Data generating function for univariate plsR models

Source: R/simul_data_UniYX.R

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

simul_data_UniYX(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

vector

\((Y,X_1,\ldots,X_{totdim})\)

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.

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 .

See also

simul_data_YX and simul_data_complete for generating multivariate data

Author

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

Examples


simul_data_UniYX(20,6)                          

#>          Y         X1         X2         X3         X4         X5         X6 
#> -5.0845940 -2.0283323 -6.7362672 -3.3100088 -5.1476176 -0.6794538 -5.6005351 
#>         X7         X8         X9        X10        X11        X12        X13 
#> -1.9725262 -3.9952421 -3.3466745 -3.6213504 -1.9200845 -5.5309980 -5.5844386 
#>        X14        X15        X16        X17        X18        X19        X20 
#> -2.0899928 -3.3650301 -3.6175759 -1.9002841 -5.5163292 -5.5791753 -2.0879278 

# \donttest{
dimX <- 6
Astar <- 2
simul_data_UniYX(dimX,Astar)

#>         Y        X1        X2        X3        X4        X5        X6 
#>  3.405154 -9.219318 -9.206206  5.151362 -9.223586 -9.222478  5.171035 
(dataAstar2 <- data.frame(t(replicate(50,simul_data_UniYX(dimX,Astar)))))

