cp_gen {rrcov3way}

Generate PARAFAC data sets, optionally with outliers

Description

Generates nsim data sets according to the given parameters. If eps > 0, the specified fraction of random outliers of the identified by the parameter type type are added to the data sets.

Usage

cp_gen(
  I = 20,
  J = 20,
  K = 20,
  nsim = 200,
  nf = 3,
  noise = 0.05,
  noise1 = 0,
  Acol = TRUE,
  Bcol = TRUE,
  Ccol = TRUE,
  congA = 0.5,
  congB = 0.5,
  congC = 0.5,
  eps = 0,
  type = c("none", "bl", "gl", "og"),
  c1 = 10,
  c2 = 0.1,
  silent = FALSE
)

Arguments

I

number of observations

J

number of variables

K

number of occasions

nsim

number of data sets to generate

nf

number of PARAFAC components

noise

level of homoscedastic (HO) noise

noise1

level of heteroscedastic (HE) noise

Acol

whether to apply collinearity with factor congA to mode A

Bcol

whether to apply collinearity with factor congB to mode B

Ccol

whether to apply collinearity with factor congC to mode C

congA

collinearity factor for mode A

congB

collinearity factor for mode B

congC

collinearity factor for mode C

eps

fraction of outliers (percent contamination)

type

type of outliers: one of "none" for no outliers (possible only of eps==0), "bl" for bad leverage points, "gl" for good leverage points and "og" for orthogonal outliers

c1

parameter for outlier generation (c1=10 for type="bl" or type="gl" and c1=1 for type="og")

c2

parameter for outlier generation (c2=0.1 for type="bl" or type="og" and c2=0 for type="gl")

silent

whether to issue warnings

Value

A list consisting of the following lists:

• As list of nsim matrices for the mode A

• Bs list of nsim matrices for the mode B

• Cs list of nsim matrices for the mode C

• Xs list of nsim PARAFAC data sets, each with dimension IxJxK

• Os list of nsim vectors containing the added outliers (if any)

• param list of parameters used for generation of the data sets

References

Todorov, V. and Simonacci, V. and Gallo, M. and Trendafilov, N. (2023). A novel estimation procedure for robust CANDECOMP/PARAFAC model fitting. Econometrics and Statistics. In press.

Tomasi, G. and Bro, R., (2006). A comparison of algorithms for fitting the PARAFAC model. Computational Statistics & Data Analysis 50 (7), 1700–1734.

Faber, N.M. and Bro, R. and Hopke, P.K. (2003). Recent developments in CANDECOMP/PARAFAC algorithms: A critical review. Chemometrics and Intelligent Laboratory Systems 65, 119–137.

Examples

 ##  Generate one PARAFAC data set (nsim=1) with R=2 components (nf=2) and dimensions
 ##  50x10x10. Apply 0.15 homoscedastic noise and 0.10 heteroscedastic noise, apply 
 ##  collinearity with congruence factor 0.5 to all modes. Add 20% bad leverage points.

 library(rrcov3way)
 xdat <- cp_gen(I=50, J=100, K=10, nsim=1, nf=2,
     noise=0.15, noise1=0.10, Acol=TRUE, Bcol=TRUE, Ccol=TRUE,
     congA=0.5, congB=0.5, congC=0.5,
     eps=0.2, type="bl")
 names(xdat)