CP function

Interactive Candecomp/Parafac analysis

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

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

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

• 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

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.

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

T3, T2, T1

Examples

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)