% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/ecoNP.R
\name{ecoNP}
\alias{ecoNP}
\title{Fitting the Nonparametric Bayesian Models of Ecological Inference in 2x2
Tables}
\usage{
ecoNP(formula, data = parent.frame(), N = NULL, supplement = NULL,
  context = FALSE, mu0 = 0, tau0 = 2, nu0 = 4, S0 = 10,
  alpha = NULL, a0 = 1, b0 = 0.1, parameter = FALSE, grid = FALSE,
  n.draws = 5000, burnin = 0, thin = 0, verbose = FALSE)
}
\arguments{
\item{formula}{A symbolic description of the model to be fit, specifying the
column and row margins of \eqn{2 \times 2} ecological tables. \code{Y ~ X}
specifies \code{Y} as the column margin (e.g., turnout) and \code{X} as the
row margin (e.g., percent African-American). Details and specific examples
are given below.}

\item{data}{An optional data frame in which to interpret the variables in
\code{formula}. The default is the environment in which \code{ecoNP} is
called.}

\item{N}{An optional variable representing the size of the unit; e.g., the
total number of voters. \code{N} needs to be a vector of same length as
\code{Y} and \code{X} or a scalar.}

\item{supplement}{An optional matrix of supplemental data. The matrix has
two columns, which contain additional individual-level data such as survey
data for \eqn{W_1} and \eqn{W_2}, respectively.  If \code{NULL}, no
additional individual-level data are included in the model. The default is
\code{NULL}.}

\item{context}{Logical. If \code{TRUE}, the contextual effect is also
modeled, that is to assume the row margin \eqn{X} and the unknown \eqn{W_1}
and \eqn{W_2} are correlated. See Imai, Lu and Strauss (2008, 2011) for
details. The default is \code{FALSE}.}

\item{mu0}{A scalar or a numeric vector that specifies the prior mean for
the mean parameter \eqn{\mu} of the base prior distribution \eqn{G_0} (see
Imai, Lu and Strauss (2008, 2011) for detailed descriptions of Dirichlete
prior and the normal base prior distribution) .  If it is a scalar, then its
value will be repeated to yield a vector of the length of \eqn{\mu},
otherwise, it needs to be a vector of same length as \eqn{\mu}.  When
\code{context=TRUE }, the length of \eqn{\mu} is 3, otherwise it is 2. The
default is \code{0}.}

\item{tau0}{A positive integer representing the scale parameter of the
Normal-Inverse Wishart prior for the mean and variance parameter
\eqn{(\mu_i, \Sigma_i)} of each observation. The default is \code{2}.}

\item{nu0}{A positive integer representing the prior degrees of freedom of
the variance matrix \eqn{\Sigma_i}. the default is \code{4}.}

\item{S0}{A positive scalar or a positive definite matrix that specifies the
prior scale matrix for the variance matrix \eqn{\Sigma_i}. If it is a
scalar, then the prior scale matrix will be a diagonal matrix with the same
dimensions as \eqn{\Sigma_i} and the diagonal elements all take value of
\code{S0}, otherwise \code{S0} needs to have same dimensions as
\eqn{\Sigma_i}. When \code{context=TRUE}, \eqn{\Sigma} is a \eqn{3 \times 3}
matrix, otherwise, it is \eqn{2 \times 2}.  The default is \code{10}.}

\item{alpha}{A positive scalar representing a user-specified fixed value of
the concentration parameter, \eqn{\alpha}. If \code{NULL}, \eqn{\alpha} will
be updated at each Gibbs draw, and its prior parameters \code{a0} and
\code{b0} need to be specified. The default is \code{NULL}.}

\item{a0}{A positive integer representing the value of shape parameter of
the gamma prior distribution for \eqn{\alpha}. The default is \code{1}.}

\item{b0}{A positive integer representing the value of the scale parameter
of the gamma prior distribution for \eqn{\alpha}. The default is \code{0.1}.}

\item{parameter}{Logical. If \code{TRUE}, the Gibbs draws of the population
parameters, \eqn{\mu} and \eqn{\Sigma}, are returned in addition to the
in-sample predictions of the missing internal cells, \eqn{W}. The default is
\code{FALSE}. This needs to be set to \code{TRUE} if one wishes to make
population inferences through \code{predict.eco}. See an example below.}

\item{grid}{Logical. If \code{TRUE}, the grid method is used to sample
\eqn{W} in the Gibbs sampler. If \code{FALSE}, the Metropolis algorithm is
used where candidate draws are sampled from the uniform distribution on the
tomography line for each unit. Note that the grid method is significantly
slower than the Metropolis algorithm.}

\item{n.draws}{A positive integer. The number of MCMC draws.  The default is
\code{5000}.}

