marg.param {ggm}

Link function of marginal log-linear parameterization

Description

Provides the contrast and marginalization matrices for the marginal parametrization of a probability vector.

Usage

marg.param(lev, type)

Arguments

lev

Integer vector containing the number of levels of each variable.

type

A character vector with elements "l", "g", "c", or "r" indicating the type of logit. The meaning is as follows: "g" for global, "c" for continuation, "r" for reverse continuation and "l" for local.

Details

See Bartolucci, Colombi and Forcina (2007).

Value

C

Matrix of constrasts (the first sum(lev)-length(r) elements are referred to univariate logits)

M

Marginalization matrix with elements 0 and 1.

G

Corresponding design matrix for the corresponding log-linear model.

Note

Assumes that the vector of probabilities is in inv lex order. The interactions are returned in order of dimension, like e.g., 1, 2, 3, 12, 13, 23, 123.

Author(s)

Francesco Bartolucci, Antonio Forcina, Giovanni M. Marchetti

References

Bartolucci, F., Colombi, R. and Forcina, A. (2007). An extended class of marginal link functions for modelling contingency tables by equality and inequality constraints. Statist. Sinica 17, 691-711.

See Also

mat.mlogit

Examples

    
marg.param(c(3,3), c("l", "g"))