T3 function

Interactive Tucker3 analysis

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

T3(data, laba, labb, labc)

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

Returns

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

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.

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

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)
## 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)