library(SmoothPLS)
library(ggplot2)
#> Warning: package 'ggplot2' was built under R version 4.4.3
library(dplyr)
#>
#> Attaching package: 'dplyr'
#> The following objects are masked from 'package:stats':
#>
#> filter, lag
#> The following objects are masked from 'package:base':
#>
#> intersect, setdiff, setequal, unionThis document show some examples of some of the package’s functions. It is divided by parts dedicated to some subjects.
Parameters
We will encounter some parameters in this package. Here we will fix them.
nind = 50 # 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 = 0.55 # Probability of starting with state 1
curve_type = 'cat'
TTRatio = 0.2 # Train Test Ratio
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 = 15 # number of basis functions
norder = 4 # 4 for cubic splines basisIntegral evaluation
evaluate_id_func_integral
This function evaluate the following integral : . With a categorical functional data which states are 0 or 1. WARNING this function as no use if is a Scalar Functional Data.
id_df = data.frame(id=rep(1,5), time=seq(0, 40, 10), state=c(0, 1, 1, 0, 1))
id_df
#> id time state
#> 1 1 0 0
#> 2 1 10 1
#> 3 1 20 1
#> 4 1 30 0
#> 5 1 40 1
func = function(t){0.01*t^2 - t}
plot(0:40, func(0:40))
evaluate_id_func_integral(id_df, func)
#> id integral
#> 1 1 -313.3333Data regularisation
regularize_time_series
This function regularize a dataframe on another time sequence. If the input dataframe get more than one id, all the ids will share the same time sequence in the output dataframe.
id_df_regul = regularize_time_series(id_df, time_seq = seq(0, 40, 2),
curve_type = 'cat')
id_df_regul
#> id time state
#> 1 1 0 0
#> 2 1 2 0
#> 3 1 4 0
#> 4 1 6 0
#> 5 1 8 0
#> 6 1 10 1
#> 7 1 12 1
#> 8 1 14 1
#> 9 1 16 1
#> 10 1 18 1
#> 11 1 20 1
#> 12 1 22 1
#> 13 1 24 1
#> 14 1 26 1
#> 15 1 28 1
#> 16 1 30 0
#> 17 1 32 0
#> 18 1 34 0
#> 19 1 36 0
#> 20 1 38 0
#> 21 1 40 1convert_to_wide_format
This function converts a regularized dataframe into a long format by pivoting the data. Useful for classic Multivariate Functional PLS or else. The input dataframe of convert_to_wide_format is the output of the function regularize_time_series because after the regularisation, all the individuals have the same time interval and time sampling which allows the pivot table.
id_df_long = convert_to_wide_format(id_df_regul)
id_df_long
#> # A tibble: 1 × 22
#> id `0` `2` `4` `6` `8` `10` `12` `14` `16` `18` `20` `22`
#> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 1 0 0 0 0 0 1 1 1 1 1 1 1
#> # ℹ 9 more variables: `24` <dbl>, `26` <dbl>, `28` <dbl>, `30` <dbl>,
#> # `32` <dbl>, `34` <dbl>, `36` <dbl>, `38` <dbl>, `40` <dbl>Other
from_fd_to_func
This function transform an fd object into a function. This function will be used to easier the integral calculation inside the PLS.
basis = create_bspline_basis(0, 100, 10, 4)
coef = c(10, 8, 6, 4, 2, 1, 3, 5, 7, 9)
fd_obj = fda::fd(coef = coef, basisobj = basis)
func_from_fd = from_fd_to_func(coef = coef, basis = basis)Here if the fd object :
plot(fd_obj)
#> [1] "done"Now we can evaluate, we should find the same values :
fda::eval.fd(fd_obj, 13)
#> reps 1
#> [1,] 6.396324Synthetic one state CFD data
This package provides some function to create some synthetic data. These data are individuals with state 0 or 1. The state law are exponential laws.
One important input is : type = ‘cat’.
generate_X_df
This function generate nind individuals, for a time between start and end, with parameters for the two exponential law for state 0 and state 1 lambda_0 and lambda_1. The first state at time = start as the probability prob_start of being 1 (binomial law).
