SO_TDI {multiblock}

Total, direct, indirect and additional effects in SO-PLS-PM.

Description

SO-PLS-PM is the use of SO-PLS for path-modelling. This particular function is used to compute effects (explained variances) in sub-paths of the directed acyclic graph.

Usage

sopls_pm(
  X,
  Y,
  ncomp,
  max_comps = min(sum(ncomp), 20),
  sel.comp = "opt",
  computeAdditional = FALSE,
  sequential = FALSE,
  B = NULL,
  k = 10,
  type = "consecutive",
  simultaneous = TRUE
)

## S3 method for class 'SO_TDI'
print(x, showComp = TRUE, heading = "SO-PLS path effects", digits = 2, ...)

sopls_pm_multiple(
  X,
  ncomp,
  max_comps = min(sum(ncomp), 20),
  sel.comp = "opt",
  computeAdditional = FALSE,
  sequential = FALSE,
  B = NULL,
  k = 10,
  type = "consecutive"
)

## S3 method for class 'SO_TDI_multiple'
print(x, heading = "SO-PLS path effects", digits = 2, ...)

Arguments

X

A list of input blocks (of type matrix).

Y

A matrix of response(s).

ncomp

An integer vector giving the number of components per block or a single integer for common number of components.

max_comps

Maximum total number of components.

sel.comp

A character or integer vector indicating the type ("opt" - minimum error / "chi" - chi-squared reduced) or exact number of components in selections.

computeAdditional

A logical indicating if additional components should be computed.

sequential

A logical indicating if sequential component optimization should be applied.

B

An integer giving the number of bootstrap replicates for variation estimation.

k

An integer indicating number of cross-validation segments (default = 10).

type

A character for selecting type of cross-validation segments (default = "consecutive").

simultaneous

logical indicating if simultaneous orthogonalisation on intermediate blocks should be performed (default = TRUE).

x

An object of type SO_TDI.

showComp

A logical indicating if components should be shown in print (default = TRUE).

heading

A character giving the heading of the print.

digits

An integer for selecting number of digits in print.

...

Not implemented

Details

sopls_pm computes 'total', 'direct', 'indirect' and 'additional' effects for the 'first' versus the 'last' input block by cross-validated explained variances. 'total' is the explained variance when doing regression of 'first' -> 'last'. 'indirect' is the the same, but controlled for the intermediate blocks. 'direct' is the left-over part of the 'total' explained variance when subtracting the 'indirect'. Finally, 'additional' is the added explained variance of 'last' for each block following 'first'.

sopls_pm_multiple is a wrapper for sopls_pm that repeats the calculation for all pairs of blocks from 'first' to 'last'. Where sopls_pm has a separate response, Y, signifying the 'last' block, sopls_pm_multiple has multiple 'last' blocks, depending on sub-path, thus collects the response(s) from the list of blocks X.

When sel.comp = "opt", the number of components for all models are optimized using cross-validation within the ncomp and max_comps supplied. If sel.comp is "chi", an optimization is also performed, but parsimonious solutions are sought through a chi-square chriterion. When setting sel.comp to a numeric vector, exact selection of number of components is performed.

When setting B to a number, e.g. 200, the procedures above are repeated B times using bootstrapping to estimate standard deviations of the cross-validated explained variances.

Value

An object of type SO_TDI containing total, direct and indirect effects, plus possibly additional effects and standard deviations (estimated by bootstrapping).

References

• Menichelli, E., Almøy, T., Tomic, O., Olsen, N. V., & Næs, T. (2014). SO-PLS as an exploratory tool for path modelling. Food quality and preference, 36, 122-134.

• Næs, T., Romano, R., Tomic, O., Måge, I., Smilde, A., & Liland, K. H. (2020). Sequential and orthogonalized PLS (SO-PLS) regression for path analysis: Order of blocks and relations between effects. Journal of Chemometrics, e3243.

See Also

Overviews of available methods, multiblock, and methods organised by main structure: basic, unsupervised, asca, supervised and complex.

Examples

# Single path for the potato data:
data(potato)
pot.pm <- sopls_pm(potato[1:3], potato[['Sensory']], c(5,5,5), computeAdditional=TRUE)
pot.pm

# Corresponding SO-PLS model:
# so <- sopls(Sensory ~ ., data=potato[c(1,2,3,9)], ncomp=c(5,5,5), validation="CV", segments=10)
# maageSeq(pot.so, compSeq = c(3,2,4))

# All path in the forward direction for the wine data:
data(wine)
pot.pm.multiple <- sopls_pm_multiple(wine, ncomp = c(4,2,9,8))
pot.pm.multiple