#>              Y         X1         X2          X3         X4         X5
#> 1   -5.4667852 -4.6368328 -4.6633727  -3.8169525 -4.6492866 -4.6343097
#> 2    2.5611245  4.4882903  4.4834136   0.7940228  4.4865642  4.4646325
#> 3    5.8534434  2.1600274  2.1642386   4.4565923  2.1785280  2.1725729
#> 4   -7.2685172 -2.9284924 -2.9155321  -5.7429226 -2.9388173 -2.8998562
#> 5   15.7429002  8.4686086  8.4947916  11.9159934  8.4771044  8.4726148
#> 6    3.7344067 -2.7395944 -2.7146311   3.9311366 -2.7377429 -2.7428695
#> 7    8.3220039 -3.5079464 -3.4918852   8.1026183 -3.4977322 -3.4983252
#> 8    0.9494198 -4.2032146 -4.1983074   1.6417675 -4.1764409 -4.2048811
#> 9  -14.9267216 -2.8222037 -2.8181578 -12.5035209 -2.7979519 -2.8153492
#> 10  12.7602184 10.4981129 10.4741489   8.9435314 10.5008709 10.4958755
#> 11  -7.1831458 -7.2682429 -7.2616761  -4.4726100 -7.2711886 -7.2758669
#> 12  -6.8634182  4.9443571  4.9398128  -6.9835797  4.9373878  4.9593859
#> 13   3.6898544 -6.7960138 -6.8062212   4.8938195 -6.8159262 -6.8215547
#> 14   1.0245038 -0.8001555 -0.8217277   1.1709703 -0.8181114 -0.8103901
#> 15  -1.9356491 -2.4355237 -2.4491487  -1.2550267 -2.4562047 -2.4410910
#> 16   9.5511311  2.4434726  2.4601161   7.8979152  2.4509083  2.4600142
#> 17   2.3699577  3.9373881  3.9325800   1.2903720  3.9270690  3.9198469
#> 18   3.0787230  1.7702339  1.7590052   2.3511337  1.7740213  1.7685472
#> 19  -5.9158249 -4.8695095 -4.8551184  -4.0128074 -4.8757767 -4.8818083
#> 20  -4.2512179  2.2564203  2.2304770  -4.3865768  2.2263642  2.2372684
#> 21   2.9481516  0.7101294  0.7239348   2.4468113  0.7359318  0.7222038
#> 22   6.9365803  4.8017027  4.8047261   5.0208553  4.7972377  4.7974923
#> 23   0.6756597 -0.6555612 -0.6596367   0.8949284 -0.6303841 -0.6422226
#> 24 -13.1447165 -5.9889274 -6.0008032 -10.1544315 -5.9949115 -6.0037904
#> 25  -1.8552695  2.2777843  2.3059150  -2.1900221  2.2958622  2.2914878
#> 26   5.2401381  3.2957539  3.3189881   3.5224658  3.3185833  3.3045925
#> 27   2.2010546 -1.9017223 -1.9024361   2.1356018 -1.9068453 -1.8923967
#> 28  13.0510899  3.6415330  3.6356619  10.6251511  3.6282661  3.6231769
#> 29  -2.4193309 -0.4165742 -0.4239745  -1.7547497 -0.4103461 -0.4345485
#> 30   6.4620509 -8.4380830 -8.4237091   7.8145126 -8.4264293 -8.4455333
#> 31  -5.7784618 -0.9027898 -0.9080020  -4.8233568 -0.9074618 -0.9041069
#> 32   1.4509866  2.0958031  2.0749671   0.9419409  2.1068536  2.0964665
#> 33   7.9214112  9.8516726  9.8565220   4.7489091  9.8680162  9.8801174
#> 34  -3.3029994  1.6935832  1.6725352  -3.2169203  1.6810599  1.6941970
#> 35   6.0773737  2.4787094  2.4617545   4.9182408  2.4543583  2.4586245
#> 36 -10.6780025 -1.5617825 -1.5663286  -9.1746997 -1.5711859 -1.5613791
#> 37   9.0285613 -1.4414365 -1.4255375   8.2122272 -1.4459823 -1.4371005
#> 38  -6.4695242 -2.9467627 -2.9357047  -5.0402549 -2.9297071 -2.9397697
#> 39   1.4662987 -1.3090126 -1.3083322   1.6270797 -1.3020824 -1.3165576
#> 40  -3.3371261 -2.5063990 -2.4953270  -2.4546657 -2.5039430 -2.4770483
#> 41  -1.4539051 -5.2468572 -5.2650928  -0.2295093 -5.2591658 -5.2512687
#> 42   6.3184639 -5.4198403 -5.4601561   6.7624950 -5.4054132 -5.4264303
#> 43   2.8317073  1.7682700  1.7577297   2.3103366  1.7716436  1.7854530
#> 44  10.6902298  5.4850914  5.4955988   8.0465319  5.5062763  5.4957139
#> 45  -0.6419986 -3.1803137 -3.1653965   0.1487841 -3.1717620 -3.1859978
#> 46   2.8169097 -7.9217699 -7.9159526   4.3848788 -7.9391640 -7.9150733
#> 47  11.1281255  3.9571348  3.9691447   9.0758530  3.9628487  3.9511548
#> 48   4.5841800  1.0845161  1.0807621   3.7481882  1.0838256  1.0968055
#> 49  -5.8178230 -5.1147009 -5.0984231  -3.9547834 -5.1007076 -5.1156178
#> 50   2.7833737 -2.0400129 -2.0192960   2.9955890 -2.0100177 -2.0300712
#>             X6
#> 1   -3.8203893
#> 2    0.7856648
#> 3    4.4714926
#> 4   -5.7694441
#> 5   11.9243584
#> 6    3.9193597
#> 7    8.1102868
#> 8    1.6474534
#> 9  -12.5035281
#> 10   8.9555033
#> 11  -4.5048317
#> 12  -7.0006527
#> 13   4.8932628
#> 14   1.1970988
#> 15  -1.2538425
#> 16   7.9037518
#> 17   1.2928187
#> 18   2.3677084
#> 19  -4.0024864
#> 20  -4.3827118
#> 21   2.4544227
#> 22   5.0210339
#> 23   0.8928215
#> 24 -10.1946654
#> 25  -2.1779188
#> 26   3.5185891
#> 27   2.1512452
#> 28  10.6244721
#> 29  -1.7780853
#> 30   7.8340958
#> 31  -4.8215752
#> 32   0.9283044
#> 33   4.7265777
#> 34  -3.2171668
#> 35   4.9220532
#> 36  -9.1730249
#> 37   8.1929077
#> 38  -5.0085114
#> 39   1.6473875
#> 40  -2.4636988
#> 41  -0.2537657
#> 42   6.7611795
#> 43   2.3123757
#> 44   8.0443681
#> 45   0.1289411
#> 46   4.4004104
#> 47   9.0678227
#> 48   3.7400793
#> 49  -3.9620494
#> 50   2.9866173
cvtable(summary(cv.plsR(Y~.,data=dataAstar2,5,NK=100, verbose=FALSE)))

