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.
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, ....