The covariate matrix. It is usually best that this is first standardized
with the normalize function to have mean-zero and variance-one columns
y
The response vector.
K
The number of desired PLS directions.
Value
A pls object list with the following entries
yThe response vector.
FThe covariate matrix.
zThe pls directions F%*%phi.
vResponse factors.
yhatK columns of fitted values for each number of directions.
fwdmodThe lm object from forward regression lm(y~z).
Details
Fits the Partial Least Squares algorithm described in Taddy (2011; Section 3.1).
In particular, we obtain loadings phi[,k] as the correlation between
F and factors v[,k], where v[,1] is initialized
at y and subsequent factors are orthogonal
to the k'th pls direction, z[,k]=F%*%phi[,k].
References
Taddy (2011), Inverse Regression for Analysis of Sentiment in Text.
http://arxiv.org/abs/1012.2098
Wold, H. (1975), Soft modeling by latent variables: The nonlinear iterative partial least squares approach.
In Perspectives in Probability and Statistics, Papers in Honour of M.S. Bartlett.
data(congress109)
F <- normalize(freq(congress109Counts))
y <- normalize(congress109Ideology$repshare)
fit <- pls(F, y, K=4)
plot(fit, pch=21, bg=c(4,3,2)[congress109Ideology$party])