This notebook present a way of performing the SmoothPLS algorithm for a Scalar Functional Data.
It shows that Smooth PLS over perform FPLS with a time vector regul_time without a lot of points, and even with a lot of points.
Parameters
nind = 100 # number of individuals (train set)
start = 0 # First time
end = 100 # end time
lambda_0 = 0.2 # Exponential law parameter for state 0
lambda_1 = 0.1 # Exponential law parameter for state 1
prob_start = 0.5 # Probability of starting with state 1
curve_type = 'num'
TTRatio = 0.2 # Train Test Ratio means we have floor(nind*TTRatio/(1-TTRatio))
# individuals in the test set
NotS_ratio = 0.2 # noise variance over total variance for Y
beta_0_real=5.4321 # Intercept value for the link between X(t) and Y
nbasis = 10 # number of basis functions
norder = 4 # 4 for cubic splines basis
regul_time = seq(start, end, 5)
regul_time_0 = seq(start, end, 1)
beta_real_func = beta_4_real_func # link between X(t) and Y
int_mode = 2 # in case of integration errors.Synthetic SFD data
We can also generate synthetic Scalar Functional Data SFD. The important input is type=‘num’.
Generate_X_df
For SFD for X_df two new arguments are important: the noise added to the signal and the seed for repeatability.
df = generate_X_df(nind = nind, start = start,end = end, curve_type = 'num',
noise_sd = 0.15, seed = 123)
head(df)
#> id time value
#> 1 1 0 1.2591356
#> 2 1 1 0.7193661
#> 3 1 2 1.0470795
#> 4 1 3 0.7297674
#> 5 1 4 0.6105385
#> 6 1 5 0.5351208
# Visualisation
ggplot(df, aes(x = time, y = value, group = id, color = factor(id))) +
geom_line(alpha = 0.8) +
labs(title = "Noised cosinus curves",
x = "Time", y = "Value",
color = "Individual") +
theme_minimal() +
theme(legend.position = "none")
Data manipulation
regularize_time_series
df_regul = regularize_time_series(df, time_seq = regul_time,
curve_type = 'num')
df_regul
#> id time value
#> 1 1 0 1.2591356058
#> 2 1 5 0.5351207804
#> 3 1 10 0.2642695075
#> 4 1 15 -0.6025342230
#> 5 1 20 -1.3168846512
#> 6 1 25 -1.8577736968
#> 7 1 30 -2.0244393652
#> 8 1 35 -2.4807905328
#> 9 1 40 -1.7434094354
#> 10 1 45 -1.4872290083
#> 11 1 50 -0.8271237339
#> 12 1 55 -0.2641780101
#> 13 1 60 -0.0009657591
#> 14 1 65 0.8215195183
#> 15 1 70 1.1315289749
#> 16 1 75 1.5800859428
#> 17 1 80 1.8865890447
#> 18 1 85 2.0962514088
#> 19 1 90 1.7692432166
#> 20 1 95 1.5935932108
#> 21 1 100 1.0862570388
#> 22 2 0 0.9378618266
#> 23 2 5 0.6455078797
#> 24 2 10 -0.0370698945
#> 25 2 15 -0.8799845182
#> 26 2 20 -0.9900684367
#> 27 2 25 -1.6936381825
#> 28 2 30 -2.2424851992
#> 29 2 35 -2.2132760824
#> 30 2 40 -2.1036663913
#> 31 2 45 -1.7408282981
#> 32 2 50 -1.0985225027
#> 33 2 55 -0.5638455170
#> 34 2 60 0.0524523369
#> 35 2 65 0.7817098787
#> 36 2 70 1.1554473231
#> 37 2 75 1.6141871697
#> 38 2 80 1.8990561806
#> 39 2 85 1.9217983057
#> 40 2 90 1.6668157353
#> 41 2 95 1.3699517140
#> 42 2 100 1.0184536195
#> 43 3 0 1.0798334185
#> 44 3 5 0.4383151798
#> 45 3 10 0.2912442676
#> 46 3 15 -0.8721678297
#> 47 3 20 -1.5021680660
#> 48 3 25 -1.8288790360
#> 49 3 30 -1.8305280202
#> 50 3 35 -1.9232728029
#> 51 3 40 -1.7840912242
#> 52 3 45 -1.7585617966
#> 53 3 50 -1.1202938975
#> 54 3 55 -0.7749669486
#> 55 3 60 0.2502846840
#> 56 3 65 0.6375337377
#> 57 3 70 1.4490852733
#> 58 3 75 1.5572768287
#> 59 3 80 1.9055420533
#> 60 3 85 1.9460774356
#> 61 3 90 1.6873656325
#> 62 3 95 1.4769868377
#> 63 3 100 1.4495398133
#> 64 4 0 1.3862407145
#> 65 4 5 0.4548514199
#> 66 4 10 0.0217277187
#> 67 4 15 -0.8048020561
#> 68 4 20 -1.2655542240
#> 69 4 25 -1.6263337737
#> 70 4 30 -1.9497806043
#> 71 4 35 -2.0044893942
#> 72 4 40 -1.8904219000
#> 73 4 45 -1.6817548622
#> 74 4 50 -0.6948858899
#> 75 4 55 -0.3850094714
#> 76 4 60 0.0458252243
#> 77 4 65 0.8028850817
#> 78 4 70 0.9981055519
#> 79 4 75 1.7543619614
#> 80 4 80 1.9864136589
#> 81 4 85 1.9106580677
#> 82 4 90 1.8102546048
#> 83 4 95 1.6483781220
#> 84 4 100 1.1146984000
#> 85 5 0 1.4356594782
#> 86 5 5 0.5954593512
#> 87 5 10 -0.2912823356
#> 88 5 15 -0.6410984717
#> 89 5 20 -1.2784589448
#> 90 5 25 -1.6726335208
#> 91 5 30 -2.0908706871
#> 92 5 35 -1.9791599689
#> 93 5 40 -1.8317834667
#> 94 5 45 -1.5189291948
#> 95 5 50 -0.9208314522
#> 96 5 55 -0.4710667657
#> 97 5 60 0.0837581049
