Sequential Loglinear Models for an N-way Table

This function takes an n-way contingency table and fits a series of sequential models to the 1-, 2-, ... n-way marginal tables, corresponding to a variety of types of loglinear models.

Usage

seq_loglm(
  x,
  type = c("joint", "conditional", "mutual", "markov", "saturated"),
  marginals = 1:nf,
  vorder = 1:nf,
  k = NULL,
  prefix = "model",
  fitted = TRUE,
  ...
)

Arguments

x

a contingency table in array form, with optional category labels specified in the dimnames(x) attribute, or else a data.frame in frequency form, with the frequency variable named "Freq".

type

type of sequential model to fit, a character string. One of "joint", "conditional", "mutual", "markov", or "saturated".

marginals

which marginal sub-tables to fit? A vector of a (sub)set of the integers, 1:nf where nf is the number of factors in the full n-way table.

vorder

order of variables, a permutation of the integers 1:nf, used to reorder the variables in the original table for the purpose of fitting sequential marginal models.

k

conditioning variable(s) for type = "joint", "conditional" or Markov chain order for type = "markov"

prefix

prefix used to give names to the sequential models

fitted

argument passed to loglm to store the fitted values in the model objects

...

other arguments, passed down

Value

An object of class "loglmlist", each of which is a class "loglm" object

Details

Sequential marginal models for an n-way tables begin with the model of equal-probability for the one-way margin (equivalent to a chisq.test) and add successive variables one at a time in the order specified by vorder.

All model types give the same result for the two-way margin, namely the test of independence for the first two factors.

Sequential models of joint independence (type="joint") have a particularly simple interpretation, because they decompose the likelihood ratio test for the model of mutual independence in the full n-way table, and hence account for "total" association in terms of portions attributable to the conditional probabilities of each new variable, given all prior variables.

Note

One-way marginal tables are a bit of a problem here, because they cannot be fit directly using loglm. The present version uses loglin, and repairs the result to look like a loglm object (sort of).

References

These functions were inspired by the original SAS implementation of mosaic displays, described in the User's Guide, http://www.datavis.ca/mosaics/mosaics.pdf

See also

loglin-utilities for descriptions of sequential models, conditional, joint, mutual, ...

loglmlist

Other loglinear models: glmlist(), joint()

Author

Michael Friendly

Examples

data(Titanic, package="datasets")
# variables are in the order Class, Sex, Age, Survived
tt <- seq_loglm(Titanic)