These functions generate lists of terms to specify a loglinear model
in a form compatible with `loglin`

and also provide for conversion to an
equivalent `loglm`

specification or a shorthand character
string representation.

They allow for a more conceptual way to specify such models by a function for their type, as opposed to just an uninterpreted list of model terms and also allow easy specification of marginal models for a given contingency table.

They are intended to be used as tools in higher-level modeling and graphics functions, but can also be used directly.

`conditional(nf, table = NULL, factors = 1:nf, with = nf)`joint(nf, table = NULL, factors = 1:nf, with = nf)

markov(nf, factors = 1:nf, order = 1)

mutual(nf, table = NULL, factors = 1:nf)

saturated(nf, table = NULL, factors = 1:nf)

loglin2formula(x, env = parent.frame())

loglin2string(x, brackets = c("[", "]"), sep = ",", collapse = " ", abbrev)

nf

number of factors for which to generate the model

table

a contingency table used only for factor names in the model, typically the output from `table`

and possibly permuted with `aperm`

factors

names of factors used in the model formula when `table`

is not specified

with

For `joint`

and `conditional`

models, `with`

gives the
indices of the factors against which all others are considered jointly
or conditionally independent

order

For `markov`

, this gives the order of the Markov chain model for the
factors. An `order=1`

Markov chain allows associations among
sequential pairs of factors, e.g., `[A,B], [B,C], [C,D]`

….
An `order=2`

Markov chain allows associations among
sequential triples.

x

For the `loglin2*`

functions,
a list of terms in a loglinear model, such as returned by `conditional`

, `joint`

,
…

env

For `loglin2formula`

, environment in which to evaluate the formula

brackets

For `loglin2string`

,
characters to use to surround model terms.
Either a single character string containing two characters (e.g., `'[]'`

or a character vector of length two.

sep

For `loglin2string`

,
the separator character string used for factor names within a given model term

collapse

For `loglin2string`

,
the character string used between terms in the the model string

abbrev

For `loglin2string`

,
whether and how to abbreviate the terms in the string representation.
This has not yet been implemented.

For the main model specification functions, `conditional`

, `joint`

,
`markov`

, …, the result is
a list of vectors (terms), where the elements in each vector are the
names of the factors. The elements of the list are given names
`term1, term2, …`

.

The main model specification functions, `conditional`

, `joint`

,
`markov`

, …, `saturated`

,
return a list of vectors indicating the marginal totals to be fit,
via the `margin`

argument to `loglin`

.
Each element of this list corresponds to a high-order
term in a hierarchical loglinear model, where, e.g., a term
like `c("A", "B")`

is equivalent to the `loglm`

term `"A:B"`

and hence automatically includes all low-order terms.

Note that these can be used to supply the `expected`

argument for
the default `mosaic`

function, when the data is supplied
as a contingency table.

The table below shows some typical results in terms of the standard shorthand notation for loglinear models, with factors A, B, C, …, where brackets are used to delimit the high-order terms in the loglinear model.

function |
3-way |
4-way |
5-way |

`mutual` |
[A] [B] [C] | [A] [B] [C] [D] | [A] [B] [C] [D] [E] |

`joint` |
[AB] [C] | [ABC] [D] | [ABCE] [E] |

`joint (with=1)` |
[A] [BC] | [A] [BCD] | [A] [BCDE] |

`conditional` |
[AC] [BC] | [AD] [BD] [CD] | [AE] [BE] [CE] [DE] |

`condit (with=1)` |
[AB] [AC] | [AB] [AC] [AD] | [AB] [AC] [AD] [AE] |

`markov (order=1)` |
[AB] [BC] | [AB] [BC] [CD] | [AB] [BC] [CD] [DE] |

`markov (order=2)` |
[A] [B] [C] | [ABC] [BCD] | [ABC] [BCD] [CDE] |

`saturated` |
[ABC] | [ABCD] | [ABCDE] |

`loglin2formula`

converts the output of one of these to a model formula
suitable as the `formula`

for of `loglm`

.

`loglin2string`

converts the output of one of these to a string
describing the loglinear model in the shorthand bracket notation,
e.g., `"[A,B] [A,C]"`

.

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

# NOT RUN { joint(3, table=HairEyeColor) # as a formula or string loglin2formula(joint(3, table=HairEyeColor)) loglin2string(joint(3, table=HairEyeColor)) joint(2, HairEyeColor) # marginal model for [Hair] [Eye] # other possibilities joint(4, factors=letters, with=1) joint(5, factors=LETTERS) joint(5, factors=LETTERS, with=4:5) conditional(4) conditional(4, with=3:4) # use in mosaic displays or other strucplots mosaic(HairEyeColor, expected=joint(3)) mosaic(HairEyeColor, expected=conditional(3)) # use with MASS::loglm cond3 <- loglin2formula(conditional(3, table=HairEyeColor)) cond3 <- loglin2formula(conditional(3)) # same, with factors 1,2,3 require(MASS) loglm(cond3, data=HairEyeColor) saturated(3, HairEyeColor) loglin2formula(saturated(3, HairEyeColor)) loglin2string(saturated(3, HairEyeColor)) loglin2string(saturated(3, HairEyeColor), brackets='{}', sep=', ') # }