#> 98 5 65 0.4704048911
#> 99 5 70 1.1045849630
#> 100 5 75 1.5907515095
#> 101 5 80 1.9831297071
#> 102 5 85 1.9587557227
#> 103 5 90 2.0211248586
#> 104 5 95 1.5504049667
#> 105 5 100 1.0405641227
#> 106 6 0 0.9881392353
#> 107 6 5 0.4800120580
#> 108 6 10 0.0522163067
#> 109 6 15 -0.8101337365
#> 110 6 20 -0.9747700549
#> 111 6 25 -1.7132780979
#> 112 6 30 -1.8045431962
#> 113 6 35 -2.0802744306
#> 114 6 40 -1.6156486566
#> 115 6 45 -1.6422105381
#> 116 6 50 -1.2585355995
#> 117 6 55 -0.4957330891
#> 118 6 60 0.0482636784
#> 119 6 65 0.7302802334
#> 120 6 70 1.1108042715
#> 121 6 75 1.4854654094
#> 122 6 80 2.0101170542
#> 123 6 85 2.2756787375
#> 124 6 90 1.9819937669
#> 125 6 95 1.4204145564
#> 126 6 100 1.2418463733
#> 127 7 0 1.1142373544
#> 128 7 5 0.4851049780
#> 129 7 10 -0.5720259605
#> 130 7 15 -0.8841496568
#> 131 7 20 -1.2416482794
#> 132 7 25 -1.5788710918
#> 133 7 30 -1.7802454338
#> 134 7 35 -1.8495685735
#> 135 7 40 -1.9708957715
#> 136 7 45 -1.6027043283
#> 137 7 50 -1.0358275702
#> 138 7 55 -0.6092822180
#> 139 7 60 -0.1794844779
#> 140 7 65 0.7024246055
#> 141 7 70 1.3099390562
#> 142 7 75 1.4678595562
#> 143 7 80 1.8876150865
#> 144 7 85 1.9956087125
#> 145 7 90 1.7148619524
#> 146 7 95 1.7720582253
#> 147 7 100 1.2071216417
#> 148 8 0 1.1410981614
#> 149 8 5 0.5079109416
#> 150 8 10 0.0329739039
#> 151 8 15 -0.7347735916
#> 152 8 20 -1.1137741771
#> 153 8 25 -1.6518347960
#> 154 8 30 -1.8783015808
#> 155 8 35 -2.0246102132
#> 156 8 40 -1.8928193526
#> 157 8 45 -1.4924624180
#> 158 8 50 -0.8574289370
#> 159 8 55 -0.4657142090
#> 160 8 60 0.0731201495
#> 161 8 65 0.5286320905
#> 162 8 70 1.1685807638
#> 163 8 75 1.6573460269
#> 164 8 80 2.0316251197
#> 165 8 85 2.0381332918
#> 166 8 90 1.8396918610
#> 167 8 95 1.5893045955
#> 168 8 100 0.8993382037
#> 169 9 0 1.3185827460
#> 170 9 5 0.4629034735
#> 171 9 10 -0.0603813954
#> 172 9 15 -0.6274078032
#> 173 9 20 -1.3330837729
#> 174 9 25 -1.5105012723
#> 175 9 30 -1.7063035995
#> 176 9 35 -1.8252200624
#> 177 9 40 -1.9361720048
#> 178 9 45 -1.3182435129
#> 179 9 50 -1.4633157230
#> 180 9 55 -0.4607217469
#> 181 9 60 0.1134147409
#> 182 9 65 0.7648043675
#> 183 9 70 1.3098583262
#> 184 9 75 1.8297805054
#> 185 9 80 2.0004325925
#> 186 9 85 2.0707662500
#> 187 9 90 2.0320682204
#> 188 9 95 1.4258057457
#> 189 9 100 1.1945851367
#> 190 10 0 1.1803785931
#> 191 10 5 0.5723232276
#> 192 10 10 -0.1166378496
#> 193 10 15 -0.5211453024
#> 194 10 20 -1.3353118175
#> 195 10 25 -1.8650336402
#> 196 10 30 -1.8811599742
#> 197 10 35 -1.8533872623
#> 198 10 40 -1.8489480902
#> 199 10 45 -1.6349338338
#> 200 10 50 -0.9326958786
#> 201 10 55 -0.4856958116
#> 202 10 60 0.3418402891
#> 203 10 65 0.9746415720
#> 204 10 70 1.3136320533
#> 205 10 75 1.6455633680
#> 206 10 80 1.5520966998
#> 207 10 85 1.9296482120
#> 208 10 90 1.8317489275
#> 209 10 95 1.8101608312
#> 210 10 100 0.8333303890
#> 211 11 0 0.9331176832
#> 212 11 5 0.6546308056
#> 213 11 10 -0.1528723330
#> 214 11 15 -0.9116440930
#> 215 11 20 -1.5559733957
#> 216 11 25 -1.4135116863
#> 217 11 30 -1.9366976400
#> 218 11 35 -2.1134180841
#> 219 11 40 -2.0190805275
#> 220 11 45 -1.7946432616
#> 221 11 50 -1.2291100526
#> 222 11 55 -0.4273251054
#> 223 11 60 0.0872057561
#> 224 11 65 0.7134863400
#> 225 11 70 1.4884126811
#> 226 11 75 1.3694656844
#> 227 11 80 1.7493179415
#> 228 11 85 1.7519147194
#> 229 11 90 1.9205069179
#> 230 11 95 1.8282478341
#> 231 11 100 1.1876505988
#> 232 12 0 0.8453409186
#> 233 12 5 0.3542108121
#> 234 12 10 -0.1385147681
#> 235 12 15 -0.6828600415
#> 236 12 20 -1.2211908832
#> 237 12 25 -1.4729744662
#> 238 12 30 -2.0598822240
#> 239 12 35 -2.0942690011
#> 240 12 40 -1.6410755575
#> 241 12 45 -1.5627758205
#> 242 12 50 -1.1972478282
#> 243 12 55 -0.4166188679
#> 244 12 60 -0.2148575130
#> 245 12 65 0.5968238570
#> 246 12 70 1.3225844768
#> 247 12 75 1.7774779441
#> 248 12 80 1.9786511242
#> 249 12 85 1.9762715775
#> 250 12 90 1.6250725112
#> 251 12 95 1.4891784390
#> 252 12 100 1.1349574354
#> 253 13 0 0.9539185183
#> 254 13 5 0.5411432876
#> 255 13 10 -0.2140366901
#> 256 13 15 -0.5199075812
#> 257 13 20 -1.3390164223
#> 258 13 25 -1.7900691555
#> 259 13 30 -2.0724620767
#> 260 13 35 -1.9965236114
#> 261 13 40 -1.7577302843
#> 262 13 45 -1.5808106622
