Data generating detailed process for multivariate plsR models

This function generates a single multivariate response value \(\boldsymbol{Y}\) and a vector of explinatory variables \((X_1,\ldots,X_{totdim})\) drawn from a model with a given number of latent components.

simul_data_complete(totdim, ncomp)

Arguments

totdim	Number of columns of the X vector (from `ncomp` to hardware limits)
ncomp	Number of latent components in the model (from 2 to 6)

Value

simX

Vector of explanatory variables

Dimension of the response \(\boldsymbol{Y}\)

eta

See Li et al.

epsilon

See Li et al.

ksi

See Li et al.

Details

This function should be combined with the replicate function to give rise to a larger dataset. The algorithm used is a port of the one described in the article of Li which is a multivariate generalization of the algorithm of Naes and Martens.

Note

The value of \(r\) depends on the value of ncomp :

`ncomp`	\(r\)
2	3
3	3
4	4

References

T. Naes, H. Martens, Comparison of prediction methods for multicollinear data, Commun. Stat., Simul. 14 (1985) 545-576.
Morris, Elaine B. Martin, Model selection for partial least squares regression, Chemometrics and Intelligent Laboratory Systems 64 (2002) 79-89, doi: 10.1016/S0169-7439(02)00051-5 .

Author

Frédéric Bertrand
frederic.bertrand@utt.fr
https://fbertran.github.io/homepage/

Examples


simul_data_complete(20,6)                          
#> $simX
#>         [,1]     [,2]      [,3]     [,4]       [,5]     [,6]      [,7]
#> [1,] 1.06026 3.060016 -4.412221 1.855302 0.02270858 2.112338 -5.478201
#>           [,8]       [,9]    [,10]      [,11]    [,12]    [,13]     [,14]
#> [1,] 0.9034829 0.06598639 3.469032 -0.6272145 -1.54431 1.745336 -3.769279
#>           [,15]    [,16]      [,17]     [,18]   [,19]     [,20]
#> [1,] 0.04506222 3.448064 -0.6301517 -1.561319 1.77159 -3.770886
#> 
#> $HH
#> [1] 4
#> 
#> $eta
#>      eta61 eta62 eta63 eta64 eta65 eta66
#> [1,]   0.5   0.5   0.5   0.5   0.5   0.5
#> [2,]   0.5   0.5   0.5   0.5   0.5   0.5
#> [3,]   0.5   0.5   0.5   0.5   0.5   0.5
#> [4,]   0.5   0.5   0.5   0.5   0.5   0.5
#> 
#> $r
#> [1] -0.50302685 -7.84362840  6.70449111  4.79369856  1.87219614  0.09247717
#> 
#> $epsilon
#>  [1] -0.002473154 -0.005267429  0.021098320 -0.001542625  0.006945066
#>  [6]  0.001547163  0.002088290  0.001130647  0.007838899  0.012400744
#> [11]  0.009294536 -0.005254007 -0.021615677  0.011767877 -0.013085273
#> [16] -0.008567859  0.006357350 -0.022263091  0.004638206  0.010161350
#> 
#> $ksi
#>            ksi1       ksi2  ksi3       ksi4       ksi5  ksi6
#>  [1,] 0.2236068  0.2672612  0.25  0.2236068  0.2672612  0.25
#>  [2,] 0.2236068 -0.2672612  0.25 -0.2236068  0.2672612 -0.25
#>  [3,] 0.2236068  0.2672612 -0.25 -0.2236068  0.2672612  0.25
#>  [4,] 0.2236068 -0.2672612 -0.25  0.2236068  0.2672612 -0.25
#>  [5,] 0.2236068  0.2672612  0.25  0.2236068 -0.2672612 -0.25
#>  [6,] 0.2236068 -0.2672612  0.25 -0.2236068 -0.2672612  0.25
#>  [7,] 0.2236068  0.2672612 -0.25 -0.2236068 -0.2672612 -0.25
#>  [8,] 0.2236068 -0.2672612 -0.25  0.2236068 -0.2672612  0.25
#>  [9,] 0.2236068 -0.1336306 -0.25  0.2236068 -0.1336306 -0.25
#> [10,] 0.2236068 -0.1336306  0.25  0.2236068 -0.1336306  0.25
#> [11,] 0.2236068  0.2672612  0.00  0.2236068  0.2672612  0.00
#> [12,] 0.2236068 -0.1336306 -0.25 -0.2236068  0.1336306  0.25
#> [13,] 0.2236068 -0.1336306  0.25 -0.2236068  0.1336306 -0.25
#> [14,] 0.2236068  0.2672612  0.00 -0.2236068 -0.2672612  0.00
#> [15,] 0.2236068 -0.1336306 -0.25  0.2236068 -0.1336306 -0.25
#> [16,] 0.2236068 -0.1336306  0.25  0.2236068 -0.1336306  0.25
#> [17,] 0.2236068  0.2672612  0.00  0.2236068  0.2672612  0.00
#> [18,] 0.2236068 -0.1336306 -0.25 -0.2236068  0.1336306  0.25
#> [19,] 0.2236068 -0.1336306  0.25 -0.2236068  0.1336306 -0.25
#> [20,] 0.2236068  0.2672612  0.00 -0.2236068 -0.2672612  0.00
#> 
#> $crossksi
#>              ksi1          ksi2 ksi3         ksi4          ksi5 ksi6
#> ksi1 1.000000e+00  0.000000e+00    0 1.387779e-17  1.387779e-17    0
#> ksi2 0.000000e+00  1.000000e+00    0 0.000000e+00 -1.387779e-17    0
#> ksi3 0.000000e+00  0.000000e+00    1 0.000000e+00  0.000000e+00    0
#> ksi4 1.387779e-17  0.000000e+00    0 1.000000e+00  0.000000e+00    0
#> ksi5 1.387779e-17 -1.387779e-17    0 0.000000e+00  1.000000e+00    0
#> ksi6 0.000000e+00  0.000000e+00    0 0.000000e+00  0.000000e+00    1
#> 
#> $f
#> [1]  0.0381026486  0.0216546430 -0.0425901405 -0.0011890025  0.0007482453
#> [6]  0.0002478923
#> 
#> $z
#> [1] -0.46492420 -7.82197375  6.66190097  4.79250956  1.87294438  0.09272506
#> 
#> $Y
#>          [,1]     [,2]     [,3]     [,4]
#> [1,] 2.611909 2.547607 2.606594 2.574473
#> 

