

Usage

plot_truth(ei.object)

Arguments

ei.object

The output of ei()

Value

a ggplot object

Examples

data(matproii)
truth <- cbind(matproii$tb, matproii$tw)
suppressMessages({
  ei_res <- ei(formula = t ~ x, total = "n", truth = truth, data = matproii)
})
plot_truth(ei_res)

---

Visualizing EI (xt-plot)

Description

$X_i$ by $T_i$ scatterplot with circles sized proportional to $N_i$.

Usage

plot_xt(
  ei.object,
  options = list(density = TRUE, fit = TRUE, CI = 0.8, goodman = FALSE)
)

Arguments

ei.object	The output of ei().
options	The list of options density: Showing density estimate. fit: Showing $X_i$ by $T_i$ on the plot with estimated $E(T_i|X_i)$ CI: Showing a confidence interval with a specfied statistical level. goodman: Goodman's regression.

Value

a ggplot object

Examples

data(matproii)
suppressMessages({
  ei_res <- ei(formula = t ~ x, total = "n", data = matproii)
})
# `plot_xt()` function
plot_xt(ei_res)
# `plot_xt()` with options
plot_xt(ei_res, options = list(CI = 0.95, fit = FALSE, goodman = TRUE))

---

Plotting Ecological Inference Estimates

Description

⁠plot' method for the class ⁠ei'.

Usage

## S3 method for class 'ei'
plot(x, ...)

Arguments

x	An ei object from the function ei.
...	A list of options to return in graphs. See values below.

Details

Returns any of a set of possible graphical objects, mirroring those in the examples in King (1997). Graphical option lci is a logical value specifying the use of the Law of Conservation of Ink, where the implicit information in the data is represented through color gradients, i.e. the color of the line is a function of the length of the tomography line. This can be passed as an argument and is used for ⁠tomogD'' and ⁠tomog” plots.

Value

tomogD	Tomography plot with the data only. See Figure 5.1, page 81.
tomog	Tomography plot with ML contours. See Figure 10.2, page 204.
tomogCI	Tomography plot with $80\%$ confidence intervals. Confidence intervals appear on the screen in red with the remainder of the tomography line in yellow. The confidence interval portion is also printed thicker than the rest of the line. See Figure 9.5, page 179.
tomogCI95	Tomography plot with $95\%$ confidence intervals. Confidence intervals appear on the screen in red with the remainder of the tomography line in yellow. The confidence interval portion is also printed thicker than the rest of the line. See Figure 9.5, page 179.
tomogE	Tomography plot with estimated mean posterior $\beta_i^b$ and $\beta_i^w$ points.
tomogP	Tomography plot with mean posterior contours.
betab	Density estimate (i.e., a smooth version of a histogram) of point estimates of $\beta_i^b$'s with whiskers.
betaw	Density estimate (i.e., a smooth version of a histogram) of point estimates of $\beta_i^w$'s with whiskers.
xt	Basic $X_i$ by $T_i$ scatterplot.
xtc	Basic $X_i$ by $T_i$ scatterplot with circles sized proportional to $N_i$.
xtfit	$X_i$ by $T_i$ plot with estimated $E(T_i|X_i)$ and conditional $80\%$ confidence intervals. See Figure 10.3, page 206.
xtfitg	xtfit with Goodman's regression line superimposed.
estsims	All the simulated $\beta_i^b$'s by all the simulated $\beta_i^w$'s. The simulations should take roughly the same shape of the mean posterior contours, except for those sampled from outlier tomography lines.
boundXb	$X_i$ by the bounds on $\beta_i^b$ (each precinct appears as one vertical line), see the lines in the left graph in Figure 13.2, page 238.
boundXw	$X_i$ by the bounds on $\beta_i^w$ (each precinct appears as one vertical line), see the lines in the right graph in Figure 13.2, page 238.
truth	Compares truth to estimates at the district and precinct-level. Requires truth in the ei object. See Figures 10.4 (page 208) and 10.5 (page 210).
movieD	For each observation, one tomography plot appears with the line for the particular observation darkened. After the graph for each observation appears, the user can choose to view the next observation (hit return), jump to a specific observation number (type in the number and hit return), or stop (hit "s" and return).
movie	For each observation, one page of graphics appears with the posterior distribution of $\beta_i^b$ and $\beta_i^w$ and a plot of the simulated values of $\beta_i^b$ and $\beta_i^w$ from the tomography line. The user can choose to view the next observation (hit return), jump to a specific observation number (type in the number and hit return), or stop (hit “s" and return).

