R: Sequential Loglinear Models for an N-way Table

seq_loglm {vcdExtra} | R Documentation

## Sequential Loglinear Models for an N-way Table

### Description

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

### 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.

### Value

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

### 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).

### Author(s)

Michael Friendly

### 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`,

### Examples

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

[Package vcdExtra version 0.7-1 Index]