tripls: Trilinear Partial Least Squares Regression
In SvenSerneels/tripls_r: Trilinear partial least squares regression

Description Usage Arguments Details Value Author(s) References Examples

This function computes trilinear partial least squares (Tri-PLS) regression estimates

1	tripls(X, y, A, scaling = TRUE, nnames = NULL, pnames = NULL, qnames = NULL)

`X`	The X data as a 3 way (n x p x q) array.
`y`	The corresponding y data as an n x 1 vector or a length n numeric
`A`	The number of latent components to estimate (integer)
`scaling`	Logical flag. If TRUE, the data are internally centered and scaled to unit variance. If FALSE, the data are only centered.
`nnames`	An optional n x 1 character matrix containing the case names.
`pnames`	An optional p x 1 character matrix containing p mode variable names.
`qnames`	An optional q x 1 character matrix containing q mode variable names.

The actual algorithm is described in Reference [4], which is a minor modification of the implementations described in references [1-3].

Returns a class "tripls" regression object containing the indivdual Tri-PLS results, i.e.:

`coefficients`	The vector of regression coeficients (pq x 1)
`intercept`	The intercept (n x 1)
`scores`	The latent variables (or scores, n x A)
`fitted.values`	The fitted responses from an A component model
`W`	The combined weighting vectors (pq x A)
`WJ`	The p mode weighting vectors (p x A)
`WK`	The q mode weighting vectors (q x A)
`YMeans`	The y mean (length 1 numeric) )
`YScales`	The y scale (length 1 numeric, 1 if scaling=FALSE)
`XMeans`	The X columnwise means (length pq numeric)
`XScales`	The X columnwise scales (length pq numeric, all ones if scaling=FALSE)
`X.scaled`	The scaled, unfolded predictor matrix (n x pq)
`y.scaled`	The scaled response (length n numeric)
`sev`	The percentage of explained covariance
`rmsec`	The root mean squared error of calibration
`inputs`	A list object containing the input data

Sven Serneels, BASF Corp.

[1] L. Staahle, Aspects of the analysis of three-way data. Chemometrics and Intelligent Laboratory Systems, 7 (1989), 95-100.

[2] R. Bro, Multiway calibration. Multilinear PLS. Journal of Chemometrics, 10 (1996), 47-61.

[3] S. de Jong, Regression coefficients in multilinear PLS. Journal of Chemometrics, 12 (1998) 77-81.

[4] S. Serneels, K. Faber, T. Verdonck, P.J. Van Espen, Case specific prediction intervals for tri-PLS1: The full local linearization. Chemometrics and Intelligent Laboratory Systems, 108 (2011), 93-99.

data(data_3)
res.tripls <- tripls(data_3$X3,data_3$y3,2)
res.tripls <- tripls(data_3$X3,data_3$y3,2,scaling=FALSE)
res.tripls <- tripls(data_3$X3,data_3$y3,1,qnames=paste("B",1:3,sep=""))