The R Project SVN R

\name{loglin}
\alias{loglin}
\title{Fitting Log-Linear Models}
\usage{
loglin(table, margin, start = rep(1, length(table)), fit = FALSE,
       eps = 0.1, iter = 20, param = FALSE, print = TRUE)
}
\description{
    \code{loglin} is used to fit log-linear models to multidimensional
    contingency tables by Iterative Proportional Fitting.  
}
\arguments{
 \item{table}{a contingency table to be fit, typically the output from
     \code{table}.}
 \item{margin}{a list of vectors with the marginal totals to be fit.

     (Hierarchical) log-linear models can be specified in term of these
     marginal totals which give the ``maximal'' factor subsets contained
     in the model.  For example, in a three-factor model,
     \code{list(c(1, 2), c(1, 3))} specifies a model which contains
     parameters for the grand mean, each factor, and the 1-2 and 1-3
     interactions, respectively (but no 2-3 or 1-2-3 interaction), i.e.,
     a model where factors 2 and 3 are independent conditional on factor
     1 (sometimes represented as `[12][13]').
     
     The names of factors (i.e., \code{names(dimnames(table))}) may be
     used rather than numeric indices.
 }
 \item{start}{a starting estimate for the fitted table.  This optional
     argument is important for incomplete tables with structural zeros
     in \code{table} which should be preserved in the fit.  In this
     case, the corresponding entries in \code{start} should be zero and
     the others can be taken as one.}
 \item{fit}{a logical indicating whether the fitted values should be
     returned.}
 \item{eps}{maximum deviation allowed between observed and fitted
     margins.}
 \item{iter}{maximum number of iterations.}
 \item{param}{a logical indicating whether the parameter values should
     be returned.}
 \item{print}{a logical.  If \code{TRUE}, the number of iterations and
     the final deviation are printed.}
}
\value{
    A list with the following components.
    \item{lrt}{the Likelihood Ratio Test statistic.}
    \item{pearson}{the Pearson test statistic (X-squared).}
    \item{df}{the degrees of freedom for the fitted model.  There is no
    adjustment for structural zeros.}
    \item{margin}{list of the margins that were fit.  Basically the same
        as the input \code{margin}, but with numbers replaced by names
    where possible.} 
    \item{fit}{An array like \code{table} containing the fitted values.
        Only returned if \code{fit} is \code{TRUE}.}
    \item{param}{A list containing the estimated parameters of the
    model.  The ``standard'' constraints of zero marginal sums
    (e.g., zero row and column sums for a two factor parameter) are
    employed.  Only returned if \code{param} is \code{TRUE}.}
}
\details{
    The Iterative Proportional Fitting algorithm as presented in
    Haberman (1972) is used for fitting the model.  At most \code{iter}
    iterations are performed, convergence is taken to occur when the
    maximum deviation between observed and fitted margins is less than
    \code{eps}.  All internal computations are done in double precision;
    there is no limit on the number of factors (the dimension of the
    table) in the model.

    Assuming that there are no structural zeros, both the Likelihood
    Ratio Test and Pearson test statistics have an asymptotic chisquare
    distribution with \code{df} degrees of freedom.
    
    Package `MASS' contains \code{loglm}, a front-end to \code{loglin}
    which allows the log-linear model to be specified and fitted in a
    formula-based manner similar to that of other fitting functions such
    as \code{lm} or \code{glm}.
}

\references{
    S. J. Haberman (1972).
    Log-linear fit for contingency tables---Algorithm AS51.
    \emph{Applied Statistics}, \bold{21}, 218--225.

    Alan Agresti (1990).
    \emph{Categorical data analysis}.
    New York: Wiley.
}
\author{Kurt Hornik}
\seealso{\code{\link{table}}}
\examples{
## Currently no appropriate data sets are available.
}
\keyword{category}
\keyword{models}