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ThreeWay (version 1.1.3)

CP: Interactive Candecomp/Parafac analysis

Description

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

Usage

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

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

Run this code
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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