Here we generate df with the declared parameters at the top of this notebook.
df = generate_X_df(nind = nind, start = start,end = end, curve_type = 'cat',
lambda_0 = lambda_0, lambda_1 = lambda_1,
prob_start = prob_start)
head(df)
#> id time state
#> 1 1 0.000000 1
#> 2 1 5.766103 0
#> 3 1 12.411377 1
#> 4 1 12.727151 0
#> 5 1 13.008206 1
#> 6 1 16.173218 0
df_2 = generate_X_df(nind=20, start = 13, end = 60, curve_type = 'cat',
lambda_0 = 0.21, lambda_1 = 0.13, prob_start = 0.55)
length(unique(df_2$id))
#> [1] 20plot_individuals
This function plots the selected first individuals of the given dataframe.
plot_CFD_individuals(df_2, n_ind_to_plot = 3)
Create df test
this function generates the test set of X. It uses the same arguments than the previous function generate_X_df plus the train test ration TTRatio. It evaluates the number of individuals to create in order to follow the TTRatio for all the individuals, Train set and test set.
nind_test = number_of_test_id(TTRatio = TTRatio, nind = nind)
df_test = generate_X_df(nind_test, start, end, curve_type = 'cat',
lambda_0, lambda_1, prob_start)
length(unique(df_test$id))
#> [1] 12
df_test_2 = generate_X_df(nind=number_of_test_id(TTRatio = TTRatio, nind = 80),
start, end, curve_type = 'cat',
lambda_0, lambda_1, prob_start)
# Here the number of individuals will be 20 because :
# 20 = 0.2 (80 + 20) or
# 20 = floor(80*TTRatio/(1-TTRatio))
length(unique(df_test_2$id))
#> [1] 20Beta_real
This package gives 3 functions to link with a scalar by the following equation : .
Other beta functions
plot(x=0:100, y=beta_4_real_func(0:100, 100), type='l', main="Beta_4")
plot(x=0:100, y=beta_5_real_func(0:100, 100), type='l', main="Beta_5")
plot(x=0:100, y=beta_6_real_func(0:100, 100), type='l', main="Beta_6")
plot(x=0:100, y=beta_7_real_func(0:100, 100), type='l', main="Beta_7")
generate_Y_df
This function generates a Y dataframe base on the following relation between and : . It also add some noise to Y. The given ration NotS_ratio gives the part of the total variance due to some gaussian noise.
Y_df = generate_Y_df(df, curve_type = 'cat',
beta_1_real_func, beta_0_real, NotS_ratio)
#> Warning: package 'future' was built under R version 4.4.3
names(Y_df)
#> [1] "id" "Y_real" "Y_noised"
head(Y_df)
#> id Y_real Y_noised
#> 1 1 70.03711 67.32771
#> 2 2 48.59410 66.94154
#> 3 3 59.85310 60.68305
#> 4 4 24.01073 25.53257
#> 5 5 56.93758 77.12549
#> 6 6 61.43766 66.86308We can look at the variance :
var(Y_df$Y_real)
#> [1] 554.2192
var(Y_df$Y_noised)
#> [1] 633.4237
var(Y_df$Y_real)/var(Y_df$Y_noised)
#> [1] 0.874958
(var(Y_df$Y_noised) - var(Y_df$Y_real))/var(Y_df$Y_noised)
#> [1] 0.125042
We can generate Y_df_test the same way by simply changing df to df_test:
Y_df_test = generate_Y_df(df_test, curve_type = 'cat',
beta_1_real_func, beta_0_real,
NotS_ratio)
head(Y_df_test)
#> id Y_real Y_noised
#> 1 1 70.03711 68.42221
#> 2 2 48.59410 59.52978
#> 3 3 59.85310 60.34778
#> 4 4 24.01073 24.91779
#> 5 5 56.93758 68.97025
#> 6 6 61.43766 64.67139Synthetic 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()
