ThreeWay (version 1.1.3)

T3: Interactive Tucker3 analysis

Description

Detects the underlying structure of a three-way array according to the Tucker3 (T3) model.

Usage

T3(data, laba, labb, labc)

Value

A list including the following components:

A

Component matrix for the A-mode

B

Component matrix for the B-mode

C

Component matrix for the C-mode

core

Matricized core array (frontal slices)

fit

Fit value expressed as a percentage

fitValues

Fit values expressed as a percentage upon convergence for all the runs of the CP algorithm (see T3func)

funcValues

Function values upon convergence for all the runs of the CP algorithm (see T3func)

cputime

Computation times for all the runs of the CP algorithm (see T3func)

iter

Numbers of iterations upon convergence for all the runs of the CP algorithm (see T3func)

fitA

Fit contributions for the A-mode entities (see T3fitpartitioning)

fitB

Fit contributions for the B-mode entities (see T3fitpartitioning)

fitC

Fit contributions for the C-mode entities (see T3fitpartitioning)

fitAB

Fit contributions for the A-and mode B component combinations (see T3fitpartitioning)

fitAC

Fit contributions for the A-and mode C component combinations (see T3fitpartitioning)

fitBC

Fit contributions for the B-and mode C component combinations (see T3fitpartitioning)

Bint

Bootstrap percentile interval of every element of B (see bootstrapT3)

Cint

Bootstrap percentile interval of every element of C (see bootstrapT3)

Kint

Bootstrap percentile interval of every element of core (see bootstrapT3)

fpint

Bootstrap percentile interval for the goodness of fit index expressed as a percentage (see bootstrapT3)

Afull

Component matrix for the A-mode (full data) from split-half analysis (see splithalfT3)

As1

Component matrix for the A-mode (split n.1) from split-half analysis (see splithalfT3)

As2

Component matrix for the A-mode (split n.2) from split-half analysis (see splithalfT3)

Bfull

Component matrix for the B-mode (full data) from split-half analysis (see splithalfT3)

Bs1

Component matrix for the B-mode (split n.1) from split-half analysis (see splithalfT3)

Bs2

Component matrix for the B-mode (split n.2) from split-half analysis (see splithalfT3)

Cfull

Component matrix for the C-mode (full data) from split-half analysis (see splithalfT3)

Cs1

Component matrix for the C-mode (split n.1) from split-half analysis (see splithalfT3)

Cs2

Component matrix for the C-mode (split n.2) from split-half analysis (see splithalfT3)

Kfull

Matricized core array (frontal slices) (full data) from split-half analysis (see splithalfT3)

Ks1

Matricized core array (frontal slices) (split n.1) from split-half analysis (see splithalfT3)

Ks2

Matricized core array (frontal slices) (split n.2) from split-half analysis (see splithalfT3)

Kss1

Matricized core array (frontal slices) (using full data solutions for A,B and C for split n.1) from split-half analysis (see splithalfT3)

Kss2

Matricized core array (frontal slices) (using full data solutions for A,B and C for split n.2) from split-half analysis (see splithalfT3)

Aplot

Coordinates for plots of the A-mode entities

Bplot

Coordinates for plots of the B-mode entities

Cplot

Coordinates for plots of the C-mode entities

CBplot

Coordinates for plots of the C and B-mode entities using the A-mode projected in it as axes (to be added in plot, i.e. coordinates in ($CBplot,$A))

ACplot

Coordinates for plots of the A and C-mode entities using the B-mode projected in it as axes (to be added in plot, i.e. coordinates in ($ACplot,$B))

BAplot

Coordinates for plots of the B and A-mode entities using the C-mode projected in it as axes (to be added in plot, i.e. coordinates in ($BAplot,$C))

A1

Component matrix for the A-mode from Principal Component Analysis of mean values (see pcamean)

B1

Component matrix for the B-mode from Principal Component Analysis of mean values (see pcamean)

C1

Component matrix for the C-mode from Principal Component Analysis of mean values (see pcamean)

A2

Component matrix for the A-mode from Principal Component Analysis of mean values (see pcamean)

B2

Component matrix for the B-mode from Principal Component Analysis of mean values (see pcamean)

C2

Component matrix for the C-mode from Principal Component Analysis of mean values (see pcamean)

laba

Vector of length n containing the labels of the A-mode entities

labb

Vector of length m containing the labels of the B-mode entities

labc

Vector of length P containing the labels of the C-mode entities

Xprep

Matrix of order (n x mp) containing the matricized array (frontal slices) after preprocessing used for the analysis

Arguments

data

Array of order n x m x p or matrix or data.frame of order (n x mp) containing the matricized array (frontal slices)

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

Author

Maria Antonietta Del Ferraro
Henk A.L. Kiers
Paolo Giordani

References

P. Giordani, H.A.L. Kiers, M.A. Del Ferraro (2014). Three-way component analysis using the R package ThreeWay. Journal of Statistical Software 57(7):1--23. http://www.jstatsoft.org/v57/i07/.
P.M. Kroonenberg (2008). Applied Multiway Data Analysis. Wiley, New Jersey.
L.R Tucker (1966). Some mathematical notes on three-mode factor analysis. Psychometrika 31:279--311.

See Also

CP,T2,T1

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)
if (FALSE) {
# interactive T3 analysis
BusT3 <- T3(Bus, laba, labb, labc)
# interactive T3 analysis (when labels are not available)
BusT3 <- T3(Bus)
}