YRCSkew | R Documentation |
A function of class "nonlin"
to specify a Yamaguchi (1990) skew-symmetric association in
the formula argument to gnm
.
YRCSkew(row, col, rowinf, rowsup, inst = NULL)
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. |
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.
A list with the required components of a "nonlin"
function:
predictors |
the expressions passed to |
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. |
Milan Bouchet-Valat
Yamaguchi, K. (1990). Some Models for the Analysis of Asymmetric Association in Square Contingency Tables with Ordered Categories. Sociol. Methodology 20, 181-212.
yrcskew
# See ?yrcskew.
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