Guttman-ordered response matrix and reproducibility

Orders persons by descending location and dichotomous items by ascending location (the Guttman scalogram arrangement), computing the reproducibility coefficient against the deterministic pattern implied by each person's total score. PCM category steps can interleave across items, so polytomous fits are rejected rather than forced into an invalid whole-item deterministic order.

Usage

guttman_table(fit)

Arguments

fit

A fitted object from rasch whose columns form one administered item set. Expanded EFRM and MFRM response-cell matrices are not accepted; one-cell-per-item reductions are.

Value

A list with the ordered score matrix matrix (persons by items, row and column names carrying the ID and item labels), the person and item orderings, and the coefficient of reproducibility CR.

References

Guttman, L. (1944). A basis for scaling qualitative data. American Sociological Review, 9(2), 139–150.

Examples

set.seed(1)
d <- seq(-2, 2, length.out = 6)
X <- matrix(rbinom(200 * 6, 1, plogis(outer(rnorm(200), d, "-"))), 200, 6)
colnames(X) <- paste0("I", 1:6)
guttman_table(rasch(X))$CR
#> [1] 0.8116667