bootstrapT3 function

Bootstrap percentile intervals for Tucker3

Produces percentile intervals for all output parameters. The percentile intervals indicate the instability of the sample solutions.

bootstrapT3(X, A, B, C, G, n, m, p, r1, r2, r3, conv, centopt, normopt, 
  optimalmatch, laba, labb, labc)

Arguments

• X: Matrix (or data.frame coerced to a matrix) of order (n x mp) containing the matricized array (frontal slices)
• A: Component matrix for the A-mode
• B: Component matrix for the B-mode
• C: Component matrix for the C-mode
• G: Matricized core array (frontal slices)
• n: Number of A-mode entities of X
• m: Number of B-mode entities of X
• p: Number of C-mode entities of X
• r1: Number of extracted components for the A-mode
• r2: Number of extracted components for the B-mode
• r3: Number of extracted components for the C-mode
• conv: Convergence criterion
• centopt: Centering option (see cent3)
• normopt: Normalization option (see norm3)
• optimalmatch: Binary indicator (0 if the procedure uses matching via orthogonal rotation towards full solutions, 1 if the procedure uses matching via optimal transformation towards full solutions)
• laba: Optional vector of length n containing the labels of the A-mode entities
• labb: Optional vector of length m containing the labels of the B-mode entities
• labc: Optional vector of length p containing the labels of the C-mode entities

Returns

A list including the following components: - Bint: Bootstrap percentile interval of every element of B

• Cint: Bootstrap percentile interval of every element of C

• Gint: Bootstrap percentile interval of matricized core array (frontal slices) G

• fpint: Bootstrap percentile interval for the goodness of fit index expressed as a percentage

Note

The preprocessing must be done in same way as for sample analysis.

The resampling mode must be the A-mode.

The starting points for every bootstrap solution are two: rational (using SVD) and solution from the observed sample.

References

H.A.L. Kiers (2004). Bootstrap confidence intervals for three-way methods. Journal of Chemometrics 18:22--36.

Author(s)

Maria Antonietta Del Ferraro mariaantonietta.delferraro@yahoo.it

Henk A.L. Kiers h.a.l.kiers@rug.nl

Paolo Giordani paolo.giordani@uniroma1.it

See Also

bootstrapCP, percentile95, T3

Examples

data(Bus)
# labels for Bus data
laba <- rownames(Bus)
labb <- substr(colnames(Bus)[1:5],1,1)
labc <- substr(colnames(Bus)[seq(1,ncol(Bus),5)],3,8)
# T3 solution
BusT3 <- T3funcrep(Bus, 7, 5, 37, 2, 2, 2, 0, 1e-6)
## Not run:

# Bootstrap analysis on T3 solution using matching via optimal transformation
boot <- bootstrapT3(Bus, BusT3$A, BusT3$B, BusT3$C, BusT3$H, 7, 5, 37, 2, 2, 2, 
 1e-6, 0, 0, 1, laba, labb, labc)
# Bootstrap analysis on T3 solution using matching via orthogonal rotation 
# (when labels are not available)
boot <- bootstrapT3(Bus, BusT3$A, BusT3$B, BusT3$C, BusT3$H, 7, 5, 37, 2, 2, 2, 
 1e-6, 0, 0, 0)
## End(Not run)