xy_Obj: Creation of a design-with-responses object

In ffmanova: Fifty-Fifty MANOVA

Creation of a design-with-responses object

Description

The function takes an object created by x_Obj as input and add response values. Further initial computations for prediction and testing is made.

Usage

xy_Obj(xObj, Y)

ffModelObj(
  xObj,
  Y,
  modelMatrix,
  modelTerms,
  model,
  xlev,
  scaleY,
  scaleX,
  centerX,
  isIntercept,
  returnY = FALSE,
  returnYhat = FALSE,
  returnYhatStd = FALSE
)

Arguments

xObj	object created by x_Obj
Y	response matrix
modelMatrix	Model matrix (output from model.matrix) to be included in output.
modelTerms	Model terms (model frame attribute) to be included in output.
scaleY	Values used to scale Y (see stdize) to be included in output.
scaleX	Values used to scale the model matrix (see stdize) to be included in output.
centerX	Values used to center the model matrix (see stdize) to be included in output.
isIntercept	A logical (whether model has intercept) to be included in output.
returnY	Matrix Y (as input) in output when TRUE.
returnYhat	Matrix Yhat of fitted values corresponding to Y in output when TRUE.
returnYhatStd	Standard errors, YhatStd, in output when TRUE.

Details

Traditionally, sums of squares and cross-products (SSC) is the multivariate generalisation of sums of squares. When there is a large number of responses this representation is inefficient and therefore linear combinations of observations (Langsrud, 2002) is stored instead, such as errorObs. The corresponding SSC matrix can be obtained by t(errorObs)%*%errorObs. When there is a large number of observations the errorObs representation is also inefficient, but it these cases it is possible to chose a representation with several zero rows. Then, errorObs is stored as a two-component list: A matrix containing the nonzero rows of errorObs and an integer representing the degrees of freedom for error (number of rows in the full errorObs matrix).

Value

A list with components

xObj	same as input
Y	same as input
ssTotFull	equals sum(Y^2)
ssTot	equals sum((center(Y))^2). That is, the total sum of squares summed over all responses.
ss	Sums of squares summed over all responses.
Beta	Output from linregEst where xObj$D_om is the regressor matrix.
Yhat	fitted values
YhatStd	standard deviations of fitted values
msError	mean square error of each response
errorObs	Error observations that can be used in multivariate testing
hypObs	Hypothesis observations that can be used in multivariate testing

Note

ffModelObj is a rewrite of xy_Obj with additional elements in output corresponding to the additional parameters in input. Furthermore, Y and YhatStd is by default not included in output.

Author(s)

Øyvind Langsrud and Bjørn-Helge Mevik

References

Langsrud, Ø. (2002) 50-50 Multivariate Analysis of Variance for Collinear Responses. The Statistician, 51, 305–317.

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