a matrix of observations. NAs and Infs are not
allowed.
Y
a vector or matrix of responses. NAs and Infs
are not allowed.
ncomp
the number of components to be used in the
modelling.
Y.add
a vector or matrix of additional responses containing
relevant information about the observations.
stripped
logical. If TRUE the calculations are stripped
as much as possible for speed; this is meant for use with
cross-validation or simulations when only the coefficients are
needed. Defaults to FALSE.
lower
a vector of lower limits for power optimisation. Defaults to 0.5.
upper
a vector of upper limits for power optimisation. Defaults to 0.5.
trunc.pow
logical . If TRUE an experimental alternative power algorithm is used. (Optional)
weights
a vector of individual weights for the observations. (Optional)
...
other arguments. Currently ignored.
Details
This function should not be called directly, but through
the generic functions cppls or mvr with the argument
method="cppls". Canonical Powered PLS (CPPLS)
is a generalisation of PLS incorporating discrete and continuous
responses (also simultaneously), additional responses, individual
weighting of observations and power methodology for sharpening
focus on groups of variables. Depending on the input to cppls it
can produce the following special cases:
PLS: uni-response continuous Y
PPLS: uni-response continuous Y, (lower || upper) != 0.5
PLS-DA (using correlation maximisation - B/W): dummy-coded descrete response Y
PPLS-DA: dummy-coded descrete response Y, (lower || upper) != 0.5
CPLS: multi-response Y (continuous, discrete or combination)
CPPLS: multi-response Y (continuous, discrete or combination), (lower || upper) != 0.5
The name "canonical" comes from canonical correlation analysis which
is used when calculating vectors of loading weights, while "powered"
refers to a reparameterisation of the vectors of loading weights
which can be optimised over a given interval.
Value
A list containing the following components is returned:
coefficients
an array of regression coefficients for 1, ...,
ncomp components. The dimensions of coefficients are
c(nvar, npred, ncomp) with nvar the number
of X variables and npred the number of variables to be
predicted in Y.
scores
a matrix of scores.
loadings
a matrix of loadings.
loading.weights
a matrix of loading weights.
Yscores
a matrix of Y-scores.
Yloadings
a matrix of Y-loadings.
projection
the projection matrix used to convert X to scores.
Xmeans
a vector of means of the X variables.
Ymeans
a vector of means of the Y variables.
fitted.values
an array of fitted values. The dimensions of
fitted.values are c(nobj, npred, ncomp) with
nobj the number samples and npred the number of
Y variables.
residuals
an array of regression residuals. It has the same
dimensions as fitted.values.
Xvar
a vector with the amount of X-variance explained by each
number of components.
Xtotvar
total variance in X.
gammas
gamma-values obtained in power optimisation.
canonical.correlations
Canonical correlation values from the
calculations of loading weights.
A
matrix containing vectors of weights a from
canonical correlation (cor(Za,Yb)).
smallNorms
vector of indices of explanatory variables
of length close to or equal to 0.
If stripped is TRUE, only the components
coefficients, Xmeans, Ymeans and gammas are returned.
Author(s)
Kristian Hovde Liland
References
Indahl, U. (2005) A twist to partial least squares regression.
Journal of Chemometrics, 19, 32–44.
Liland, K.H and Indahl, U.G (2009) Powered partial least squares
discriminant analysis, Journal of Chemometrics, 23, 7–18.
Indahl, U.G., Liland, K.H. and Næs, T. (2009) Canonical partial least
squares - a unified PLS approach to classification and regression problems.
Journal of Chemometrics, 23, 495–504.