\item{burnin}{A positive integer. The burnin interval for the Markov chain;
i.e. the number of initial draws that should not be stored. The default is
\code{0}.}

\item{thin}{A positive integer. The thinning interval for the Markov chain;
i.e. the number of Gibbs draws between the recorded values that are skipped.
The default is \code{0}.}

\item{verbose}{Logical. If \code{TRUE}, the progress of the Gibbs sampler is
printed to the screen. The default is \code{FALSE}.}
}
\value{
An object of class \code{ecoNP} containing the following elements:
\item{call}{The matched call.} 
\item{X}{The row margin, \eqn{X}.}
\item{Y}{The column margin, \eqn{Y}.} 
\item{burnin}{The number of initial burnin draws.} 
\item{thin}{The thinning interval.} 
\item{nu0}{The prior degrees of freedom.} 
\item{tau0}{The prior scale parameter.} 
\item{mu0}{The prior mean.} 
\item{S0}{The prior scale matrix.} 
\item{a0}{The prior shape parameter.} 
\item{b0}{The prior scale parameter.} 
\item{W}{A three dimensional array storing the posterior in-sample predictions 
of \eqn{W}. The first dimension indexes the Monte Carlo draws, the second dimension
indexes the columns of the table, and the third dimension represents the observations.} 
\item{Wmin}{A numeric matrix storing the lower bounds of \eqn{W}.} 
\item{Wmax}{A numeric matrix storing the upper bounds of \eqn{W}.}
The following additional elements are included in the output when
\code{parameter = TRUE}.  
\item{mu}{A three dimensional array storing the
posterior draws of the population mean parameter, \eqn{\mu}. The first
dimension indexes the Monte Carlo draws, the second dimension indexes the
columns of the table, and the third dimension represents the observations.}
\item{Sigma}{A three dimensional array storing the posterior draws of the
population variance matrix, \eqn{\Sigma}. The first dimension indexes the
Monte Carlo draws, the second dimension indexes the parameters, and the
third dimension represents the observations. } 
\item{alpha}{The posterior draws of \eqn{\alpha}.} 
\item{nstar}{The number of clusters at each Gibbs draw.}
}
\description{
\code{ecoNP} is used to fit the nonparametric Bayesian model (based on a
Dirichlet process prior) for ecological inference in \eqn{2 \times 2} tables
via Markov chain Monte Carlo. It gives the in-sample predictions as well as
out-of-sample predictions for population inference.  The models and
algorithms are described in Imai, Lu and Strauss (2008, 2011).
}
\examples{


## load the registration data
data(reg)

## NOTE: We set the number of MCMC draws to be a very small number in
## the following examples; i.e., convergence has not been properly
## assessed. See Imai, Lu and Strauss (2006) for more complete examples.

## fit the nonparametric model to give in-sample predictions
## store the parameters to make population inference later
\dontrun{res <- ecoNP(Y ~ X, data = reg, n.draws = 50, param = TRUE, verbose = TRUE)

##summarize the results
summary(res)

## obtain out-of-sample prediction
out <- predict(res, verbose = TRUE)

## summarize the results
summary(out)

## density plots of the out-of-sample predictions
par(mfrow=c(2,1))
plot(density(out[,1]), main = "W1")
plot(density(out[,2]), main = "W2")


## load the Robinson's census data
data(census)

## fit the parametric model with contextual effects and N 
## using the default prior specification

res1 <- ecoNP(Y ~ X, N = N, context = TRUE, param = TRUE, data = census, 
n.draws = 25, verbose = TRUE)

## summarize the results
summary(res1)

## out-of sample prediction 
pres1 <- predict(res1)
summary(pres1)}

}
\references{
Imai, Kosuke, Ying Lu and Aaron Strauss. (2011).  \dQuote{eco: R
Package for Ecological Inference in 2x2 Tables} Journal of Statistical
Software, Vol. 42, No. 5, pp. 1-23. available at
\url{http://imai.princeton.edu/software/eco.html}

Imai, Kosuke, Ying Lu and Aaron Strauss. (2008).  \dQuote{Bayesian and
Likelihood Inference for 2 x 2 Ecological Tables: An Incomplete Data
Approach} Political Analysis, Vol. 16, No. 1 (Winter), pp. 41-69. available
at \url{http://imai.princeton.edu/research/eiall.html}
}
\seealso{
\code{eco}, \code{ecoML}, \code{predict.eco}, \code{summary.ecoNP}
}
\author{
Kosuke Imai, Department of Politics, Princeton University,
\email{kimai@Princeton.Edu}, \url{http://imai.princeton.edu}; Ying Lu,
Center for Promoting Research Involving Innovative Statistical Methodology
(PRIISM), New York University \email{ying.lu@nyu.Edu}
}
\keyword{models}