emerson.poly {CA3variants}R Documentation

Orthogonal polynomials

Description

This function is called from the function oca3basic when in CA3variants we set ca3type = "OCA3". It allows the analyst to compute the orthogonal polynomials of the ordered categorical variable. The number of the polynomials is equal to the variable category less one. The function computes the polynomial transformation of the ordered categorical variable.

Usage

emerson.poly(mj, pj)

Arguments

mj

The ordered scores of an ordered variable. By default mj = NULL, the natural scores (1,2,...) are computed.

pj

The marginals, relative frequencies of the ordered variable.

Value

Describe the value returned

B

The matrix of the orthogonal polynomials without the trivial polynomial.

Note

Note that the sum of the marginals of the ordered variables should be one.

Author(s)

Rosaria Lombardo and Eric J Beh.

References

Beh EJ and Lombardo R 2014 Correspondence Analysis: Theory, Practice and New Strategies. John Wiley & Sons.
Emerson PL 1968 Numerical construction of orthogonal polynomials from a general recurrence formula. Biometrics, 24 (3), 695-701.
Lombardo R Beh EJ Variants of Simple Correspondence Analysis. The R Journal, 8 (2), 167–184.

Examples

emerson.poly(c(1,2,3,4,5), as.vector(c(.1,.2,.3,.2,.2)))

[Package CA3variants version 3.0 Index]