emerson.poly {CAvariants}

Orthogonal polynomials

Description

This function is called from the functions docabasic, socabasic, sonscabasic and donscabasic. It computes the orthogonal polynomials for the ordered categorical variables. The number of the polynomials is equal to the number of categories for that variable less one. The function computes the polynomial transformation of the ordered categorical variable.

Usage

emerson.poly(mj, pj)

Arguments

mj

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

pj

The marginal relative frequencies of the ordered variable.

Value

Describe the value returned

B

the matrix of the orthogonal polynomials with the trivial polynomial removed.

Note

Note that the sum of the marginal relative frequencies of the ordered variables must be one.

Author(s)

Rosaria Lombardo and Eric J Beh

References

Beh EJ and Lombardo R 2014 Correspondence Analysis: Theory, Practice and New Strategies. Wiley.
Emerson PL 1968 Numerical construction of orthogonal polynomials from a general recurrence formula. Biometrics, 24 (3), 695-701.
Lombardo R Beh EJ 2016 Variants of Simple Correspondence Analysis. The R Journal, 8 (2), 167–184.
Lombardo R Beh EJ and Kroonenberg PM 2016 Modelling Trends in Ordered Correspondence Analysis Using Orthogonal Polynomials. Psychometrika, 81(2), 325-349.