Checks analysis with partial bootstrap resampling.

## Usage

bootstrap(object, ...)

# S4 method for numeric
bootstrap(object, do, n, ...)

# S4 method for integer
bootstrap(object, do, n, ...)

# S4 method for BootstrapVector
summary(
object,
level = 0.95,
type = c("student", "normal"),
probs = c(0.25, 0.75),
na.rm = FALSE,
...
)

# S4 method for CA
bootstrap(object, n = 30)

# S4 method for PCA
bootstrap(object, n = 30)

## Arguments

object

A numeric or an integer vector or a CA or PCA object (see below).

...

Currently not used.

do

A function that takes object as an argument and returns a single numeric value.

n

A non-negative integer giving the number of bootstrap replications.

level

A length-one numeric vector giving the confidence level. Must be a single number between $$0$$ and $$1$$. If NULL, no confidence interval are computed.

type

A character string giving the type of confidence interval to be returned. It must be one "student" (default) or "normal". Any unambiguous substring can be given. Only used if level is not NULL.

probs

A numeric vector of probabilities with values in $$[0,1]$$ (see stats::quantile()). If NULL, quantiles are not computed.

na.rm

A logical scalar: should missing values be removed from object before the sample statistics are computed?

## Value

If object is a numeric or an integer vector, bootstrap()returns a BootstrapVector object (i.e. a numeric vector of the nbootstrap values of do). If object is a CA or a PCA object, bootstrap()returns a BootstrapCA or a BootstrapPCA object. summary() returns a numeric vector with the following elements:

min

Minimum value.

mean

Mean value.

max

Maximum value.

lower

Lower bound of the confidence interval.

upper

Upper bound of the confidence interval.

Q*

Sample quantile to * probability.

## Methods (by class)

• numeric: Samples randomly from the elements of object with replacement.

• integer: Samples observations from a multinomial distribution.

## References

Greenacre, Michael J. Theory and Applications of Correspondence Analysis. London: Academic Press, 1984.

Lebart, L., Piron, M. and Morineau, A. Statistique exploratoire multidimensionnelle: visualisation et inférence en fouille de données. Paris: Dunod, 2006.

Other resampling methods: jackknife()

N. Frerebeau

## Examples

library(ggrepel)

## Random samples from x with replacement
x <- rnorm(20) # numeric
boot <- bootstrap(x, do = mean, n = 100) # Sample mean
summary(boot)
#>        min       mean        max      lower      upper        Q25        Q75
#> -0.5513971 -0.2265232  0.1135029 -0.2539695 -0.1990769 -0.3070494 -0.1453175

## Sample observations from a multinomial distribution
x <- sample(1:100, 100, TRUE) # integer
boot <- bootstrap(x, do = median, n = 100)
summary(boot)
#>      min     mean      max    lower    upper      Q25      Q75
#> 47.50000 52.24000 55.50000 51.92422 52.55578 51.00000 53.12500

## Partial bootstrap on CA
## Data from Lebart et al. 2006, p. 170-172
color <- data.frame(
brun = c(68, 15, 5, 20),
chatain = c(119, 54, 29, 84),
roux = c(26, 14, 14, 17),
blond = c(7, 10, 16, 94),
row.names = c("marron", "noisette", "vert", "bleu")
)