dimX <- 6
Astar <- 2
simul_data_complete(dimX,Astar)
#> $simX
#>            [,1]       [,2]      [,3]       [,4]       [,5]      [,6]
#> [1,] -0.5482509 -0.5432202 0.5972068 -0.5327074 -0.5391291 0.5942088
#> 
#> $HH
#> [1] 3
#> 
#> $eta
#>          eta21      eta22
#> [1,] 0.4082483  0.0000000
#> [2,] 0.8164966  0.4472136
#> [3,] 0.4082483 -0.8944272
#> 
#> $r
#> [1] -0.3874627  1.3288243
#> 
#> $epsilon
#> [1] -0.006471384 -0.001440722 -0.011809249  0.009072156  0.002650392
#> [6] -0.014807232
#> 
#> $ksi
#>           ksi1       ksi2
#> [1,] 0.4082483 -0.2886751
#> [2,] 0.4082483 -0.2886751
#> [3,] 0.4082483  0.5773503
#> [4,] 0.4082483 -0.2886751
#> [5,] 0.4082483 -0.2886751
#> [6,] 0.4082483  0.5773503
#> 
#> $crossksi
#>      ksi1 ksi2
#> ksi1    1    0
#> ksi2    0    1
#> 
#> $f
#> [1] -0.1830176 -0.1290406
#> 
#> $z
#> [1] -0.5704803  1.1997837
#> 
#> $Y
#>           [,1]       [,2]      [,3]
#> [1,] -0.267157 0.06555643 -1.317072
#> 


