YRCSkew {logmult}

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) = \delta_{rowinf} * \mu_{row} * (\mu_{col} - \mu_{row}) + \delta_{rowsup} * \nu_{col} * (\nu_{row} - \nu_{col})

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

YRCSkew_{ij} = \delta_{i<j} \nu_i (\nu_j - \nu_i) - \delta_{i>j} \nu_j (\nu_i - \nu_j) = (\delta_{i<j} - \delta_{i>j}) \nu_{min(i,j)} (\nu_{max(i,j)} - \nu_{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.

See Also

yrcskew

Examples

  # See ?yrcskew.