

   FFiittttiinngg LLoogg--LLiinneeaarr MMooddeellss

        loglin(table, margin, start = rep(1, length(table)), fit = FALSE,
               eps = 0.1, iter = 20, param = FALSE, print = TRUE)

   AArrgguummeennttss::

      table: a contingency table to be fit, typically the out-
             put from `table'.

     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, `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., `names(dim-
             names(table))') may be used rather than numeric
             indices.

      start: a starting estimate for the fitted table.  This
             optional argument is important for incomplete
             tables with structural zeros in `table' which
             should be preserved in the fit.  In this case, the
             corresponding entries in `start' should be zero
             and the others can be taken as one.

        fit: a logical indicating whether the fitted values
             should be returned.

        eps: maximum deviation allowed between observed and
             fitted margins.

       iter: maximum number of iterations.

      param: a logical indicating whether the parameter values
             should be returned.

      print: a logical.  If `TRUE', the number of iterations
             and the final deviation are printed.

   DDeessccrriippttiioonn::

        `loglin' is used to fit log-linear models to multidi-
        mensional contingency tables by Iterative Proportional
        Fitting.

   DDeettaaiillss::

        The Iterative Proportional Fitting algorithm as pre-
        sented in Haberman (1972) is used for fitting the
        model.  At most `iter' iterations are performed, con-
        vergence is taken to occur when the maximum deviation
        between observed and fitted margins is less than `eps'.
        All internal computations are done in double precision;
        there is no limit on the number of factors (the dimen-
        sion 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 `df' degrees
        of freedom.

        Package `MASS' contains `loglm', a front-end to
        `loglin' which allows the log-linear model to be speci-
        fied and fitted in a formula-based manner similar to
        that of other fitting functions such as `lm' or `glm'.

   VVaalluuee::

        A list with the following components.

        lrt: the Likelihood Ratio Test statistic.

    pearson: the Pearson test statistic (X-squared).

         df: the degrees of freedom for the fitted model.
             There is no adjustment for structural zeros.

     margin: list of the margins that were fit.  Basically the
             same as the input `margin', but with numbers
             replaced by names where possible.

        fit: An array like `table' containing the fitted val-
             ues.  Only returned if `fit' is `TRUE'.

      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 `param' is `TRUE'.

   AAuutthhoorr((ss))::

        Kurt Hornik

   RReeffeerreenncceess::

        S. J. Haberman (1972).  Log-linear fit for contingency
        tables--Algorithm AS51.  Applied Statistics, 21,
        218-225.

        Alan Agresti (1990).  Categorical data analysis.  New
        York: Wiley.

   SSeeee AAllssoo::

        `table'

   EExxaammpplleess::

        ## Currently no appropriate data sets are available.