#> ____************************************************____
#> Error in is.data.frame(data): objet 'dataAstar2' introuvable

dimX <- 6
Astar <- 3
simul_data_UniYX(dimX,Astar)

#>        Y       X1       X2       X3       X4       X5       X6 
#> 6.053029 3.689110 5.648481 3.172013 3.670531 5.644560 3.157390 
(dataAstar3 <- data.frame(t(replicate(50,simul_data_UniYX(dimX,Astar)))))

#>              Y           X1           X2           X3          X4           X5
#> 1   -1.2631029   8.62015665   6.04550745  -1.49610045   8.6160142   6.05222905
#> 2  -12.3698859  -0.48149600  -4.65999133  -8.29663001  -0.4840979  -4.65283898
#> 3  -13.3752100  -6.97607422  -2.68919756 -12.85550026  -6.9666058  -2.69496482
#> 4   14.2908966  -3.62743325   1.43095860  10.48074941  -3.6419478   1.42740649
#> 5    2.4915184  -0.59570169   3.04622831   0.03618188  -0.5690905   3.05831672
#> 6   -5.4694637  -2.77612155  -1.43404561  -4.99781690  -2.7602286  -1.43484884
#> 7    1.7861353   2.16944238   4.04352277  -0.02322489   2.1749004   4.05232934
#> 8    2.3985486   6.26214976   5.96461765   0.65653362   6.2437259   5.95757890
#> 9   -6.0663365  -4.39230852 -15.66552289   2.88280042  -4.4049851 -15.65584589
#> 10 -15.6835317   0.19271747  -4.10346903 -11.22824331   0.1826909  -4.09846771
#> 11  -0.4386717  -5.33677744  -5.26431305   1.17388905  -5.3167378  -5.24378213
#> 12   4.3304125   6.35930562   5.89927537   2.64391214   6.3656704   5.90267001
#> 13   0.1274229  -0.10746146   1.07272349  -0.80201933  -0.1117411   1.06870638
#> 14   2.4091915  -2.63053475  -5.41727258   4.45902327  -2.6294751  -5.39713624
#> 15 -10.7028579  -4.33248793  -2.37373200  -9.50593652  -4.3263525  -2.37293718
#> 16   6.1543136   0.66106856   1.45416854   4.82886012   0.6601333   1.43686959
#> 17  10.4264607  -2.96023385  10.55086507   1.32669810  -2.9635919  10.56579664
#> 18  16.0744100   7.86199101   7.13609641  12.56368148   7.8605900   7.12647545
#> 19  -3.6138262  -0.02355808  -2.47788102  -1.50647583  -0.0203125  -2.47837657
#> 20   9.3973883   4.50813781   8.22232139   4.83660938   4.5237641   8.19718909
#> 21  18.2721088   0.89258367   5.49504693  13.06479204   0.8844241   5.48651201
#> 22  -3.2215266   6.41564713   0.14303933  -0.59247563   6.3904457   0.12424621
#> 23  -3.9488421  -7.27075522  -0.14128497  -6.06273021  -7.2647811  -0.14521253
#> 24  -4.7866183  -5.78671556  -0.32164800  -6.17099344  -5.7999207  -0.31957270
#> 25  -7.0728021  -0.90612814 -14.92094368   2.88273912  -0.9096703 -14.94422828
#> 26   5.6918581   4.81284500  -0.08035738   6.88998112   4.8037946  -0.07958272
#> 27  -1.2880336 -15.13225525  -9.14634162  -1.13436363 -15.1413876  -9.14017794
#> 28   3.6608278  -4.91671305  -4.70634163   4.16494827  -4.9210192  -4.73362385
