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

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.

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 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 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

Value

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

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.

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.

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
#>  direct indirect     total additional1 additional2 overall
#>   0 (0)    52.44 52.44 (3)    4.09 (3)   14.01 (2)   70.55

# 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
#> $`Smell at rest->View`
#>     direct indirect     total
#>  32.68 (1)        0 32.68 (1)
#> 
#> $`Smell at rest->Smell after shaking`
#>  direct indirect     total
#>   0 (0)    40.03 40.03 (4)
#> 
#> $`Smell at rest->Tasting`
#>  direct indirect     total
#>   0 (0)    11.52 11.52 (2)
#> 
#> $`Smell at rest->Global quality`
#>  direct indirect     total
#>   0 (0)    25.25 25.25 (3)
#> 
#> $`View->Smell after shaking`
#>     direct indirect     total
#>  30.97 (2)        0 30.97 (2)
#> 
#> $`View->Tasting`
#>  direct indirect     total
#>   0 (0)    41.09 41.09 (2)
#> 
#> $`View->Global quality`
#>  direct indirect     total
#>   0 (0)    30.87 30.87 (2)
#> 
#> $`Smell after shaking->Tasting`
#>     direct indirect     total
#>  56.67 (3)        0 56.67 (3)
#> 
#> $`Smell after shaking->Global quality`
#>  direct indirect     total
#>   0 (0)    70.15 70.15 (2)
#> 
#> $`Tasting->Global quality`
#>     direct indirect     total
#>  78.12 (2)        0 78.12 (2)
#>