generate_Y_df
Y_df = generate_Y_df(df = df, curve_type = 'num',
beta_real_func_or_list = beta_1_real_func,
beta_0_real = beta_0_real, NotS_ratio = NotS_ratio,
seed = 123)
head(Y_df)
#> id Y_real Y_noised
#> 1 1 211.9966 211.4010
#> 2 2 214.7040 214.4594
#> 3 3 213.1712 214.8276
#> 4 4 210.1414 210.2163
#> 5 5 208.3050 208.4424
#> 6 6 208.4381 210.2606regularize_time_series
id_df_regul = regularize_time_series(df, time_seq = seq(0, 40, 2),
curve_type = 'num')
id_df_regul
#> id time value
#> 1 1 0 1.2591356058
#> 2 1 2 1.0470795456
#> 3 1 4 0.6105384880
#> 4 1 6 0.5772717305
#> 5 1 8 0.3897052156
#> 6 1 10 0.2642695075
#> 7 1 12 -0.3285942560
#> 8 1 14 -0.4137112833
#> 9 1 16 -0.8502908980
#> 10 1 18 -1.1726978392
#> 11 1 20 -1.3168846512
#> 12 1 22 -1.4634608174
#> 13 1 24 -1.6335783757
#> 14 1 26 -1.8702501514
#> 15 1 28 -1.9036260161
#> 16 1 30 -2.0244393652
#> 17 1 32 -1.8498600658
#> 18 1 34 -1.9505031276
#> 19 1 36 -2.1013011431
#> 20 1 38 -2.1228567127
#> 21 1 40 -1.7434094354
#> 22 2 0 0.9378618266
#> 23 2 2 0.7434194922
#> 24 2 4 0.5710908042
#> 25 2 6 0.2988864544
#> 26 2 8 -0.1065048437
#> 27 2 10 -0.0370698945
#> 28 2 12 -0.3484747650
#> 29 2 14 -0.7353814234
#> 30 2 16 -0.8242910066
#> 31 2 18 -1.1362559723
#> 32 2 20 -0.9900684367
#> 33 2 22 -1.4153393419
#> 34 2 24 -1.7560478382
#> 35 2 26 -1.5307901643
#> 36 2 28 -1.8494326149
#> 37 2 30 -2.2424851992
#> 38 2 32 -2.2019664985
#> 39 2 34 -1.7136062723
#> 40 2 36 -1.8802647271
#> 41 2 38 -2.1756015392
#> 42 2 40 -2.1036663913
#> 43 3 0 1.0798334185
#> 44 3 2 0.7917233066
#> 45 3 4 0.6835971888
#> 46 3 6 0.4334818825
#> 47 3 8 0.2999560291
#> 48 3 10 0.2912442676
#> 49 3 12 -0.3692027318
#> 50 3 14 -0.5761542822
#> 51 3 16 -0.7595543941
#> 52 3 18 -0.9953022656
#> 53 3 20 -1.5021680660
#> 54 3 22 -1.3506431684
#> 55 3 24 -1.6358876156
#> 56 3 26 -1.8390420419
#> 57 3 28 -1.7237129323
#> 58 3 30 -1.8305280202
#> 59 3 32 -2.4794722969
#> 60 3 34 -1.8660989277
#> 61 3 36 -2.1649851394
#> 62 3 38 -1.7940243789
#> 63 3 40 -1.7840912242
#> 64 4 0 1.3862407145
#> 65 4 2 0.9746713772
#> 66 4 4 0.5378987760
#> 67 4 6 0.4907170842
#> 68 4 8 -0.0526197316
#> 69 4 10 0.0217277187
#> 70 4 12 -0.1816099026
#> 71 4 14 -0.5088027268
#> 72 4 16 -0.7393761679
#> 73 4 18 -0.9677282488
#> 74 4 20 -1.2655542240
#> 75 4 22 -1.6289124330
#> 76 4 24 -1.3838866864
#> 77 4 26 -2.0553062161
#> 78 4 28 -1.8857347055
#> 79 4 30 -1.9497806043
#> 80 4 32 -1.8390196812
#> 81 4 34 -1.9915692977
#> 82 4 36 -2.2485179812
#> 83 4 38 -2.0255574240
#> 84 4 40 -1.8904219000
#> 85 5 0 1.4356594782
#> 86 5 2 0.6194322814
#> 87 5 4 0.7398972830
#> 88 5 6 0.4124369274
#> 89 5 8 -0.0584388402
#> 90 5 10 -0.2912823356
#> 91 5 12 -0.7180680445
#> 92 5 14 -0.5176320984
#> 93 5 16 -0.8660876258
#> 94 5 18 -0.8794712397
#> 95 5 20 -1.2784589448
#> 96 5 22 -1.6312787821
#> 97 5 24 -1.7550310860
#> 98 5 26 -1.6800101500
#> 99 5 28 -1.8051039179
#> 100 5 30 -2.0908706871
#> 101 5 32 -2.0625145614
#> 102 5 34 -1.8956366850
