# Loglinear Model Utilities

`loglin-utilities.Rd`

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.

## Usage

```
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)
```

## Arguments

- 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.

## Details

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]"`

.

## Value

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, ...`

.

## 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

## Examples

```
joint(3, table=HairEyeColor)
#> $term1
#> [1] "Hair" "Eye"
#>
#> $term2
#> [1] "Sex"
#>
# as a formula or string
loglin2formula(joint(3, table=HairEyeColor))
#> ~Hair:Eye + Sex
#> <environment: 0x0000024a5eaf5040>
loglin2string(joint(3, table=HairEyeColor))
#> [1] "[Hair,Eye] [Sex]"
joint(2, HairEyeColor) # marginal model for [Hair] [Eye]
#> $term1
#> [1] "Hair"
#>
#> $term2
#> [1] "Eye"
#>
# other possibilities
joint(4, factors=letters, with=1)
#> $term1
#> [1] "b" "c" "d"
#>
#> $term2
#> [1] "a"
#>
joint(5, factors=LETTERS)
#> $term1
#> [1] "A" "B" "C" "D"
#>
#> $term2
#> [1] "E"
#>
joint(5, factors=LETTERS, with=4:5)
#> $term1
#> [1] "A" "B" "C"
#>
#> $term2
#> [1] "D" "E"
#>
conditional(4)
#> $term1
#> [1] 1 4
#>
#> $term2
#> [1] 2 4
#>
#> $term3
#> [1] 3 4
#>
conditional(4, with=3:4)
#> $term1
#> [1] 1 3 4
#>
#> $term2
#> [1] 2 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)
#> Call:
#> loglm(formula = cond3, data = HairEyeColor)
#>
#> Statistics:
#> X^2 df P(> X^2)
#> Likelihood Ratio 156.6779 18 0
#> Pearson 147.9440 18 0
saturated(3, HairEyeColor)
#> $term1
#> [1] "Hair" "Eye" "Sex"
#>
loglin2formula(saturated(3, HairEyeColor))
#> ~Hair:Eye:Sex
#> <environment: 0x0000024a5eaf5040>
loglin2string(saturated(3, HairEyeColor))
#> [1] "[Hair,Eye,Sex]"
loglin2string(saturated(3, HairEyeColor), brackets='{}', sep=', ')
#> [1] "{Hair, Eye, Sex}"
```