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# crossings model (Goodman, 1972)
# Ref:
#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.
crossings <- function(i, j, n) {
npar <- n - 1
result <- list()
for(c in 1:npar) {
overi <- c >= i
overj <- c >= j
result[[c]] <- (overi & !overj) + (overj & !overi)
}
result <- matrix(unlist(result), length(i), npar)
colnames(result) <- paste('C', 1:npar, sep='')
result
}
Crossings <- function(...) {
dots <- list(...)
if (length(dots) != 2) stop("Crossings() is defined for only two factors")
if (length(dots[[1]]) != length(dots[[2]]))
stop("arguments to Crossings() must all have same length")
dots <- lapply(dots, as.factor)
n <- nlevels(dots[[1]])
if (nlevels(dots[[2]]) != n)
stop("arguments to Crossings() must all have same number of levels")
result <- crossings(as.numeric(dots[[1]]), as.numeric(dots[[2]]), n)
rownames(result) <- do.call("paste", c(dots, sep = ""))
result
}
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