#> 263 13 50 -1.1055618166
#> 264 13 55 -0.5248271648
#> 265 13 60 -0.0449239287
#> 266 13 65 0.5374668779
#> 267 13 70 1.4474553115
#> 268 13 75 1.6458282047
#> 269 13 80 2.0124232127
#> 270 13 85 1.9842524644
#> 271 13 90 1.7245877621
#> 272 13 95 1.2058907889
#> 273 13 100 0.9422999610
#> 274 14 0 1.0637206790
#> 275 14 5 0.4418738691
#> 276 14 10 -0.3429290744
#> 277 14 15 -0.6807588944
#> 278 14 20 -1.1311863246
#> 279 14 25 -1.6216686939
#> 280 14 30 -2.1097118593
#> 281 14 35 -1.9251249715
#> 282 14 40 -2.0042703533
#> 283 14 45 -1.4546741930
#> 284 14 50 -0.9847011379
#> 285 14 55 -0.6857812998
#> 286 14 60 0.2331324839
#> 287 14 65 0.6414487997
#> 288 14 70 1.3007899785
#> 289 14 75 1.6408405277
#> 290 14 80 1.9806066274
#> 291 14 85 2.0939265744
#> 292 14 90 1.7743093191
#> 293 14 95 1.5058292406
#> 294 14 100 0.6763052064
#> 295 15 0 0.9242134979
#> 296 15 5 0.5491348779
#> 297 15 10 -0.2577505234
#> 298 15 15 -0.8122698287
#> 299 15 20 -1.3428963474
#> 300 15 25 -1.7906432883
#> 301 15 30 -2.1321959463
#> 302 15 35 -2.2256600689
#> 303 15 40 -1.9919063419
#> 304 15 45 -1.5736327548
#> 305 15 50 -1.2937988592
#> 306 15 55 -0.6390054707
#> 307 15 60 0.0289696526
#> 308 15 65 0.7746519270
#> 309 15 70 1.0125676916
#> 310 15 75 1.6170996123
#> 311 15 80 1.8138296715
#> 312 15 85 1.8153919362
#> 313 15 90 1.6220896723
#> 314 15 95 1.2723238465
#> 315 15 100 1.0143650949
#> 316 16 0 1.1899962569
#> 317 16 5 0.5323385060
#> 318 16 10 -0.1318397693
#> 319 16 15 -0.5892413895
#> 320 16 20 -1.1878358703
#> 321 16 25 -1.7614859743
#> 322 16 30 -1.9241128170
#> 323 16 35 -2.2344407985
#> 324 16 40 -1.9399600315
#> 325 16 45 -1.6666654743
#> 326 16 50 -0.9803622189
#> 327 16 55 -0.4761905048
#> 328 16 60 0.2407138832
#> 329 16 65 0.4698082497
#> 330 16 70 1.4038925353
#> 331 16 75 1.6030017590
#> 332 16 80 1.9487680216
#> 333 16 85 1.9460400122
#> 334 16 90 1.9914783153
#> 335 16 95 1.5231057634
#> 336 16 100 1.1447845849
#> 337 17 0 1.1214100774
#> 338 17 5 0.3138064599
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#> 343 17 30 -1.9630292062
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#> 351 17 70 1.2792507802
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#> 357 17 100 1.0455336827
#> 358 18 0 1.2116549137
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#> 378 18 100 1.2108555589
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#> 399 19 100 0.6823048354
#> 400 20 0 1.5030172531
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#> 420 20 100 0.9314326363
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#> 441 21 100 1.3309668721
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#> 497 24 65 0.9697979768
#> 498 24 70 1.3620399222
#> 499 24 75 1.6729601880
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#> 501 24 85 2.1155010300
#> 502 24 90 1.8627092998
#> 503 24 95 1.6205858958
#> 504 24 100 0.8460435056
#> 505 25 0 0.9544764549
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#> 518 25 65 1.0847396864
#> 519 25 70 1.1567634967
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#> 523 25 90 1.7708497393
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#> 525 25 100 1.0181712749
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#> 539 26 65 0.6596210683
#> 540 26 70 1.4331483118
#> 541 26 75 1.6977154170
#> 542 26 80 2.0433239352
#> 543 26 85 2.0705440913
#> 544 26 90 1.9193725293
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#> 1654 79 75 1.7330380420
#> 1655 79 80 2.0626953438
#> 1656 79 85 1.8538497427
#> 1657 79 90 1.5828052849
#> 1658 79 95 1.5783241042
#> 1659 79 100 1.0286147988
#> 1660 80 0 1.1969318481
#> 1661 80 5 0.2594358794
#> 1662 80 10 0.0920970332
#> 1663 80 15 -0.6569782468
#> 1664 80 20 -1.0607211499
#> 1665 80 25 -1.9361520922
#> 1666 80 30 -1.6558195554
#> 1667 80 35 -2.2837590214
#> 1668 80 40 -1.7024691782
#> 1669 80 45 -1.4948891911
#> 1670 80 50 -1.0713676878
#> 1671 80 55 -0.5999484196
#> 1672 80 60 0.0573813551
#> 1673 80 65 0.8952346936
#> 1674 80 70 1.1449582445
#> 1675 80 75 1.5621674500
#> 1676 80 80 1.8982565406
#> 1677 80 85 2.0534220982
#> 1678 80 90 1.9942954653
#> 1679 80 95 1.3146439699
#> 1680 80 100 1.1543351823
#> 1681 81 0 1.0273806386
#> 1682 81 5 0.5555273941
