linregEst {ffmanova} | R Documentation |
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).
linregEst(X, Y) linregStart(X, rank_lim = 1e-9) linregEnd(Umodel, Y)
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 |
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).
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 |
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.
Øyvind Langsrud and Bjørn-Helge Mevik