YRCSkew-nonlin: Specify a Skew-Symmetric Association in a gnm Model Formula
In logmult: Log-Multiplicative Models, Including Association Models

YRCSkew

R Documentation

Specify a Skew-Symmetric Association in a gnm Model Formula

Description

A function of class "nonlin" to specify a Yamaguchi (1990) skew-symmetric association in the formula argument to gnm.

Usage

YRCSkew(row, col, rowinf, rowsup, inst = NULL)

Arguments

`row`	for each cell in the table, the row category.
`col`	for each cell in the table, the column category.
`rowinf`	must be 1 for cells above the diagonal, 0 for cells below and on the diagonal.
`rowsup`	must be 1 for cells below the diagonal, 0 for cells above and on the diagonal.
`inst`	a positive integer specifying the instance number of the term.

Details

This function is used by yrcskew to fit the “row-column-effect skew-symmetric association (logbilinear) model with full quasi-symmetry (QS+RC_SK)” proposed by Yamaguchi (1990). It can be used directly to fit custom variants of the model not supported by yrcskew.

This function combines its arguments in the following way:

YRCSkew(row, col, rowinf, rowsup) = δ_{rowinf} * μ_{row} * (μ_{col} - μ_{row}) + δ_{rowsup} * ν_{col} * (ν_{row} - ν_{col})

When arguments are set according to what is suggested above, and the skew δ parameter is constrained to 1, this amounts to the equation:

YRCSkew_{ij} = δ_{i<j} ν_i (ν_j - ν_i) - δ_{i>j} ν_j (ν_i - ν_j) = (δ_{i<j} - δ_{i>j}) ν_{min(i,j)} (ν_{max(i,j)} - ν_{min(i,j)})

where YRCSkew_{ij} is the skew association for the cell at the intersection of row i and column j of the table. See reference for mathematical details, and the code of yrcskew for real-world usage.

Value

A list with the required components of a "nonlin" function:

`predictors`	the expressions passed to `Mult`
`term`	a function to create a deparsed mathematical expression of the term, given labels for the predictors.
`call`	the call to use as a prefix for parameter labels.

Author(s)

Milan Bouchet-Valat

References

Yamaguchi, K. (1990). Some Models for the Analysis of Asymmetric Association in Square Contingency Tables with Ordered Categories. Sociol. Methodology 20, 181-212.