#> 1683 81 10 0.0464987391
#> 1684 81 15 -0.7394319212
#> 1685 81 20 -1.3423572917
#> 1686 81 25 -1.9866288856
#> 1687 81 30 -1.7995231433
#> 1688 81 35 -1.9493729598
#> 1689 81 40 -2.0509925462
#> 1690 81 45 -1.1402672801
#> 1691 81 50 -1.0220548724
#> 1692 81 55 -0.6387352413
#> 1693 81 60 -0.0019497536
#> 1694 81 65 1.0533157555
#> 1695 81 70 1.3594904616
#> 1696 81 75 1.5266479263
#> 1697 81 80 1.7795201595
#> 1698 81 85 1.9897375882
#> 1699 81 90 1.8954005046
#> 1700 81 95 1.3087207115
#> 1701 81 100 1.0787840500
#> 1702 82 0 1.3343989934
#> 1703 82 5 0.3417780445
#> 1704 82 10 -0.0006179739
#> 1705 82 15 -0.5495809049
#> 1706 82 20 -1.2003396355
#> 1707 82 25 -1.6966652183
#> 1708 82 30 -1.9527410634
#> 1709 82 35 -2.1202034323
#> 1710 82 40 -1.9130672487
#> 1711 82 45 -1.5834608455
#> 1712 82 50 -1.1767910249
#> 1713 82 55 -0.4410483504
#> 1714 82 60 -0.0826427858
#> 1715 82 65 0.4994731144
#> 1716 82 70 1.2834525424
#> 1717 82 75 1.8515429529
#> 1718 82 80 2.0220459437
#> 1719 82 85 2.0683142553
#> 1720 82 90 1.7014612956
#> 1721 82 95 1.5571302635
#> 1722 82 100 1.3953320873
#> 1723 83 0 1.0671814223
#> 1724 83 5 0.4728575795
#> 1725 83 10 -0.0325672461
#> 1726 83 15 -0.8470077628
#> 1727 83 20 -1.2743205390
#> 1728 83 25 -1.7615243690
#> 1729 83 30 -1.8250997040
#> 1730 83 35 -1.9140950374
#> 1731 83 40 -1.8902562533
#> 1732 83 45 -1.2632348405
#> 1733 83 50 -0.8616880378
#> 1734 83 55 -0.4280315536
#> 1735 83 60 0.1550099770
#> 1736 83 65 0.8002093150
#> 1737 83 70 1.3464181534
#> 1738 83 75 1.8492243504
#> 1739 83 80 2.0830110296
#> 1740 83 85 2.3071395336
#> 1741 83 90 1.8505898188
#> 1742 83 95 1.6151102290
#> 1743 83 100 0.8010706792
#> 1744 84 0 1.0988480082
#> 1745 84 5 0.4339581490
#> 1746 84 10 -0.0059122833
#> 1747 84 15 -0.6534855205
#> 1748 84 20 -1.0848055855
#> 1749 84 25 -1.6999469030
#> 1750 84 30 -1.9299642632
#> 1751 84 35 -2.1619259327
#> 1752 84 40 -1.7539055096
#> 1753 84 45 -1.6133781840
#> 1754 84 50 -0.9828356700
#> 1755 84 55 -0.6125236438
#> 1756 84 60 0.0748538222
#> 1757 84 65 0.7189280701
#> 1758 84 70 1.4300964997
#> 1759 84 75 1.5854890416
#> 1760 84 80 2.1328030381
#> 1761 84 85 1.8429224635
#> 1762 84 90 1.8869959580
#> 1763 84 95 1.3888179254
#> 1764 84 100 0.9957114746
#> 1765 85 0 0.9867572112
#> 1766 85 5 0.4414084310
#> 1767 85 10 -0.1511860160
#> 1768 85 15 -0.5382109413
#> 1769 85 20 -1.3184815741
#> 1770 85 25 -1.8310265867
#> 1771 85 30 -1.9181449494
#> 1772 85 35 -1.9230703705
#> 1773 85 40 -1.7582895350
#> 1774 85 45 -1.6474058045
#> 1775 85 50 -0.9919717369
#> 1776 85 55 -0.5090282879
#> 1777 85 60 0.3590004212
#> 1778 85 65 0.5528024839
#> 1779 85 70 1.4543655903
#> 1780 85 75 1.6824812474
#> 1781 85 80 2.0793847264
#> 1782 85 85 1.9568461298
#> 1783 85 90 1.8684507759
#> 1784 85 95 1.9323259862
#> 1785 85 100 1.1119841156
#> 1786 86 0 1.0854224515
#> 1787 86 5 0.7691810759
#> 1788 86 10 -0.1303952451
#> 1789 86 15 -0.8434348381
#> 1790 86 20 -1.3837227155
#> 1791 86 25 -1.5023882444
#> 1792 86 30 -1.8369138106
#> 1793 86 35 -2.1756645182
#> 1794 86 40 -2.0936401720
#> 1795 86 45 -1.5759720383
#> 1796 86 50 -1.1624472165
#> 1797 86 55 -0.6752078619
#> 1798 86 60 0.0062073300
#> 1799 86 65 0.7069760367
#> 1800 86 70 1.2611460139
#> 1801 86 75 1.6936216647
#> 1802 86 80 1.8804584542
#> 1803 86 85 2.2125636226
#> 1804 86 90 1.7802663197
#> 1805 86 95 1.9671965589
#> 1806 86 100 1.0881507951
#> 1807 87 0 0.9682010000
#> 1808 87 5 0.6256374259
#> 1809 87 10 -0.2104413492
#> 1810 87 15 -0.6215795540
#> 1811 87 20 -1.1606519672
#> 1812 87 25 -1.9262050715
#> 1813 87 30 -1.7075500651
#> 1814 87 35 -2.0728314385
#> 1815 87 40 -1.8671984500
#> 1816 87 45 -1.6275894391
#> 1817 87 50 -1.3263711635
#> 1818 87 55 -0.2650990994
#> 1819 87 60 0.0257848609
#> 1820 87 65 0.9311073355
#> 1821 87 70 1.3158664893
#> 1822 87 75 1.9101223241
#> 1823 87 80 1.9187079566
#> 1824 87 85 2.1235168110
#> 1825 87 90 1.8436506227
#> 1826 87 95 1.6901633718
#> 1827 87 100 1.2519519205
#> 1828 88 0 1.0674850442
#> 1829 88 5 0.5481308252
#> 1830 88 10 -0.3688368907
#> 1831 88 15 -0.9448425576
#> 1832 88 20 -1.3195945122
#> 1833 88 25 -1.8749041713
#> 1834 88 30 -1.9381448087
#> 1835 88 35 -2.0407844036
#> 1836 88 40 -2.0307479525
#> 1837 88 45 -1.2436891127
