T3: Interactive Tucker3 analysis
In ThreeWay: Three-Way Component Analysis

Description Usage Arguments Value Author(s) References See Also Examples

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

1 2	T3(data, laba, labb, labc)

`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

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

Maria Antonietta Del Ferraro mariaantonietta.delferraro@yahoo.it
Henk A.L. Kiers h.a.l.kiers@rug.nl
Paolo Giordani paolo.giordani@uniroma1.it

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.

CP,T2,T1

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)
## Not run: 
# interactive T3 analysis
BusT3 <- T3(Bus, laba, labb, labc)
# interactive T3 analysis (when labels are not available)
BusT3 <- T3(Bus)

## End(Not run)