#> 29  -3.6655422   2.66036687   1.76746287  -3.35407991   2.6724442   1.77644851
#> 30   3.6261631   0.13638598  -3.53965032   5.61811174   0.1329447  -3.53582833
#> 31  -4.5235299  -1.34526120  -4.49217504  -1.68546591  -1.3631599  -4.46227885
#> 32   0.5336358  -4.80599611  -2.89209085   0.20148673  -4.8028437  -2.91002282
#> 33   2.7720865  -1.31651928  -1.63071326   2.95885467  -1.3167790  -1.63173290
#> 34  -1.3689187   5.01480278  -0.87924751   1.14393219   4.9787169  -0.88435741
#> 35   1.1236208  -1.97113906  -3.67058364   2.53246112  -1.9808060  -3.66871834
#> 36  -8.0788317  -6.85527676  -8.90216766  -4.04987639  -6.8605611  -8.92140282
#> 37  10.8330856   6.73874440   6.31953696   7.94135761   6.7247610   6.31102728
#> 38  -6.7092777   4.54326509   3.68547090  -6.44612867   4.5694655   3.67870490
#> 39  17.8047903  -3.64214154   6.75758963  10.26631932  -3.6456385   6.75897518
#> 40   1.7188822  -0.66164125  -2.12005974   2.72266937  -0.6751113  -2.13097620
#> 41   2.0740758   8.64534352   7.75893962   0.09814661   8.6705006   7.75768112
#> 42   2.1918392  10.12305454   7.81187451   0.81836595  10.1390035   7.79293651
#> 43  -8.9227240   4.28635751  -2.57562809  -4.76351301   4.2976642  -2.59746949
#> 44 -11.2815228   3.50930834  -2.77125713  -6.95490126   3.5206084  -2.77651025
#> 45   6.8816529   0.63782974   8.82733953   0.84597403   0.6535855   8.84792883
#> 46  16.1412754 -10.99838112  -0.79792407  10.22086356 -11.0001737  -0.78112049
#> 47  -1.2611036   0.72047062  -5.29236306   2.26971048   0.7138796  -5.28629422
#> 48   2.8611984   3.81337089   5.61122467   0.22487215   3.8227395   5.62362256
#> 49 -10.0928842  -5.97677779 -16.09687820  -1.02309093  -5.9752951 -16.10369720
#> 50  -8.8170314  -6.24581075  -1.37996681  -8.98467137  -6.2564990  -1.35358203
#>              X6
#> 1   -1.48515137
#> 2   -8.28858160
#> 3  -12.82380723
#> 4   10.47335101
#> 5    0.01861043
#> 6   -5.03323849
#> 7   -0.02389704
#> 8    0.65396427
#> 9    2.89431774
#> 10 -11.22803875
#> 11   1.16691778
#> 12   2.62803467
#> 13  -0.78829971
#> 14   4.45073685
#> 15  -9.50750556
#> 16   4.83696488
#> 17   1.30877531
#> 18  12.54138664
#> 19  -1.52207372
#> 20   4.82644495
#> 21  13.06699614
#> 22  -0.57938774
#> 23  -6.05199059
#> 24  -6.17072102
#> 25   2.90496499
#> 26   6.88111811
#> 27  -1.14813428
#> 28   4.17677628
#> 29  -3.35299545
#> 30   5.62432629
#> 31  -1.68738207
#> 32   0.19618725
#> 33   2.95462372
#> 34   1.14520928
#> 35   2.52270998
#> 36  -4.06258119
#> 37   7.89446223
#> 38  -6.46647250
#> 39  10.27335078
#> 40   2.69709957
#> 41   0.11457280
#> 42   0.80744420
#> 43  -4.76265500
#> 44  -6.95500441
#> 45   0.83309667
#> 46  10.22908306
#> 47   2.25425415
#> 48   0.22155741
#> 49  -1.03060202
#> 50  -8.97960486
cvtable(summary(cv.plsR(Y~.,data=dataAstar3,5,NK=100, verbose=FALSE)))