#> 1838 88 50 -1.1753370232
#> 1839 88 55 -0.6154760902
#> 1840 88 60 -0.0219206204
#> 1841 88 65 0.7336482174
#> 1842 88 70 1.3358584010
#> 1843 88 75 1.7293293211
#> 1844 88 80 1.9504810370
#> 1845 88 85 2.4063762478
#> 1846 88 90 1.9132694718
#> 1847 88 95 1.5813889232
#> 1848 88 100 1.1722411865
#> 1849 89 0 1.0081391630
#> 1850 89 5 0.6916586620
#> 1851 89 10 -0.0774676084
#> 1852 89 15 -0.7513507883
#> 1853 89 20 -1.4160033237
#> 1854 89 25 -1.6036443355
#> 1855 89 30 -2.1298524345
#> 1856 89 35 -1.9820489840
#> 1857 89 40 -1.8673732496
#> 1858 89 45 -1.5052849952
#> 1859 89 50 -1.1696429910
#> 1860 89 55 -0.8686521948
#> 1861 89 60 0.1338065021
#> 1862 89 65 0.4779418321
#> 1863 89 70 0.9329689562
#> 1864 89 75 1.6658025091
#> 1865 89 80 1.9364756858
#> 1866 89 85 1.8842724253
#> 1867 89 90 1.5157021471
#> 1868 89 95 1.5552494362
#> 1869 89 100 1.0813193505
#> 1870 90 0 1.0483525423
#> 1871 90 5 0.5448200646
#> 1872 90 10 -0.1340001714
#> 1873 90 15 -0.6456680838
#> 1874 90 20 -1.1595077673
#> 1875 90 25 -1.3775320475
#> 1876 90 30 -1.7109503136
#> 1877 90 35 -2.3821851695
#> 1878 90 40 -1.9921557228
#> 1879 90 45 -1.5203222747
#> 1880 90 50 -0.9092334709
#> 1881 90 55 -0.6165016540
#> 1882 90 60 0.0124738978
#> 1883 90 65 0.4994469061
#> 1884 90 70 1.2273511323
#> 1885 90 75 1.6310632184
#> 1886 90 80 1.9144070027
#> 1887 90 85 1.9847308819
#> 1888 90 90 1.8991977740
#> 1889 90 95 1.1848686863
#> 1890 90 100 0.9877279281
#> 1891 91 0 0.9921949119
#> 1892 91 5 0.6042874577
#> 1893 91 10 -0.2786373826
#> 1894 91 15 -0.5957755462
#> 1895 91 20 -1.4975064045
#> 1896 91 25 -1.7894424992
#> 1897 91 30 -2.0099732995
#> 1898 91 35 -2.0206880493
#> 1899 91 40 -1.9979910267
#> 1900 91 45 -1.6664485063
#> 1901 91 50 -1.0124140509
#> 1902 91 55 -0.5292427257
#> 1903 91 60 0.0126923076
#> 1904 91 65 0.9374432799
#> 1905 91 70 0.8767186272
#> 1906 91 75 1.5604641735
#> 1907 91 80 1.9122489049
#> 1908 91 85 2.0550282137
#> 1909 91 90 1.8086666372
#> 1910 91 95 1.7308653187
#> 1911 91 100 1.1097751470
#> 1912 92 0 1.1092239579
#> 1913 92 5 0.5831885689
#> 1914 92 10 -0.3253022664
#> 1915 92 15 -0.6634641848
#> 1916 92 20 -1.1873928535
#> 1917 92 25 -1.7970771362
#> 1918 92 30 -2.2410696788
#> 1919 92 35 -2.0788247576
#> 1920 92 40 -1.7939281280
#> 1921 92 45 -1.4528338593
#> 1922 92 50 -1.0908272682
#> 1923 92 55 -0.6109352436
#> 1924 92 60 0.1405762906
#> 1925 92 65 0.8825858558
#> 1926 92 70 1.2399016056
#> 1927 92 75 1.7722573250
#> 1928 92 80 1.8351873357
#> 1929 92 85 2.1854719749
#> 1930 92 90 2.1543966970
#> 1931 92 95 1.4758534785
#> 1932 92 100 1.0500987342
#> 1933 93 0 1.3514536814
#> 1934 93 5 0.2771297979
#> 1935 93 10 -0.1302929793
#> 1936 93 15 -0.8900629214
#> 1937 93 20 -1.5366518902
#> 1938 93 25 -1.3918208308
#> 1939 93 30 -1.8869571631
#> 1940 93 35 -1.9749473377
#> 1941 93 40 -1.7831725341
#> 1942 93 45 -1.5863619019
#> 1943 93 50 -1.2113675589
#> 1944 93 55 -0.4669642946
#> 1945 93 60 0.1112157961
#> 1946 93 65 0.6299134313
#> 1947 93 70 1.3970443260
#> 1948 93 75 1.7059071496
#> 1949 93 80 1.9062861120
#> 1950 93 85 1.9350369464
#> 1951 93 90 1.9604615923
#> 1952 93 95 1.7458690164
#> 1953 93 100 1.0545107534
#> 1954 94 0 1.1831944808
#> 1955 94 5 0.3676721990
#> 1956 94 10 0.1420782687
#> 1957 94 15 -0.8347190057
#> 1958 94 20 -1.2819826168
#> 1959 94 25 -1.4321359178
#> 1960 94 30 -2.0375416826
#> 1961 94 35 -2.0284234698
#> 1962 94 40 -2.0769722512
#> 1963 94 45 -1.6274058064
#> 1964 94 50 -1.1001804921
#> 1965 94 55 -0.2878290811
#> 1966 94 60 -0.2278238932
#> 1967 94 65 0.5313312064
#> 1968 94 70 1.1821757849
#> 1969 94 75 1.7069561107
#> 1970 94 80 2.0031771338
#> 1971 94 85 2.1639405308
#> 1972 94 90 1.9656377548
#> 1973 94 95 1.4744891565
#> 1974 94 100 1.2305892548
#> 1975 95 0 1.1636092986
#> 1976 95 5 0.3164202746
#> 1977 95 10 -0.1466510632
#> 1978 95 15 -0.4824516861
#> 1979 95 20 -1.0694085761
#> 1980 95 25 -1.7518591094
#> 1981 95 30 -2.1074945012
#> 1982 95 35 -2.1068905913
#> 1983 95 40 -1.6555545677
#> 1984 95 45 -1.6765900017
#> 1985 95 50 -0.9856287959
#> 1986 95 55 -0.2646908484
#> 1987 95 60 0.0252296195
#> 1988 95 65 0.4918614750
#> 1989 95 70 1.0865840685
#> 1990 95 75 1.7108482965
#> 1991 95 80 1.9435224653
#> 1992 95 85 1.9955157852
