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\name{bounds}
\alias{bounds}
\title{Deterministic bounds for units satisfying row thresholds}
\description{Calculates the deterministic bounds on the proportion of
row members within a specified column.}
\usage{
bounds(formula, data, rows, column, excluded = NULL,
threshold = 0.9, total = NULL)
}
\arguments{
\item{formula}{a formula of the form \code{cbind(col1, col2, ...) ~
cbind(row1, row2, ...)}. Column and row marginals must have the
same total for each ecological unit.}
\item{data}{a data frame containing the variables specified in
\code{formula} and (optionally) \code{total}}
\item{rows}{a character vector specifying the rows of interest}
\item{column}{a character string specifying the column marginal of
interest}
\item{excluded}{an optional character string (or vector of character
strings) specifying the columns to be excluded from the bounds
calculation. For example, if the quantity of interest is Democratic
share of the two-party vote, non-voters would be excluded.}
\item{threshold}{the minimum proportion of the unit that row members must
comprise for the bounds to be calculated for the unit. If
\code{threshold = 0}, bounds will be calculated for all units.}
\item{total}{if row and/or column marginals are given as proportions,
\code{total} identifies the name of the variable in \code{data} containing the
total number of individuals in each unit}
}
\value{ A list with elements
\item{bounds}{a list of deterministic bounds for all units in which
row proportions meet the threshold}
\item{intersection}{if the intersection of the deterministic bounding
intervals is non-empty, the intersection is returned. Otherwise,
\code{NA} is returned.}
}
\seealso{\code{plot.bounds}}
\references{
Otis Dudley Duncan and Beverley Davis. 1953. ``An Alternative to Ecological
Correlation.'' \emph{American Sociological Review} 18: 665-666.
}
\author{
Ryan T. Moore <\email{rtm@american.edu}>
}
\keyword{models}
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