#> ____************************************************____
#> Error in is.data.frame(data): objet 'dataAstar3' introuvable

dimX <- 6
Astar <- 4
simul_data_UniYX(dimX,Astar)

#>          Y         X1         X2         X3         X4         X5         X6 
#>  0.4059092 -4.0821333 -1.8371446  0.0473401  3.7340274  5.9658261  7.8456856 
(dataAstar4 <- data.frame(t(replicate(50,simul_data_UniYX(dimX,Astar)))))

#>              Y          X1           X2          X3          X4           X5
#> 1    7.0860363   4.0077909   4.06328324   6.3135785   3.3732500   3.41441693
#> 2    3.2681636   3.8055202   2.88710074   3.1131039   4.8430419   3.90157594
#> 3   -5.5916689   4.1398696   2.09025553  -5.5012952   5.1036469   3.05082740
#> 4   -3.4812368   1.0812169  -3.56726928  -0.8844031   2.7101705  -1.91881738
#> 5    8.6998880   5.3209857  -1.57912545  11.7385645   5.1918862  -1.70338527
#> 6   -1.8177046   0.5288969   0.09212778  -1.4624162   1.1020394   0.67115647
#> 7    1.3130510   1.8923981   2.10155047   0.6735591  -1.9498672  -1.74709353
#> 8   -4.3528103   4.8175512   0.99410090  -3.3312504   8.5083742   4.71271220
#> 9   -6.6671333   5.4931079  -4.98381888  -1.3392754   7.0428168  -3.42019505
#> 10 -14.1121061  -4.4194137  -8.54532906 -10.4867272  -0.2922796  -4.41798755
#> 11   0.7893536  -2.5107756   2.55473097  -1.5876833   1.9294318   6.96547630
#> 12 -14.6659334 -13.4754624 -14.90632084 -10.6617973  -9.3796285 -10.83554464
#> 13  -4.8847046  -5.4799913  -7.34615481  -2.4885477 -12.3439363 -14.18168328
#> 14 -24.8442962  -1.4454725 -10.07022847 -19.5121917   7.4572480  -1.17494720
#> 15 -12.9907409   8.2072337   0.61655987 -10.5130039   9.4398693   1.83828922
#> 16  -7.9234206   6.5872042   6.95069928  -9.9410551   7.8117832   8.19090233
#> 17  -4.2994817   5.2259581   9.09634220  -8.2222844   6.0090566   9.87140088
#> 18   1.6788246  -3.6292430   5.70844721  -3.5083969  -4.3953353   4.89685271
#> 19   5.3021566  -7.0752056   2.38187759   1.3895094  -6.9567767   2.49787517
#> 20  -1.6790057   3.9200279   0.05154530  -0.3589290   3.7403832  -0.11499637
#> 21 -10.8000504   6.4974959  -0.92296670  -7.7566747   8.4503062   1.02867665
#> 22  -0.4863779  -4.4441857   2.87496170  -3.9959782  -7.3146995   0.02180724
#> 23  -3.4001711   1.7879384   8.15605900  -7.9657665   5.5112933  11.88189282
#> 24  -5.3414180   8.5248892  -0.67177546  -1.7274359  12.6155492   3.41984167
#> 25  -6.3438209  -2.5733347   0.62345602  -8.0413668  -4.7518035  -1.55507143
#> 26  -6.4234839  -1.6636694  -1.56350839  -6.2522811  -3.5514117  -3.49728423
#> 27   3.4144158  -3.5859721  -4.38209947   4.8260256  -6.6334912  -7.43415878
#> 28  -0.7504636   7.2490796   5.26112976  -1.2329636   0.4842377  -1.53521244
#> 29   7.4083635  -9.7439560  -1.97081900   4.9855246  -9.7335145  -1.98420476