#> 1993 95 90 1.9277938328
#> 1994 95 95 1.2325008316
#> 1995 95 100 1.2981492554
#> 1996 96 0 1.0393793988
#> 1997 96 5 0.3360586914
#> 1998 96 10 0.2320713846
#> 1999 96 15 -0.8392346802
#> 2000 96 20 -1.5446749306
#> 2001 96 25 -1.5277646519
#> 2002 96 30 -2.1125780809
#> 2003 96 35 -1.9054329137
#> 2004 96 40 -1.7274091582
#> 2005 96 45 -1.8208910903
#> 2006 96 50 -1.2286412552
#> 2007 96 55 -0.6226267694
#> 2008 96 60 0.0089212983
#> 2009 96 65 1.0852016533
#> 2010 96 70 1.2489766647
#> 2011 96 75 1.4743936614
#> 2012 96 80 1.7271483539
#> 2013 96 85 1.9543513345
#> 2014 96 90 1.8824441730
#> 2015 96 95 1.3453143513
#> 2016 96 100 1.0373231914
#> 2017 97 0 1.3633336097
#> 2018 97 5 0.4052424102
#> 2019 97 10 -0.2954159945
#> 2020 97 15 -0.9171959282
#> 2021 97 20 -1.2502807798
#> 2022 97 25 -1.9279304487
#> 2023 97 30 -2.0118762218
#> 2024 97 35 -1.9770206826
#> 2025 97 40 -2.0192569381
#> 2026 97 45 -1.6213295397
#> 2027 97 50 -1.0137613267
#> 2028 97 55 -0.2993252663
#> 2029 97 60 0.0600768817
#> 2030 97 65 0.7122201307
#> 2031 97 70 1.3063327133
#> 2032 97 75 1.6356296881
#> 2033 97 80 1.9246810242
#> 2034 97 85 2.1286986310
#> 2035 97 90 1.8698308612
#> 2036 97 95 1.5646597004
#> 2037 97 100 1.1981534890
#> 2038 98 0 1.0816591601
#> 2039 98 5 0.5551979550
#> 2040 98 10 -0.0304407647
#> 2041 98 15 -0.5818339142
#> 2042 98 20 -1.2514536747
#> 2043 98 25 -1.4971334774
#> 2044 98 30 -2.0836342607
#> 2045 98 35 -1.9812021828
#> 2046 98 40 -1.9439519235
#> 2047 98 45 -1.4369176308
#> 2048 98 50 -1.1690504443
#> 2049 98 55 -0.6043970143
#> 2050 98 60 0.1487444872
#> 2051 98 65 0.6816098231
#> 2052 98 70 1.0217672993
#> 2053 98 75 1.5772613452
#> 2054 98 80 2.0942376043
#> 2055 98 85 1.9955945970
#> 2056 98 90 1.7919549904
#> 2057 98 95 1.6174364997
#> 2058 98 100 1.2790108783
#> 2059 99 0 1.0584272408
#> 2060 99 5 0.4932045870
#> 2061 99 10 -0.3280718800
#> 2062 99 15 -0.8897639007
#> 2063 99 20 -1.4663989445
#> 2064 99 25 -1.6360091076
#> 2065 99 30 -1.8131498991
#> 2066 99 35 -2.1379219321
#> 2067 99 40 -1.7733229307
#> 2068 99 45 -1.6035504712
#> 2069 99 50 -1.0252689985
#> 2070 99 55 -0.4589940176
#> 2071 99 60 -0.0454230550
#> 2072 99 65 0.8845501267
#> 2073 99 70 1.4257391765
#> 2074 99 75 1.6029707592
#> 2075 99 80 1.9443142210
#> 2076 99 85 1.8978744326
#> 2077 99 90 2.2082011032
#> 2078 99 95 1.4857033217
#> 2079 99 100 1.2302939591
#> 2080 100 0 1.0419876847
#> 2081 100 5 0.5514407363
#> 2082 100 10 -0.0428374503
#> 2083 100 15 -0.6527186146
#> 2084 100 20 -1.0963691263
#> 2085 100 25 -1.4532470660
#> 2086 100 30 -1.9515669907
#> 2087 100 35 -2.0183386128
#> 2088 100 40 -2.0658645588
#> 2089 100 45 -1.5986642771
#> 2090 100 50 -1.0937385183
#> 2091 100 55 -0.5878865454
#> 2092 100 60 0.0520201140
#> 2093 100 65 0.7630773304
#> 2094 100 70 1.3992468335
#> 2095 100 75 1.4944830189
#> 2096 100 80 1.8401948997
#> 2097 100 85 1.9987338761
#> 2098 100 90 1.9023847932
#> 2099 100 95 1.5463361966
#> 2100 100 100 1.2067560848convert_to_wide_format
df_wide = convert_to_wide_format(df_regul)
df_wide
#> # A tibble: 100 × 22
#> id `0` `5` `10` `15` `20` `25` `30` `35` `40` `45` `50`
#> <int> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 1 1.26 0.535 0.264 -0.603 -1.32 -1.86 -2.02 -2.48 -1.74 -1.49 -0.827
#> 2 2 0.938 0.646 -0.0371 -0.880 -0.990 -1.69 -2.24 -2.21 -2.10 -1.74 -1.10
#> 3 3 1.08 0.438 0.291 -0.872 -1.50 -1.83 -1.83 -1.92 -1.78 -1.76 -1.12
#> 4 4 1.39 0.455 0.0217 -0.805 -1.27 -1.63 -1.95 -2.00 -1.89 -1.68 -0.695
#> 5 5 1.44 0.595 -0.291 -0.641 -1.28 -1.67 -2.09 -1.98 -1.83 -1.52 -0.921
#> 6 6 0.988 0.480 0.0522 -0.810 -0.975 -1.71 -1.80 -2.08 -1.62 -1.64 -1.26
#> 7 7 1.11 0.485 -0.572 -0.884 -1.24 -1.58 -1.78 -1.85 -1.97 -1.60 -1.04
#> 8 8 1.14 0.508 0.0330 -0.735 -1.11 -1.65 -1.88 -2.02 -1.89 -1.49 -0.857
#> 9 9 1.32 0.463 -0.0604 -0.627 -1.33 -1.51 -1.71 -1.83 -1.94 -1.32 -1.46
#> 10 10 1.18 0.572 -0.117 -0.521 -1.34 -1.87 -1.88 -1.85 -1.85 -1.63 -0.933
#> # ℹ 90 more rows
#> # ℹ 10 more variables: `55` <dbl>, `60` <dbl>, `65` <dbl>, `70` <dbl>,
#> # `75` <dbl>, `80` <dbl>, `85` <dbl>, `90` <dbl>, `95` <dbl>, `100` <dbl>generate_Y_df
plot(regul_time_0, beta_real_func(regul_time_0))
WARNING! Here we have to regularize X(t) before evaluating Y!
