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

[Michael Friendly]

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] 1 2

$term2
[1] 3

WANTED:  ~ 1:2 + 3

 > condit(3)
$term1
[1] 1 3

$term2
[1] 2 3

WANTED: ~ 1:2 + 2:3

 > mutual(3)
$term1
[1] 1

$term2
[1] 2

$term3
[1] 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[1]))
     if (nf == 2) return (list(term1=factors[1], term2=factors[2]))
     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[1]))
     if (nf == 2) return (list(term1=factors[1], term2=factors[2]))
     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
Toronto, ONT  M3J 1P3 CANADA