a base plot

Author(s)

Gary King <<email: [email protected]>> and Molly Roberts <<email: [email protected]>>

References

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

Examples

data(sample_ei)
formula <- t ~ x
dbuf <- ei(formula = formula, total = "n", data = sample_ei)
plot(dbuf, "tomog")
plot(dbuf, "tomog", "betab", "betaw", "xtfit")

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Sample Dataset

Description

Sample EI data for RxC with estimates for White, Black, and Hispanic groups.

Format

A data frame containing 60 observations.

Source

Sample data

References

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

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Sample Data for Black Votes

Description

A sample data.frame containing turnout, proportion Black, and total voters.

Format

A data.frame containing 141 observations.

Source

Sample data

References

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

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Summarize Ecological Inference Estimates

Description

⁠summary' method for the class ⁠ei'.

Usage

## S3 method for class 'ei'
summary(object, ...)

Arguments

object	An ei object from the function ei.
...	A list of options to return in graphs. See values below.

Value

formatted summary object

Author(s)

Gary King <<email: [email protected]>> and Molly Roberts <<email: [email protected]>>

References

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

Examples

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

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Plotting Ecological Inference Estimates with eiRxC information

Description

A tomography plot for an estimated Ecological Inference model in RxC data.

Usage

tomogRxC(formula, data, total = NULL, refine = 100)

Arguments

formula	A formula of the form cbind(col1, col2,...)~cbind(row1,row2,...)
data	data that contains the data that corresponds to the formula
total	‘total’ is the name of the variable in the dataset that contains the number of individuals in each unit
refine	specifies the amount of refinement for the image. Higher numbers mean better resolution.

Author(s)

Gary King <<email: [email protected]>> and Molly Roberts <<email: [email protected]>>

References

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

Examples

data(RxCdata)
formula <- cbind(turnout, noturnout) ~ cbind(white, black, hisp)
tomogRxC(formula, data = RxCdata)

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Plotting 2x3 Ecological Inference Estimates in 3 dimensions

Description

A tomography plot in 3 dimensions for RxC Ecological Inference data and an estimated Ecological Inference model in RxC data.

Usage

tomogRxC3d(
  formula,
  data,
  total = NULL,
  lci = TRUE,
  estimates = FALSE,
  ci = FALSE,
  level = 0.95,
  seed = 1234,
  color = hcl(h = 30, c = 100, l = 60),
  transparency = 0.75,
  light = FALSE,
  rotate = TRUE
)

Arguments

formula	A formula of the form cbind(col1, col2,...)~cbind(row1,row2,...)
data	data that contains the data that corresponds to the formula
total	‘total’ is the name of the variable in the dataset that contains the number of individuals in each unit
lci	logical value specifying the use of the Law of Conservation of Ink, where the implicit information in the data is represented through color gradients, i.e. the color of the plane is a function of the area of the tomography plane.
estimates	logical value specifying whether the point estimates of $\beta$'s are included for each observation on the tomography plot.
ci	logical value specifying whether the estimated confidence ellipse is included on the tomography plot.
level	numeric value from 0 to 1 specifying the significance level of the confidence ellipse; eg. .95 refers to 95% confidence ellipse.
seed	seed value for model estimation.
color	color of tomography planes if lci=F.
transparency	numeric value from 0 to 1 specifying transparency of tomography planes; 0 is entirely transparent.
light	logical value specifying whether lights should be included in the rgl interface. The inclusion of lights will create shadows in the plot that may distort colors.
rotate	logical value specifying whether the plot will rotate for 20 seconds.

Details

Requires rgl package and rgl viewer.

Value

a base plot

Author(s)

Gary King <<email: [email protected]>>; Molly Roberts <<email: [email protected]>>; Soledad Prillaman <<email: [email protected]..

References

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

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Returning an element in the ei object

Description

Returning an element in the ei object

Usage

values_ei(object, name)

Arguments

object	An ei object from the function ei.
name	The name of the element to extract from the ei object.

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