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 = NULL,
  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. If NULL (the default), uses an abbreviation of type: "joint", "cond", "mutual", "markov", or "sat".
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

Author

Michael Friendly

Examples


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

# Models of joint independence
tit.joint <- seq_loglm(Titanic, type = "joint")

# compare the models
LRstats(tit.joint)
#> Likelihood summary table:
#>            AIC    BIC LR Chisq Df Pr(>Chisq)    
#> joint.1 509.95 509.33   475.81  3  < 2.2e-16 ***
#> joint.2 478.75 479.14   412.60  3  < 2.2e-16 ***
#> joint.3 257.88 264.83   159.10  7  < 2.2e-16 ***
#> joint.4 833.36 858.28   671.96 15  < 2.2e-16 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

#' # Models of conditional independence
tit.cond <- seq_loglm(Titanic, type = "conditional")

# compare the models
LRstats(tit.cond)
#> Likelihood summary table:
#>           AIC    BIC LR Chisq Df Pr(>Chisq)    
#> cond.1 509.95 509.33   475.81  3  < 2.2e-16 ***
#> cond.2 478.75 479.14   412.60  3  < 2.2e-16 ***
#> cond.3 500.87 508.60   400.09  6  < 2.2e-16 ***
#> cond.4 760.13 777.72   608.73 20  < 2.2e-16 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1