#> 103 5 36 -1.8799886424
#> 104 5 38 -1.8146567911
#> 105 5 40 -1.8317834667
#> 106 6 0 0.9881392353
#> 107 6 2 0.8413847437
#> 108 6 4 0.4721727293
#> 109 6 6 0.5302785878
#> 110 6 8 0.0314144624
#> 111 6 10 0.0522163067
#> 112 6 12 -0.1788248241
#> 113 6 14 -0.5463845070
#> 114 6 16 -0.7511323959
#> 115 6 18 -1.2757571815
#> 116 6 20 -0.9747700549
#> 117 6 22 -1.2758593193
#> 118 6 24 -1.7030529198
#> 119 6 26 -1.7884600091
#> 120 6 28 -1.7499924606
#> 121 6 30 -1.8045431962
#> 122 6 32 -2.1626638417
#> 123 6 34 -1.6354378098
#> 124 6 36 -1.8587967412
#> 125 6 38 -1.7731732026
#> 126 6 40 -1.6156486566
#> 127 7 0 1.1142373544
#> 128 7 2 0.9414393267
#> 129 7 4 0.5587006907
#> 130 7 6 0.2974429359
#> 131 7 8 0.2267813064
#> 132 7 10 -0.5720259605
#> 133 7 12 -0.4680774622
#> 134 7 14 -0.5640876072
#> 135 7 16 -1.0683921560
#> 136 7 18 -0.7741183066
#> 137 7 20 -1.2416482794
#> 138 7 22 -1.4035909012
#> 139 7 24 -1.4545044130
#> 140 7 26 -1.8367329910
#> 141 7 28 -1.8499892394
#> 142 7 30 -1.7802454338
#> 143 7 32 -1.8893790242
#> 144 7 34 -2.0051889404
#> 145 7 36 -1.9647435458
#> 146 7 38 -2.1323362365
#> 147 7 40 -1.9708957715
#> 148 8 0 1.1410981614
#> 149 8 2 0.6019094854
#> 150 8 4 0.3987282026
#> 151 8 6 0.4227256720
#> 152 8 8 0.1645914982
#> 153 8 10 0.0329739039
#> 154 8 12 -0.2321493728
#> 155 8 14 -0.3979893436
#> 156 8 16 -0.7632008543
#> 157 8 18 -1.0771752668
#> 158 8 20 -1.1137741771
#> 159 8 22 -1.3021079909
#> 160 8 24 -1.5121069635
#> 161 8 26 -2.0790677596
#> 162 8 28 -1.9280190764
#> 163 8 30 -1.8783015808
#> 164 8 32 -1.9993270361
#> 165 8 34 -1.9678781107
#> 166 8 36 -2.0035914511
#> 167 8 38 -1.9699986374
#> 168 8 40 -1.8928193526
#> 169 9 0 1.3185827460
#> 170 9 2 1.0334221485
#> 171 9 4 0.7165430739
#> 172 9 6 0.3932556888
#> 173 9 8 0.2541603805
#> 174 9 10 -0.0603813954
#> 175 9 12 -0.4060219772
#> 176 9 14 -0.5857318073
#> 177 9 16 -0.7815001996
#> 178 9 18 -1.1479262340
#> 179 9 20 -1.3330837729
#> 180 9 22 -1.4138837146
#> 181 9 24 -1.8192634658
#> 182 9 26 -1.5965026428
#> 183 9 28 -1.9885465407
#> 184 9 30 -1.7063035995
#> 185 9 32 -1.9468733539
#> 186 9 34 -2.2286288900
#> 187 9 36 -1.7449607139
#> 188 9 38 -2.1239175066
#> 189 9 40 -1.9361720048
#> 190 10 0 1.1803785931
#> 191 10 2 0.8468320241
#> 192 10 4 1.0013244638
#> 193 10 6 0.4135014652
#> 194 10 8 0.1366059697
#> 195 10 10 -0.1166378496
#> 196 10 12 -0.4673485420
#> 197 10 14 -0.6401014488
#> 198 10 16 -0.6845750022
#> 199 10 18 -1.3155598240
#> 200 10 20 -1.3353118175
#> 201 10 22 -1.5500384191
#> 202 10 24 -1.6526094733
#> 203 10 26 -1.7686620566
#> 204 10 28 -1.8321941971
#> 205 10 30 -1.8811599742
#> 206 10 32 -1.9497637942
#> 207 10 34 -2.2131380748
#> 208 10 36 -1.8679067455
#> 209 10 38 -1.9162744672
#> 210 10 40 -1.8489480902
#> 211 11 0 0.9331176832
#> 212 11 2 0.9790427071
#> 213 11 4 0.7844295240
#> 214 11 6 0.0377999710
#> 215 11 8 0.3617221425
#> 216 11 10 -0.1528723330
#> 217 11 12 -0.4044646727
#> 218 11 14 -0.5306261473
#> 219 11 16 -0.7873160845
#> 220 11 18 -1.1347969452
#> 221 11 20 -1.5559733957
