# [R] converting a list of loglin terms to a model formula

Michael Friendly friendly at yorku.ca
Wed Jul 3 23:55:50 CEST 2013

```I'm developing some functions to create symbolic specifications for
loglinear models of different types.
I don't really know how to 'compute' with model formulas, so I've done
this in the notation
for stats::loglin(), which is a list of high-order terms in the model.

What I'd like is a function to turn the results of these into a model
formula, suitable for
MASS::loglm.  That's the reverse of what loglm does.

For example, the simplest versions of models for 3-way tables for joint,
conditional, and marginal independence can be computed as follows.
After each, I indicated
the WANTED model formula I'd like from the result

> joint(3)
\$term1
 1 2

\$term2
 3

WANTED:  ~ 1:2 + 3

> condit(3)
\$term1
 1 3

\$term2
 2 3

WANTED: ~ 1:2 + 2:3

> mutual(3)
\$term1
 1

\$term2
 2

\$term3
 3

WANTED: ~ 1 + 2 + 3

In case anyone want to play with the code, here are the current, not too
elegant definitions
of the functions, and some further test cases,

# models of joint independence
joint <- function(nf, factors=1:nf, with=nf) {
if (nf == 1) return (list(term1=factors))
if (nf == 2) return (list(term1=factors, term2=factors))
others <- setdiff(1:nf, with)
result <- list(term1=factors[others], term2=factors[with])
result
}
# conditional independence
condit <- function(nf, factors=1:nf, with=nf) {
if (nf == 1) return (list(term1=factors))
if (nf == 2) return (list(term1=factors, term2=factors))
main <- setdiff(1:nf, with)
others <- matrix(factors[with], length(with), length(main))
result <- rbind(factors[main], others)
result <- as.list(as.data.frame(result, stringsAsFactors=FALSE))
names(result) <- paste('term', 1:length(result), sep='')
result
}
# mutual independence
mutual <- function(nf, factors=1:nf) {
result <- sapply(factors[1:nf], list)
names(result) <- paste('term', 1:length(result), sep='')
result
}

### some comparisons

loglin(HairEyeColor, list(c(1, 2), c(1, 3), c(2, 3)))\$lrt
loglm(~1:2 + 1:3 +2:3, HairEyeColor)

# use factor names
joint(3, factors=names(dimnames(HairEyeColor)))
condit(3, factors=names(dimnames(HairEyeColor)))

loglin(HairEyeColor, joint(3))\$lrt
loglm(~1:2 + 3, HairEyeColor)

loglin(HairEyeColor, condit(3))\$lrt
loglm(~1:3 + 2:3, HairEyeColor)

--
Michael Friendly     Email: friendly AT yorku DOT ca
Professor, Psychology Dept. & Chair, Quantitative Methods
York University      Voice: 416 736-2100 x66249 Fax: 416 736-5814
4700 Keele Street    Web:   http://www.datavis.ca