Interactive Candecomp/Parafac analysis

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Description

Detects the underlying structure of a three-way array according to the Candecomp/Parafac (CP) model.

Usage

1
 CP(data,laba,labb,labc)

Arguments

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

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

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

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

References

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.

See Also

T3, T2, T1

Examples

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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)

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