#> 222 11 22 -1.4825437982
#> 223 11 24 -1.6681873661
#> 224 11 26 -1.6607301568
#> 225 11 28 -1.7079685605
#> 226 11 30 -1.9366976400
#> 227 11 32 -2.2781079422
#> 228 11 34 -1.9372450525
#> 229 11 36 -2.2806345791
#> 230 11 38 -1.7169544029
#> 231 11 40 -2.0190805275
#> 232 12 0 0.8453409186
#> 233 12 2 0.8467306825
#> 234 12 4 0.4807691868
#> 235 12 6 0.2811762993
#> 236 12 8 0.3310350576
#> 237 12 10 -0.1385147681
#> 238 12 12 -0.4136820187
#> 239 12 14 -0.5933901364
#> 240 12 16 -0.9539398374
#> 241 12 18 -0.8831107062
#> 242 12 20 -1.2211908832
#> 243 12 22 -1.5943247366
#> 244 12 24 -1.5858036121
#> 245 12 26 -1.7298538554
#> 246 12 28 -1.8138733162
#> 247 12 30 -2.0598822240
#> 248 12 32 -2.0328386231
#> 249 12 34 -2.0172550641
#> 250 12 36 -2.2883356762
#> 251 12 38 -1.8255339892
#> 252 12 40 -1.6410755575
#> 253 13 0 0.9539185183
#> 254 13 2 0.6682354156
#> 255 13 4 0.4870681951
#> 256 13 6 0.3831386231
#> 257 13 8 0.0661497495
#> 258 13 10 -0.2140366901
#> 259 13 12 -0.3160981984
#> 260 13 14 -0.7033404149
#> 261 13 16 -0.6900601089
#> 262 13 18 -1.2235350384
#> 263 13 20 -1.3390164223
#> 264 13 22 -1.3318701952
#> 265 13 24 -1.7038643098
#> 266 13 26 -1.6988353660
#> 267 13 28 -1.9215604644
#> 268 13 30 -2.0724620767
#> 269 13 32 -2.1961272723
#> 270 13 34 -1.9813362745
#> 271 13 36 -2.1848787658
#> 272 13 38 -1.7462127925
#> 273 13 40 -1.7577302843
#> 274 14 0 1.0637206790
#> 275 14 2 0.9867996528
#> 276 14 4 0.5968392579
#> 277 14 6 0.3523994262
#> 278 14 8 0.0488685749
#> 279 14 10 -0.3429290744
#> 280 14 12 -0.5392539002
#> 281 14 14 -0.7373764084
#> 282 14 16 -0.8639021194
#> 283 14 18 -1.1812635237
#> 284 14 20 -1.1311863246
#> 285 14 22 -1.4511843740
#> 286 14 24 -1.7270318971
#> 287 14 26 -1.4624523428
#> 288 14 28 -1.6845595294
#> 289 14 30 -2.1097118593
#> 290 14 32 -1.7870812574
#> 291 14 34 -1.9304023865
#> 292 14 36 -2.0592431724
#> 293 14 38 -1.7454660467
#> 294 14 40 -2.0042703533
#> 295 15 0 0.9242134979
#> 296 15 2 0.7677176004
#> 297 15 4 0.7044010432
#> 298 15 6 0.5948757826
#> 299 15 8 0.2934112221
#> 300 15 10 -0.2577505234
#> 301 15 12 -0.3041902078
#> 302 15 14 -0.5851766102
#> 303 15 16 -0.7924700195
#> 304 15 18 -0.9699806221
#> 305 15 20 -1.3428963474
#> 306 15 22 -1.3644906680
#> 307 15 24 -1.5745129548
#> 308 15 26 -1.9465366346
#> 309 15 28 -1.7906993642
#> 310 15 30 -2.1321959463
#> 311 15 32 -2.0275037775
#> 312 15 34 -1.8363751162
#> 313 15 36 -1.7576388893
#> 314 15 38 -1.9516658315
#> 315 15 40 -1.9919063419
#> 316 16 0 1.1899962569
#> 317 16 2 0.9030292852
#> 318 16 4 0.8373242521
#> 319 16 6 0.6218662956
#> 320 16 8 0.2282660072
#> 321 16 10 -0.1318397693
#> 322 16 12 -0.4780780068
#> 323 16 14 -0.4657018761
#> 324 16 16 -1.0367477954
#> 325 16 18 -1.2295541538
#> 326 16 20 -1.1878358703
#> 327 16 22 -1.3016253305
#> 328 16 24 -1.5313469967
#> 329 16 26 -1.9201559933
#> 330 16 28 -1.8199068294
#> 331 16 30 -1.9241128170
#> 332 16 32 -2.0875954831
#> 333 16 34 -2.0929140656
#> 334 16 36 -1.8625881567
#> 335 16 38 -1.9087041192
