vcdExtra (version 0.9.6)

Crossings: Crossings Interaction of Factors

Description

Given two ordered factors in a square, n x n frequency table, Crossings creates an n-1 column matrix corresponding to different degrees of difficulty in crossing from one level to the next, as described by Goodman (1972).

Usage

Crossings(...)

Value

For two factors of n levels, returns a binary indicator matrix of n*n rows and n-1 columns.

Arguments

...

Two factors

Author

Michael Friendly and Heather Turner

Details

Instead of treating all mobility as equal, this model posits that the difficulty of moving between categories increases with the number of boundaries (or "crossings") that must be crossed, and that associations between categories decrease with their separation.

References

Goodman, L. (1972). Some multiplicative models for the analysis of cross-classified data. In: Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, Berkeley, CA: University of California Press, pp. 649-696.

See Also

glm, gnm for model fitting functions for frequency tables; Diag, Mult, Symm, Topo for similar extensions to terms in model formulas.

Examples

data(Hauser79)
# display table
structable(~Father + Son, data=Hauser79)

hauser.indep <- gnm(Freq ~ Father + Son,
                    data=Hauser79,
                    family=poisson)

hauser.CR <- update(hauser.indep,
                    ~ . + Crossings(Father,Son))
LRstats(hauser.CR)

hauser.CRdiag <- update(hauser.indep,
                        ~ . + Crossings(Father,Son) + Diag(Father,Son))
LRstats(hauser.CRdiag)

# what does Crossings do?
cr <- with(Hauser79, Crossings(Father, Son))
head(cr)
# Show the codings for varying Crossings levels
matrix(cr[,1], nrow=5)
matrix(cr[,2], nrow=5)
matrix(cr[,3], nrow=5)
matrix(cr[,4], nrow=5)