#> 30   5.7853092  -1.6532324   3.57872694   2.8154206  -3.2990248   1.97155943
#> 31  -6.9793358   7.9468889   3.73835668  -5.9855478   3.7810241  -0.43252565
#> 32   5.2515916   2.6148493   0.12630245   6.2152971   6.6018613   4.12486101
#> 33   2.9752351   6.4926577   2.09436511   4.4754807   2.6936139  -1.71428669
#> 34   0.4066783   0.5076861  -5.16077721   3.9753799   0.4040819  -5.25373158
#> 35 -10.4071769  -5.4812078  -0.19262102 -12.4536746   3.9826979   9.24336478
#> 36  -9.7794709  -6.4040239  -7.26107489  -7.9502710  -7.2702174  -8.10474474
#> 37  -2.0201677 -13.2442964  -8.93150993  -1.3866178 -12.6631673  -8.31700198
#> 38   3.6619746   0.3415699  -2.81462956   5.4965395  -1.2137836  -4.37407399
#> 39  -6.9419179   2.2302566  -3.13643196  -4.2791230   1.1430958  -4.23543725
#> 40   2.3037179  -3.2868051   3.38500646  -1.2059138  -5.3003900   1.36300313
#> 41   3.6031236   6.3998541   4.93581611   2.9612245   6.9695118   5.46054133
#> 42   5.9014586   1.2349944   9.02842983   0.8490823   7.0163082  14.82390162
#> 43 -10.5298275   1.9760547  -4.80487417  -7.0049679   2.2800038  -4.53197233
#> 44  10.1265270   3.2538745   5.90448127   8.0841510   2.1753411   4.75239423
#> 45  11.7102146   0.1374255   2.16258534  10.7257386  -7.9401930  -5.88978411
#> 46  -3.2704082  -0.8205507  -4.74192894  -0.7030350   2.2991397  -1.63150303
#> 47  -6.2444004   8.9693756   3.93758579  -5.2276113   9.1272766   4.09124436
#> 48  -2.9445481   9.4963015   4.65220369  -2.4615317   6.9488980   2.10959746
#> 49   6.0849343  -6.2542975  -8.32715839   8.8008016  -7.9973740 -10.08662071
#> 50   5.2883991   2.0531857   1.49476346   5.4397378  -2.8415246  -3.41788867
#>             X6
#> 1    5.6699687
#> 2    4.1530111
#> 3   -4.5505915
#> 4    0.7741691
#> 5   11.6260502
#> 6   -0.8787134
#> 7   -3.1763859
#> 8    0.3632350
#> 9    0.2103480
#> 10  -6.3657143
#> 11   2.8151935
#> 12  -6.5670103
#> 13  -9.3192052
#> 14 -10.5774788
#> 15  -9.2731471
#> 16  -8.7195966
#> 17  -7.4680694
#> 18  -4.3051505
#> 19   1.4770180
#> 20  -0.5422467
#> 21  -5.8153162
#> 22  -6.8549195
#> 23  -4.2340823
#> 24   2.3557439
#> 25 -10.2299941
#> 26  -8.1407991
#> 27   1.7575952
#> 28  -8.0136838
#> 29   4.9526456
#> 30   1.2158937
#> 31 -10.1443635
#> 32  10.1624363
#> 33   0.6592251
#> 34   3.9106523
#> 35  -2.9754729
#> 36  -8.8201143
#> 37  -0.7951902
#> 38   3.9645935
#> 39  -5.3811771
#> 40  -3.2334664
#> 41   3.5009140
#> 42   6.6509663
#> 43  -6.7620323
#> 44   6.9603385
#> 45   2.6636970
#> 46   2.4322911
#> 47  -5.0789155
#> 48  -5.0192015
#> 49   7.0272046
#> 50   0.5318266
cvtable(summary(cv.plsR(Y~.,data=dataAstar4,5,NK=100, verbose=FALSE)))

#> ____************************************************____
#> Error in is.data.frame(data): objet 'dataAstar4' introuvable

rm(list=c("dimX","Astar","dataAstar2","dataAstar3","dataAstar4"))
# }