linregEst: Linear regression estimation

In ffmanova: Fifty-Fifty MANOVA

Linear regression estimation

Description

Function that performs multivariate multiple linear regression modelling (Y = XB + E) according to a principal component regression (PCR) approach where the number of components equals the number of nonzero eigenvalues (generalised inverse).

Usage

linregEnd(Umodel, Y)

linregEst(X, Y)

linregStart(X, rank_lim = 1e-09)

Arguments

Umodel	this matrix is returned by linregStart
Y	response matrix
X	regressor matrix
rank_lim	tuning parameter for the rank. The default value corresponds to the rank function in Matlab.

Details

The function linregEst performs the calculations in two steps by calling linregStart and linregEnd. The former functions function makes all calculations that can be done without knowing Y. The singular value decomposition (SVD) is an essential part of the calculations and some of the output variables are named according to SVD (‘⁠U⁠’, ‘⁠S⁠’ and ‘⁠V⁠’).

Value

linregEst returns a list with seven components. The first three components is returned by linregStart - the rest by linregEnd.

Umodel	Matrix of score values according to the PCR model.
VmodelDivS	Matrix that can be used to calculate Umodel from X. That is, Umodel equals X %*% VmodelDivS.
VextraDivS1	Matrix that can be used to check estimability. That is, predictions for a new X cannot be made if Xnew %*% VextraDivS1 is (close to) zero.
BetaU	Matrix of regression parameters according to the PCR model.
msError	Mean square error of each response
errorObs	Error observations that can be used in multivariate testing
Yhat	Fitted values. Equals Umodel %*% BetaU

Note

When the number of error degrees of freedom exceeds the number of linearly independent responses, then the matrix of error observations is made so that several rows are zero. In this case the zero rows are omitted and a list with components errorObs and df_error is returned.

Author(s)

Øyvind Langsrud and Bjørn-Helge Mevik

See Also

ffmanova

ffmanova documentation built on Oct. 18, 2023, 5:08 p.m.