I have a question about the model matrix and parameter matrix of the linear multivariate model fit to the iris data set in R. This is the code (function lm) I am using and the outputs:
> (fm = lm(cbind(iris[,1],iris[,2],iris[,3],iris[,4])~(iris[,5])))
Call:
lm(formula = cbind(iris[, 1], iris[, 2], iris[, 3], iris[, 4]) ~
(iris[, 5]))
Coefficients:
[,1] [,2] [,3] [,4]
(Intercept) 5.006 3.428 1.462 0.246
iris[, 5]versicolor 0.930 -0.658 2.798 1.080
iris[, 5]virginica 1.582 -0.454 4.090 1.780
My objective is to get the decomposition of the model in matrices:
The model matrix A and the 4 by 4 parameter matrix β for the multivariate model X = Aβ + E
From my knowledge the matrix β is the Coefficient matrix just obtained above:
[,1] [,2] [,3] [,4]
(Intercept) 5.006 3.428 1.462 0.246
iris[, 5]versicolor 0.930 -0.658 2.798 1.080
iris[, 5]virginica 1.582 -0.454 4.090 1.780
Therefore, is not the matrix β a 3 by 4 matrix (3 rows and 4 columns) instead of a 4 x 4 matrix?
You can query how R codes the Species predictor:
contrasts( iris$Species )
## and verify how this applies to your model matrix:
model.matrix( fm )
In short - you don't need an intercept and 4 parameters. In this case setosa is the intercept. Thus a 3x4. Is this what you were asking for?