ComDim: Common Dimensions Analysis

Description

Performs ComDim analysis on a set of quantitative blocks of variables. ComDim can be viewed as a Multiblock Weighted Principal Components Analysis (MBWPCA)

Usage

ComDim(
  X,
  block,
  name.block = NULL,
  ncomp = NULL,
  scale = TRUE,
  scale.block = TRUE,
  threshold = 1e-08
)

Value

Returns a list of the following elements:

optimalcrit: Numeric vector of the optimal value of the criterion (sum of squared saliences) obtained for each dimension.
saliences: Matrix of the specific weights of each block of variables 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 (normed).
Proj.g: Matrix of global projection (to compute scores from pretreated X).
explained.X: Matrix of percentages of inertia explained in each block of variables.
cumexplained: Matrix giving the percentages, and cumulative percentages, of total inertia of X blocks explained by the global components.
Block: A list containing block components (T.b) and block weights (W.b)

Arguments

X: Dataset obtained by horizontally merging all the blocks of variables.
block: Vector indicating the number of variables in each block.
name.block: names of the 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) then variables are scaled to unit variance (all variables are centered anyway).
scale.block: Logical, if TRUE (by default) each block of variables is divided by the square root of its inertia (Frobenius norm).
threshold: Convergence threshold

References

E.M. Qannari, I. Wakeling, P. Courcoux, J.M. MacFie (2000). Defining the underlying sensory dimensions, Food Quality and Preference, 11: 151-154.

E. Tchandao Mangamana, V. Cariou, E. Vigneau, R. Glèlè Kakaï, E.M. Qannari (2019). Unsupervised multiblock data analysis: A unified approach and extensions, Chemometrics and Intelligent Laboratory Systems, 194, 103856.

Examples

Run this code

data(ham)
X=ham$X
block=ham$block
res.comdim <- ComDim(X,block,name.block=names(block))
summary(res.comdim)
plot(res.comdim)