loglin                 package:stats                 R Documentation

Fitting Log-Linear Models

Description:

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

Usage:

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

Arguments:

   table: a contingency table to be fit, typically the output from
          'table'.

  margin: a list of vectors with the marginal totals to be fit.

          (Hierarchical) log-linear models can be specified in terms 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(dimnames(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.

Details:

     The Iterative Proportional Fitting algorithm as presented in
     Haberman (1972) is used for fitting the model.  At most 'iter'
     iterations are performed, convergence 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 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
     chi-squared distribution with 'df' degrees of freedom.

     Note that the IPF steps are applied to the factors in the order
     given in 'margin'.  Hence if the model is decomposable and the
     order given in 'margin' is a running intersection property
     ordering then IPF will converge in one iteration.

     Package 'MASS' contains 'loglm', a front-end to '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 'lm' or 'glm'.

Value:

     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 values. 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'.

Author(s):

     Kurt Hornik

References:

     Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) _The New S
     Language_. Wadsworth & Brooks/Cole.

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

     Agresti, A. (1990) _Categorical data analysis_. New York: Wiley.

See Also:

     'table'.

     'loglm' in package 'MASS' for a user-friendly wrapper.

     'glm' for another way to fit log-linear models.

Examples:

     ## Model of joint independence of sex from hair and eye color.
     fm <- loglin(HairEyeColor, list(c(1, 2), c(1, 3), c(2, 3)))
     fm
     1 - pchisq(fm$lrt, fm$df)
     ## Model with no three-factor interactions fits well.