dimX <- 6
Astar <- 3
simul_data_complete(dimX,Astar)
#> $simX
#>           [,1]      [,2]      [,3]      [,4]      [,5]      [,6]
#> [1,] -2.224627 -2.048888 -16.38738 -2.243378 -2.054283 -16.39231
#> 
#> $HH
#> [1] 3
#> 
#> $eta
#>          eta31      eta32      eta33
#> [1,] 0.4082483  0.0000000 -0.9128709
#> [2,] 0.8164966  0.4472136  0.3651484
#> [3,] 0.4082483 -0.8944272  0.1825742
#> 
#> $r
#> [1] -16.8923041 -16.4574340   0.1714454
#> 
#> $epsilon
#> [1]  0.006498340  0.010792021  0.010580756 -0.012252740  0.005396356
#> [6]  0.005645281
#> 
#> $ksi
#>           ksi1       ksi2 ksi3
#> [1,] 0.4082483 -0.2886751 -0.5
#> [2,] 0.4082483 -0.2886751  0.5
#> [3,] 0.4082483  0.5773503  0.0
#> [4,] 0.4082483 -0.2886751 -0.5
#> [5,] 0.4082483 -0.2886751  0.5
#> [6,] 0.4082483  0.5773503  0.0
#> 
#> $crossksi
#>      ksi1 ksi2 ksi3
#> ksi1    1    0    0
#> ksi2    0    1    0
#> ksi3    0    0    1
#> 
#> $f
#> [1] 0.004308391 0.032973494 0.032566475
#> 
#> $z
#> [1] -16.8879957 -16.4244605   0.2040119
#> 
#> $Y
#>           [,1]      [,2]     [,3]
#> [1,] -7.110327 -21.06778 7.788813
#> 


dimX <- 6
Astar <- 4
simul_data_complete(dimX,Astar)
#> $simX
#>          [,1]       [,2]     [,3]      [,4]      [,5]     [,6]
#> [1,] 4.211792 -0.1688283 14.90254 0.6037496 -3.774891 11.31224
#> 
#> $HH
#> [1] 4
#> 
#> $eta
#>          eta41      eta42      eta43      eta44
#> [1,] 0.4082483  0.0000000  0.0000000 -0.9128709
#> [2,] 0.8164966  0.4472136  0.1825742  0.3651484
#> [3,] 0.4082483 -0.8944272 -0.3651484  0.1825742
#> [4,] 0.0000000  0.4472136 -0.9128709  0.0000000
#> 
#> $r
#> [1] 11.044762 14.892826 -4.375129  4.400491
#> 
#> $epsilon
#> [1]  0.0179179644  0.0124265112 -0.0013332675  0.0028616024 -0.0006504671
#> [6]  0.0013477424
#> 
#> $ksi
#>           ksi1       ksi2 ksi3       ksi4
#> [1,] 0.4082483 -0.2886751 -0.5  0.4082483
#> [2,] 0.4082483 -0.2886751  0.5  0.4082483
#> [3,] 0.4082483  0.5773503  0.0  0.4082483
#> [4,] 0.4082483 -0.2886751 -0.5 -0.4082483
#> [5,] 0.4082483 -0.2886751  0.5 -0.4082483
#> [6,] 0.4082483  0.5773503  0.0 -0.4082483
#> 
#> $crossksi
#>               ksi1 ksi2 ksi3          ksi4
#> ksi1  1.000000e+00    0    0 -5.551115e-17
#> ksi2  0.000000e+00    1    0  0.000000e+00
#> ksi3  0.000000e+00    0    1  0.000000e+00
#> ksi4 -5.551115e-17    0    0  1.000000e+00
#> 
#> $f
#> [1]  0.273126924 -0.109400697  0.006242271  0.004362657
#> 
#> $z
#> [1] 11.317889 14.783426 -4.368887  4.404854
#> 
#> $Y
#>           [,1]     [,2]      [,3]     [,4]
#> [1,] 0.6092864 16.66938 -6.147391 10.59473
#> 

rm(list=c("dimX","Astar"))

Data generating detailed process for multivariate plsR models

Arguments

Value

Details

Note

References

See also

Author

Examples