CP: Interactive Candecomp/Parafac 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 Candecomp/Parafac (CP) model.

1	CP(data,laba,labb,labc)

`data`	Array of order `n` by `m` by `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
`fit`	Fit value expressed as a percentage
`tripcos`	Matrix of the triple cosines among pairs of components (to inspect degeneracy)
`fitValues`	Fit values expressed as a percentage upon convergence for all the runs of the CP algorithm (see `CPfunc`)
`funcValues`	Function values upon convergence for all the runs of the CP algorithm (see `CPfunc`)
`cputime`	Computation times for all the runs of the CP algorithm (see `CPfunc`)
`iter`	Numbers of iterations upon convergence for all the runs of the CP algorithm (see `CPfunc`)
`fitA`	Fit contributions for the `A`-mode entities (see `CPfitpartitioning`)
`fitB`	Fit contributions for the `B`-mode entities (see `CPfitpartitioning`)
`fitC`	Fit contributions for the `C`-mode entities (see `CPfitpartitioning`)
`Bint`	Bootstrap percentile interval of every element of `B` (see `bootstrapCP`)
`Cint`	Bootstrap percentile interval of every element of `C` (see `bootstrapCP`)
`fpint`	Bootstrap percentile interval for the goodness of fit index expressed as a percentage (see `bootstrapCP`)
`Afull`	Component matrix for the `A`-mode (full data) from split-half analysis (see `splithalfCP`)
`As1`	Component matrix for the `A`-mode (split n.1) from split-half analysis (see `splithalfCP`)
`As2`	Component matrix for the `A`-mode (split n.2) from split-half analysis (see `splithalfCP`)
`Bfull`	Component matrix for the `B`-mode (full data) from split-half analysis (see `splithalfCP`)
`Bs1`	Component matrix for the `B`-mode (split n.1) from split-half analysis (see `splithalfCP`)
`Bs2`	Component matrix for the `B`-mode (split n.2) from split-half analysis (see `splithalfCP`)
`Cfull`	Component matrix for the `C`-mode (full data) from split-half analysis (see `splithalfCP`)
`Cs1`	Component matrix for the `C`-mode (split n.1) from split-half analysis (see `splithalfCP`)
`Cs2`	Component matrix for the `C`-mode (split n.2) from split-half analysis (see `splithalfCP`)
`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

J.D. Carroll and J.J. Chang (1970). Analysis of individual differences in multidimensional scaling via an N-way generalization of 'Eckart-Young' decomposition. Psychometrika 35:283–319.
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/.
R.A. Harshman (1970). Foundations of the Parafac procedure: models and conditions for an 'explanatory' multi-mode factor analysis. UCLA Working Papers in Phonetics 16:1–84.
P.M. Kroonenberg (2008). Applied Multiway Data Analysis. Wiley, New Jersey.

T3, T2, T1

data(TV)
TVdata=TV[[1]]
labSCALE=TV[[2]]
labPROGRAM=TV[[3]]
labSTUDENT=TV[[4]]
# permutation of the modes so that the A-mode refers to students
TVdata <- permnew(TVdata, 16, 15, 30)
TVdata <- permnew(TVdata, 15, 30, 16)
## Not run: 
# interactive CP analysis
TVcp <- CP(TVdata, labSTUDENT, labSCALE, labPROGRAM)
# interactive CP analysis (when labels are not available)
TVcp <- CP(TVdata)

## End(Not run)