MBPLS {MBAnalysis}

Multiblock Partial Least Squares (MB-PLS) regression

Description

MB-PLS regression applied to a set of quantitative blocks of variables.

Usage

MBPLS(
  X,
  Y,
  block,
  name.block = NULL,
  ncomp = NULL,
  scale = TRUE,
  scale.block = TRUE,
  scale.Y = TRUE
)

Arguments

X

Dataset obtained by horizontally merging all the predictor blocks of variables.

Y

Response block of variables.

block

Vector indicating the number of variables in each predictor block.

name.block

Names of the predictor blocks of variables (NULL by default).

ncomp

Number of dimensions to compute. By default (NULL), all the global components are extracted.

scale

Logical, if TRUE (by default) the variables in X are scaled to unit variance (all variables in X are centered anyway).

scale.block

Logical, if TRUE (by default) each predictor block of variables is divided by the square root of its inertia (Frobenius norm).

scale.Y

Logical, if TRUE (by default) then variables in Y are scaled to unit variance (all variables in Y are centered anyway).

Value

Returns a list of the following elements:

optimalcrit

Numeric vector of the optimal value of the criterion (sum of saliences) obtained for each dimension.

saliences

Matrix of the specific weights of each predictor block on the global components, for each dimension.

T.g

Matrix of normed global components.

Scor.g

Matrix of global components (scores of individuals).

W.g

Matrix of global weights (normed) associated with deflated X.

Load.g

Matrix of global loadings.

Proj.g

Matrix of global projection (to compute scores from pretreated X).

explained.X

Matrix of percentages of inertia explained in each predictor block.

cumexplained

Matrix giving the percentages, and cumulative percentages, of total inertia of X and Y blocks explained by the global components.

Y

A list containing un-normed Y components (U), normed Y weights (W.Y) and Y loadings (Load.Y)

Block

A list containing block components (T.b) and block weights (W.b)

References

S. Wold (1984). Three PLS algorithms according to SW. In: Symposium MULDAST (Multivariate Analysis in Science and Technology), Umea University, Sweden. pp. 26–30.

E. Tchandao Mangamana, R. Glèlè Kakaï, E.M. Qannari (2021). A general strategy for setting up supervised methods of multiblock data analysis. Chemometrics and Intelligent Laboratory Systems, 217, 104388.

See Also

summary.MBPLS plot.MBPLS

Examples

data(ham)
X=ham$X
block=ham$block
Y=ham$Y
res.mbpls <- MBPLS(X, Y, block, name.block = names(block))
summary(res.mbpls)
plot(res.mbpls)