Y_df = generate_Y_df(df = df_regul, curve_type = 'num',
beta_real_func_or_list = beta_real_func,
beta_0_real = beta_0_real, NotS_ratio = NotS_ratio,
seed = 123)
Y = Y_df$Y_noised
head(Y_df)
#> id Y_real Y_noised
#> 1 1 -201.7150 -203.2424
#> 2 2 -197.9957 -198.6230
#> 3 3 -198.3660 -194.1184
#> 4 4 -199.5417 -199.3496
#> 5 5 -197.7755 -197.4232
#> 6 6 -198.4119 -193.7382
Basis
basis = create_bspline_basis(start, end, nbasis, norder)
#basis = fda::create.fourier.basis(rangeval=c(start, end), nbasis=(nbasis))
plot(basis, main=paste0(nbasis, " Function basis"))
Naive PLS
naive_pls_obj = naivePLS(df_list = df, Y = Y_df$Y_noised,
regul_time_obj = regul_time,
curve_type_obj = 'num',
id_col_obj = 'id', time_col_obj = 'time',
print_steps = TRUE, plot_rmsep = TRUE,
print_nbComp = TRUE, plot_reg_curves = TRUE)
#> ### Naive PLS ###
#> => Input format assertions.
#> => Input format assertions OK.
#> => Data formatting.
#> => PLS model.
#> [1] "Optimal number of PLS components : 4"
Regression coefficients
for(i in 2:length(naive_pls_obj$reg_obj)){
plot(naive_pls_obj$reg_obj[[i]])
title(naive_pls_obj$curves_names[i-1])
}
plot(naive_pls_obj$reg_obj$Num_1,
xlab='regul_time', ylab='beta coefficient value',
main="naive pls regression coefficients")
lines(x = regul_time, y = naive_pls_obj$reg_obj$Num_1[, 2], col='blue')
lines(x = regul_time_0, y=beta_real_func(start:end, end), col='red')
FPLS
fpls_obj = funcPLS(df_list = df, Y = Y_df$Y_noised,
basis_obj = basis,
curve_type_obj = 'num',
regul_time_obj = regul_time,
id_col_obj = 'id',time_col_obj = 'time',
print_steps = TRUE, plot_rmsep = TRUE,
print_nbComp = TRUE, plot_reg_curves = TRUE)
#> ### Functional PLS ###
#> => Input format assertions.
#> => Input format assertions OK.
#> => Building alpha matrix.
#> => Building curve names.
#> ==> Evaluating alpha for : NumFD_1.
#> => Evaluate metrix and root_metric.
#> => plsr(Y ~ trans_alphas).
#> Optimal number of PLS components : 2 .
#> => Build Intercept and regression curves for optimal number of components.
#> ==> Build regression curve for : NumFD_1
#Smooth PLS
spls_obj = smoothPLS(df_list = df, Y = Y_df$Y_noised, basis_obj = basis,
orth_obj = TRUE, curve_type_obj = curve_type,
regul_time_obj = regul_time,
int_mode = int_mode, print_steps = TRUE, plot_rmsep = TRUE,
print_nbComp = TRUE, plot_reg_curves = TRUE)
#> ### Smooth PLS ###
#> ## Use parallelization in case of heavy computational load. ##
#> ## Threshold can be manualy adjusted : (default 2500) ##
#> ## >options(SmoothPLS.parallel_threshold = 500) ##
#> => Input format assertions.
#> => Input format assertions OK.
#> => Orthonormalize basis.
#> => Data objects formatting.
#> => Evaluate Lambda matrix.
#> ==> Lambda for : NumFD_1_value.
#> Warning: package 'future' was built under R version 4.4.3
#> => PLSR model.
#> => Optimal number of PLS components : 9
#> => Evaluate SmoothPLS functions and <w_i, p_j> coef.
#> => Build regression functions and intercept.
#> ==> Build regression curve for : NumFD_1_value
Delta
delta_0 = spls_obj$reg_obj$Intercept
print(delta_0)
#> [1] -13.72161
delta = spls_obj$reg_obj$NumFD_1
y_lim = eval_max_min_y(f_list = list(beta_real_func, delta),
regul_time = regul_time)
plot(regul_time, beta_real_func(regul_time), type='l', xlab="Beta_t",
ylim = y_lim)
plot(delta, add=TRUE, col='blue')
#> [1] "done"Curve comparison
cat("curve_1 : smooth PLS regression curve.\n")
#> curve_1 : smooth PLS regression curve.
cat("curve_2 : functional PLS regression curve.\n")
#> curve_2 : functional PLS regression curve.
cat("curve_3 : naive PLS regression coefficients\n")
#> curve_3 : naive PLS regression coefficients
evaluate_curves_distances(real_f = beta_real_func,
regul_time = regul_time,
fun_fd_list = list(
delta,
fpls_obj$reg_obj$NumFD_1,
approxfun(x = regul_time,
y = naive_pls_obj$opti_reg_coef)
)
)
#> [1] "real_f -> curve_1 / INPROD : 5.42764621642823 / DIST : 3.50987893386841"
#> [1] "real_f -> curve_2 / INPROD : 6.66383089607853 / DIST : 3.40650741798858"
#> [1] "real_f -> curve_3 / INPROD : 247.075818435331 / DIST : 68.8619172938924"
y_lim = eval_max_min_y(f_list = list(spls_obj$reg_obj$NumFD_1,
fpls_obj$reg_obj$NumFD_1,
approxfun(x = regul_time,
y = naive_pls_obj$opti_reg_coef),
beta_real_func ),
regul_time = regul_time_0)
plot(regul_time_0, beta_real_func(regul_time_0), col = 'black',
ylim = y_lim, xlab = 'Time', ylab = 'Value', type = 'l')
lines(regul_time_0, approxfun(x = regul_time,
y = naive_pls_obj$opti_reg_coef)(regul_time_0),
col = 'green')
title(paste0(names(spls_obj$reg_obj)[2], " regression curves"))
plot(spls_obj$reg_obj$NumFD_1, col = 'blue', add = TRUE)
#> [1] "done"
plot(fpls_obj$reg_obj$NumFD_1, col = 'red', add = TRUE)
#> [1] "done"
legend("bottomleft",
legend = c("Real curve", "NaivePLS coef",
"SmoothPLS reg curve", "FunctionalPLS reg curve"),
col = c("black", "green", "blue", "red"),
lty = 1,
lwd = 1)
y_lim = eval_max_min_y(f_list = list(beta_real_func,