#> 336 16 40 -1.9399600315
#> 337 17 0 1.1214100774
#> 338 17 2 0.6686152687
#> 339 17 4 0.4825252958
#> 340 17 6 0.2557828961
#> 341 17 8 0.3413891086
#> 342 17 10 -0.0915248051
#> 343 17 12 -0.3193518689
#> 344 17 14 -0.4948623730
#> 345 17 16 -0.9423474442
#> 346 17 18 -1.0261220419
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#> 909 44 10 -0.2363904647
#> 910 44 12 -0.1268494400
#> 911 44 14 -0.5621768945
#> 912 44 16 -0.7787125449
#> 913 44 18 -1.0047832838
#> 914 44 20 -1.1709760084
#> 915 44 22 -1.3425799142
#> 916 44 24 -1.4600763852
#> 917 44 26 -1.7184071517
#> 918 44 28 -2.0167407363
#> 919 44 30 -2.1088630980
#> 920 44 32 -2.1431404592
#> 921 44 34 -1.8708385340
#> 922 44 36 -2.2623110033
#> 923 44 38 -2.3130590300
#> 924 44 40 -2.0914868668
#> 925 45 0 0.9665176888
#> 926 45 2 0.6517275546
#> 927 45 4 0.6716093375
#> 928 45 6 -0.1751083018
#> 929 45 8 0.2213158258
#> 930 45 10 -0.2281376137
#> 931 45 12 -0.4505924817
#> 932 45 14 -0.7481413140
#> 933 45 16 -0.6818760452
#> 934 45 18 -1.0110345325
#> 935 45 20 -1.2007856217
#> 936 45 22 -1.3646598497
#> 937 45 24 -1.4311875542
#> 938 45 26 -1.8533180368
#> 939 45 28 -1.8968171292
#> 940 45 30 -1.6915975219
#> 941 45 32 -1.8794725461
#> 942 45 34 -2.1842356574
#> 943 45 36 -1.9453177616
#> 944 45 38 -2.1491543657
#> 945 45 40 -1.3451498679
#> 946 46 0 1.0111914703
#> 947 46 2 1.0386024043
#> 948 46 4 0.7668296243
#> 949 46 6 0.4777105815
#> 950 46 8 0.0086116454
#> 951 46 10 -0.0065903153
#> 952 46 12 -0.3586709234
#> 953 46 14 -0.7207051900
#> 954 46 16 -0.6315040357
#> 955 46 18 -0.7056103103
#> 956 46 20 -1.3448625670
#> 957 46 22 -1.2894458645
#> 958 46 24 -1.5392721478
#> 959 46 26 -1.9535020942
#> 960 46 28 -2.2095849490
#> 961 46 30 -1.7152843519
#> 962 46 32 -1.9915168829
#> 963 46 34 -2.0185312311
#> 964 46 36 -2.2122173902
#> 965 46 38 -1.9910180626
#> 966 46 40 -1.8323294698
#> 967 47 0 1.1144154734
#> 968 47 2 0.7641761488
#> 969 47 4 0.6081678509
#> 970 47 6 0.2601679496
#> 971 47 8 0.0969303487
#> 972 47 10 0.2112205066
#> 973 47 12 -0.2036120502
#> 974 47 14 -0.4689443871
#> 975 47 16 -0.8327075974
#> 976 47 18 -0.8634717548
#> 977 47 20 -0.8483647336
#> 978 47 22 -1.4416843302
#> 979 47 24 -1.4512687163
#> 980 47 26 -1.7008624676
#> 981 47 28 -1.7091556252
#> 982 47 30 -1.7379500309
#> 983 47 32 -1.9493577762
#> 984 47 34 -1.9650201733
#> 985 47 36 -2.0472937586
#> 986 47 38 -2.0916687100
#> 987 47 40 -1.8757018970
#> 988 48 0 0.9638961916
#> 989 48 2 0.9231859621
#> 990 48 4 0.5781714449
#> 991 48 6 0.3029205963
#> 992 48 8 0.2879991275
#> 993 48 10 -0.0817489640
#> 994 48 12 -0.4160427414
#> 995 48 14 -0.7139002155
#> 996 48 16 -0.8404711827
#> 997 48 18 -1.2540404454
#> 998 48 20 -1.3887406377
#> 999 48 22 -1.2970107285
#> 1000 48 24 -1.6166787173
#> 1001 48 26 -1.7758926982
#> 1002 48 28 -1.8619847267
#> 1003 48 30 -2.0680402960
#> 1004 48 32 -2.0799211527
#> 1005 48 34 -1.8272424692
#> 1006 48 36 -2.3178217351
#> 1007 48 38 -2.0799212996
#> 1008 48 40 -1.8419869127
#> 1009 49 0 1.0263890075
