# emerson.poly: Orthogonal polynomials In CAvariants: Correspondence Analysis Variants

## Description

This function is called from the functions `docabasic, socabasic, sonscabasic` and `donscabasic`. 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

 `1` ```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 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.

## Examples

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

### Example output

```Loading required package: tools
\$B
[,1]       [,2]        [,3]       [,4]
[1,] -1.7614097  1.9490178 -1.32656790  0.5822225
[2,] -0.9607689 -0.1461763  1.30369604 -1.1644450
[3,] -0.1601282 -0.9745089  0.04574372  1.1644450
[4,]  0.6405126 -0.5359799 -1.39518348 -1.1644450
[5,]  1.4411534  1.1694107  0.68615581  0.2911113

\$BT
[,1]       [,2]       [,3]        [,4]       [,5]
[1,]    1 -1.7614097  1.9490178 -1.32656790  0.5822225
[2,]    1 -0.9607689 -0.1461763  1.30369604 -1.1644450
[3,]    1 -0.1601282 -0.9745089  0.04574372  1.1644450
[4,]    1  0.6405126 -0.5359799 -1.39518348 -1.1644450
[5,]    1  1.4411534  1.1694107  0.68615581  0.2911113
```

CAvariants documentation built on Sept. 21, 2018, 6:33 p.m.