spls_obj$reg_obj$NumFD_1,
fpls_obj$reg_obj$NumFD_1),
regul_time = regul_time)
plot(regul_time_0, beta_real_func(regul_time_0), type='l', xlab="Beta_t",
ylim = y_lim, lwd = 2)
plot(spls_obj$reg_obj$NumFD_1, add=TRUE, col='blue', lwd = 1)
#> [1] "done"
plot(fpls_obj$reg_obj$NumFD_1, add=TRUE, col='red', lwd = 1)
#> [1] "done"
legend("bottomleft",
legend = c("Real curve",
"SmoothPLS reg curve", "FunctionalPLS reg curve"),
col = c("black", "blue", "red"),
lty = 1,
lwd = 1)
evaluate_curves_distances(real_f = beta_real_func,
regul_time = regul_time,
fun_fd_list = list(spls_obj$reg_obj$NumFD_1,
fpls_obj$reg_obj$NumFD_1))
#> [1] "real_f -> curve_1 / INPROD : 5.42764621642823 / DIST : 3.50987893386841"
#> [1] "real_f -> curve_2 / INPROD : 6.66383089607853 / DIST : 3.40650741798858"Plot the second derivatives for the smoothness :
plot((fda::deriv.fd(expr = spls_obj$reg_obj$NumFD_1, Lfdobj = 2)),
col='blue')
#> [1] "done"
plot((fda::deriv.fd(expr = fpls_obj$reg_obj$NumFD_1, Lfdobj = 2)),
add=TRUE, col='red')
#> [1] "done"
title("Second derivatives")
legend("bottomleft",
legend = c("delta_SmoothPLS''", "delta_FPLS''"),
col = c("blue", "red"),
lty = 1,
lwd = 1)
Results
train_results = data.frame(matrix(ncol = 5, nrow = 3))
colnames(train_results) = c("PRESS", "RMSE", "MAE", "R2", "var_Y")
rownames(train_results) = c("NaivePLS", "FPLS", "SmoothPLS")
test_results = train_resultsTrain Set
Y_train = Y_df$Y_noised
# Naive
Y_hat = predict(naive_pls_obj$plsr_model,
ncomp = naive_pls_obj$nbCP_opti,
newdata = as.matrix(df_wide[, -c(1)]))
train_results["NaivePLS", ] = evaluate_results(Y_train, Y_hat)
# FPLS
Y_hat_fpls = (predict(fpls_obj$plsr_model, ncomp = fpls_obj$nbCP_opti,
newdata = fpls_obj$trans_alphas)
+ fpls_obj$reg_obj$Intercept
+ mean(Y))
Y_hat_fpls = smoothPLS_predict(df_predict_list = df,
delta_list = fpls_obj$reg_obj,
curve_type_obj = curve_type,
int_mode = int_mode,
regul_time_obj = regul_time)
train_results["FPLS", ] = evaluate_results(Y_train, Y_hat_fpls)
# Smooth PLS
Y_hat_spls = smoothPLS_predict(df_predict_list = df,
delta_list = spls_obj$reg_obj,
curve_type_obj = curve_type,
int_mode = int_mode,
regul_time_obj = regul_time)
train_results["SmoothPLS", ] = evaluate_results(Y_train, Y_hat_spls)
train_results["NaivePLS", "nb_cp"] = naive_pls_obj$nbCP_opti
train_results["FPLS", "nb_cp"] = fpls_obj$nbCP_opti
train_results["SmoothPLS", "nb_cp"] = spls_obj$nbCP_opti
train_results
#> PRESS RMSE MAE R2 var_Y nb_cp
#> NaivePLS 447.7783 2.116077 1.658857 0.8713332 87.13332 4
#> FPLS 2958.4590 5.439172 4.598839 0.1499018 14.96341 2
#> SmoothPLS 15533.5802 12.463378 11.223560 -3.4634956 13.79539 9Test Set
Test set creation
nind_test = number_of_test_id(TTRatio = TTRatio, nind = nind)
df_test = generate_X_df(nind = nind_test, start = start, end = end,
curve_type = curve_type, lambda_0 = lambda_0, lambda_1 = lambda_1,
prob_start = prob_start)
Y_df_test = generate_Y_df(df_test, curve_type = curve_type,
beta_real_func_or_list = beta_real_func,
beta_0_real, NotS_ratio,
id_col = 'id', time_col = 'time')
df_test_regul = regularize_time_series(df_test, time_seq = regul_time,
curve_type = curve_type)
df_test_wide = convert_to_wide_format(df_test_regul)Evaluation
Y_test = Y_df_test$Y_noised
# Naive
Y_hat = predict(naive_pls_obj$plsr_model,
ncomp = naive_pls_obj$nbCP_opti,
newdata = as.matrix(df_test_wide[, -c(1)]))
test_results["NaivePLS", ] = evaluate_results(Y_test, Y_hat)
# FPLS
Y_hat_fpls = smoothPLS_predict(df_predict_list = df_test,
delta_list = fpls_obj$reg_obj,
curve_type_obj = curve_type,
int_mode = int_mode,
regul_time_obj = regul_time)
test_results["FPLS", ] = evaluate_results(Y_test, Y_hat_fpls)
# Smooth PLS
Y_hat_spls = smoothPLS_predict(df_predict_list = df_test,
delta_list = list(delta_0, delta),
curve_type_obj = curve_type,
int_mode = int_mode,
regul_time_obj = regul_time)
test_results["SmoothPLS", ] = evaluate_results(Y_test, Y_hat_spls)
test_results["NaivePLS", "nb_cp"] = naive_pls_obj$nbCP_opti
test_results["FPLS", "nb_cp"] = fpls_obj$nbCP_opti
test_results["SmoothPLS", "nb_cp"] = spls_obj$nbCP_opti
test_results
#> PRESS RMSE MAE R2 var_Y nb_cp
#> NaivePLS 222.84261 2.985583 2.3244464 -2.813555 232.68890 4
#> FPLS 31.38556 1.120456 0.9331762 0.462892 81.55013 2
#> SmoothPLS 3881.27654 12.459978 12.4399294 -65.421150 76.32215 9Plot results
train_results
#> PRESS RMSE MAE R2 var_Y nb_cp
#> NaivePLS 447.7783 2.116077 1.658857 0.8713332 87.13332 4
#> FPLS 2958.4590 5.439172 4.598839 0.1499018 14.96341 2
#> SmoothPLS 15533.5802 12.463378 11.223560 -3.4634956 13.79539 9
test_results
#> PRESS RMSE MAE R2 var_Y nb_cp
#> NaivePLS 222.84261 2.985583 2.3244464 -2.813555 232.68890 4
#> FPLS 31.38556 1.120456 0.9331762 0.462892 81.55013 2
#> SmoothPLS 3881.27654 12.459978 12.4399294 -65.421150 76.32215 9
plot_model_metrics_base(train_results, test_results)
plot_model_metrics_base(train_results, test_results,
models_to_plot = c('FPLS', 'SmoothPLS'))