#> 1010 49 2 0.8253872723
#> 1011 49 4 0.5189880311
#> 1012 49 6 0.4797608752
#> 1013 49 8 0.3660056599
#> 1014 49 10 -0.1596055090
#> 1015 49 12 -0.1929393572
#> 1016 49 14 -0.5606604034
#> 1017 49 16 -0.9783594305
#> 1018 49 18 -1.0464800348
#> 1019 49 20 -1.1613717556
#> 1020 49 22 -1.3274057656
#> 1021 49 24 -2.0563987902
#> 1022 49 26 -1.7822339812
#> 1023 49 28 -1.7113439732
#> 1024 49 30 -2.0492979976
#> 1025 49 32 -1.9636796837
#> 1026 49 34 -2.1210153603
#> 1027 49 36 -1.9345465245
#> 1028 49 38 -1.8414319874
#> 1029 49 40 -1.7624879347
#> 1030 50 0 1.0524457884
#> 1031 50 2 1.0625242446
#> 1032 50 4 0.7568469508
#> 1033 50 6 0.3830199342
#> 1034 50 8 0.1508943759
#> 1035 50 10 -0.2701229931
#> 1036 50 12 -0.4250614052
#> 1037 50 14 -0.4933546980
#> 1038 50 16 -0.6446609839
#> 1039 50 18 -1.0804185093
#> 1040 50 20 -1.3849398686
#> 1041 50 22 -1.4256773981
#> 1042 50 24 -1.3272737902
#> 1043 50 26 -2.1413544390
#> 1044 50 28 -1.8395057090
#> 1045 50 30 -1.9134134239
#> 1046 50 32 -1.8939959223
#> 1047 50 34 -2.1257810952
#> 1048 50 36 -2.0261674250
#> 1049 50 38 -1.7934236471
#> 1050 50 40 -1.5736598054convert_to_wide_format
id_df_long = convert_to_wide_format(id_df_regul)
id_df_long
#> # A tibble: 50 × 22
#> id `0` `2` `4` `6` `8` `10` `12` `14` `16` `18`
#> <int> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 1 1.26 1.05 0.611 0.577 0.390 0.264 -0.329 -0.414 -0.850 -1.17
#> 2 2 0.938 0.743 0.571 0.299 -0.107 -0.0371 -0.348 -0.735 -0.824 -1.14
#> 3 3 1.08 0.792 0.684 0.433 0.300 0.291 -0.369 -0.576 -0.760 -0.995
#> 4 4 1.39 0.975 0.538 0.491 -0.0526 0.0217 -0.182 -0.509 -0.739 -0.968
#> 5 5 1.44 0.619 0.740 0.412 -0.0584 -0.291 -0.718 -0.518 -0.866 -0.879
#> 6 6 0.988 0.841 0.472 0.530 0.0314 0.0522 -0.179 -0.546 -0.751 -1.28
#> 7 7 1.11 0.941 0.559 0.297 0.227 -0.572 -0.468 -0.564 -1.07 -0.774
#> 8 8 1.14 0.602 0.399 0.423 0.165 0.0330 -0.232 -0.398 -0.763 -1.08
#> 9 9 1.32 1.03 0.717 0.393 0.254 -0.0604 -0.406 -0.586 -0.782 -1.15
#> 10 10 1.18 0.847 1.00 0.414 0.137 -0.117 -0.467 -0.640 -0.685 -1.32
#> # ℹ 40 more rows
#> # ℹ 11 more variables: `20` <dbl>, `22` <dbl>, `24` <dbl>, `26` <dbl>,
#> # `28` <dbl>, `30` <dbl>, `32` <dbl>, `34` <dbl>, `36` <dbl>, `38` <dbl>,
#> # `40` <dbl>Synthetic multi state CFD
N_states = 4
# Initialized the lambdas values
lambdas = lambda_determination(N_states)
lambdas
#> [1] 0.1699978 0.1165647 0.1477226 0.2408948
# Initialized the transition matrix
transition_df = transfer_probabilities(N_states)
transition_df
#> dir1 dir2 dir3 dir4
#> state_1 0.00000000 0.3860865 0.5865265 0.02738700
#> state_2 0.65394701 0.0000000 0.3027449 0.04330805
#> state_3 0.03592216 0.5487636 0.0000000 0.41531427
#> state_4 0.10975895 0.2783398 0.6119012 0.00000000Data generation
df = generate_X_df_multistates(nind = 100, N_states, start=0, end=100,
lambdas, transition_df)
head(df)
#> id time state
#> 1 1 0.00000 2
#> 2 1 27.71333 1
#> 3 1 29.57513 2
#> 4 1 38.92673 1
#> 5 1 39.09822 3
#> 6 1 42.34901 4We can plot some individuals with the plot_individual() function.
