linregEst: Linear regression estimation

View source: R/linregEst.R

linregEstR Documentation

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

linregEst(X, Y)

Arguments

X

regressor matrix

Y

response matrix

rank_lim

tuning parameter for the rank. The default value corresponds to the rank function in Matlab.

Umodel

this matrix is returned by linregStart

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 March 28, 2022, 5:05 p.m.

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