plotData
We can use the package cfda and its functions to make some analysis on the data.
cfda::plotData(df)
## estimate_pt We can still use the CFDA package to estimate the
probabilities :
proba = cfda::estimate_pt(df)
plot(proba, ribbon = TRUE)
Multi state CFD manipulation
Before performing the fpls or the smooth-PLS, we have to manipulate the categorical functional data of multiple states into multiple categorical functional data of one state each.
head(df)
#> id time state
#> 1 1 0.00000 2
#> 2 1 27.71333 1
#> 3 1 29.57513 2
#> 4 1 38.92673 1
#> 5 1 39.09822 3
#> 6 1 42.34901 4We need to order the states
str(df$state)
#> num [1:1680] 2 1 2 1 3 4 3 2 3 2 ...
unique(df$state)
#> [1] 2 1 3 4
order(unique(df$state)) # Warning, give the indices of the order!
#> [1] 2 1 3 4
state_ordered = unique(df$state)[order(unique(df$state))]
state_ordered
#> [1] 1 2 3 4state_indicator
This function transform a categorical functional data with its indicator function into a dedicated list of all the state (one per different state)
This function sort the states by ascending order (if numeric) and put the name ‘state_X’ as the column of the output concerning the ‘X’ state.
This function will also work with character states.
Now for the different lists, the [[i]] element of a list concern the [[i]] states ordered.
si_df = state_indicator(df, id_col='id', time_col='time')
names(si_df)
#> [1] "id" "time" "state_1" "state_2" "state_3" "state_4"
head(si_df)
#> id time state_1 state_2 state_3 state_4
#> 1 1 0.00000 0 1 0 0
#> 2 1 27.71333 1 0 0 0
#> 3 1 29.57513 0 1 0 0
#> 4 1 38.92673 1 0 0 0
#> 5 1 39.09822 0 0 1 0
#> 6 1 42.34901 0 0 0 1split_in_state_df
This function transform a categorical functional data with its indicator function into a dedicated list of all the state (one per different state)
split_df = split_in_state_df(si_df, id_col='id', time_col='time')
names(split_df)
#> [1] "state_1" "state_2" "state_3" "state_4"
mode(split_df)
#> [1] "list"build_df_per_state
This function takes the data_list with one dataframe per state indicator function and remove the duplicated state of each state indicator with the function remove_duplicate_states().
states_df = build_df_per_state(split_df, id_col='id', time_col='time')
names(states_df)
#> [1] "state_1" "state_2" "state_3" "state_4"
mode(states_df)
#> [1] "list"
plot_CFD_individuals(states_df[[1]])
cat_data_to_indicator
This function apply all functions to go from a categorical functional data with different states to a list of one dataframe per state indicator function. whose duplicated states where removed
df_list = cat_data_to_indicator(df)
names(df_list)
#> [1] "state_1" "state_2" "state_3" "state_4"
head(df_list$state_1)
#> id time state
#> 1 1 0.00000 0
#> 2 1 27.71333 1
#> 3 1 29.57513 0
#> 4 1 38.92673 1
#> 5 1 39.09822 0
#> 11 1 85.56434 1Now the data is ready for the different operations needed for the Smooth PLS or the FPLS.