## Compute correspondence analysis
X <- ca(color)

## Plot results
plot(X) +
ggrepel::geom_label_repel()

## Bootstrap (30 replicates)
Y <- bootstrap(X, n = 30)

# \donttest{
## Get replicated coordinates
get_replications(Y, margin = 1)
#> , , 1
#>
#>                  F1          F2          F3
#> marron   -0.4968409 -0.04052014 -0.03448478
#> noisette -0.2801690  0.20991548 -0.08570937
#> vert      0.1915258  0.47303899  0.05672297
#> bleu      0.6681489 -0.04706335  0.09370971
#>
#> , , 2
#>
#>                  F1          F2          F3
#> marron   -0.4266518 -0.08965565  0.01612008
#> noisette -0.1342900  0.14072659 -0.18957888
#> vert      0.1902645  0.41381118 -0.02292729
#> bleu      0.5993245 -0.05458878 -0.00108376
#>
#> , , 3
#>
#>                   F1          F2          F3
#> marron   -0.50527923 -0.10880017  0.05160920
#> noisette -0.28601734  0.16528556 -0.21062051
#> vert      0.09873293  0.41035293  0.24913979
#> bleu      0.60452358 -0.01664752  0.02504948
#>
#> , , 4
#>
#>                  F1          F2          F3
#> marron   -0.4954443 -0.06264414  0.01338949
#> noisette -0.2743768  0.05372142 -0.16906055
#> vert      0.2201216  0.43043519  0.27186302
#> bleu      0.4737709 -0.06126353  0.06875306
#>
#> , , 5
#>
#>                  F1          F2          F3
#> marron   -0.4785781 -0.22411964  0.02433008
#> noisette -0.1187314  0.27249073 -0.03024807
#> vert      0.1164296  0.43053511  0.18204483
#> bleu      0.6291912 -0.09128479  0.02233978
#>
#> , , 6
#>
#>                  F1          F2          F3
#> marron   -0.5078252 -0.04102762  0.06874547
#> noisette -0.1230552  0.09780219 -0.11043461
#> vert      0.1671452  0.60015320  0.56604576
#> bleu      0.6870312  0.02339697  0.11180070
#>
#> , , 7
#>
#>                   F1          F2           F3
#> marron   -0.51189928 -0.04501766  0.028384753
#> noisette -0.31921420  0.22260054 -0.066571295
#> vert      0.05672785  0.28218536 -0.283326965
#> bleu      0.54927232 -0.07269472  0.003922112
#>
#> , , 8
#>
#>                  F1          F2           F3
#> marron   -0.5383825 -0.20287009  0.073645619
#> noisette -0.3656142  0.14344170 -0.117080228
#> vert      0.3113755  0.39336768 -0.082046866
#> bleu      0.5532826 -0.09154363  0.005212133
#>
#> , , 9
#>
#>                  F1           F2          F3
#> marron   -0.4886783 -0.001307766 -0.07175611
#> noisette -0.1442102  0.296500137 -0.21460999
#> vert      0.1907226  0.557960934  0.10661186
#> bleu      0.5855256 -0.076942869 -0.03069651
#>
#> , , 10
#>
#>                  F1           F2          F3
#> marron   -0.5143124 -0.094541388  0.13561883
#> noisette -0.2841814  0.249033864 -0.12938756
#> vert      0.1025561  0.502291077  0.16009193
#> bleu      0.4443887 -0.004232189 -0.02911958
#>
#> , , 11
#>
#>                   F1         F2          F3
#> marron   -0.55231194 -0.2581747  0.11602764
#> noisette -0.17238176  0.1742198 -0.25507409
#> vert      0.05766812  0.1005296 -0.18748527
#> bleu      0.68315232 -0.1091198  0.06008005
#>
#> , , 12
#>
#>                  F1          F2          F3
#> marron   -0.4545648  0.00751877 -0.06010826
#> noisette -0.2357174  0.27527322 -0.16388842
#> vert      0.0382763  0.38303264  0.07677478
#> bleu      0.6014437 -0.12646372  0.03458661
#>
#> , , 13
#>
#>                  F1          F2            F3
#> marron   -0.4700825 -0.08142334  0.0049320566
#> noisette -0.2515297  0.14386093 -0.0360870827
#> vert      0.1145290  0.22828078  0.2511933718
#> bleu      0.5419223 -0.10750104 -0.0006808738
#>
#> , , 14
#>
#>                  F1          F2           F3
#> marron   -0.5343218 -0.14652139  0.046857581
#> noisette -0.1961443  0.05525988  0.018576513
#> vert      0.1642068  0.29359199  0.006815422
#> bleu      0.5169950 -0.09129082 -0.046587497
#>
#> , , 15
#>
#>                  F1         F2           F3
#> marron   -0.5181599 -0.2082055  0.125672234
#> noisette -0.2394027  0.1765941 -0.149003801
#> vert      0.1664211  0.1678250  0.002383024
#> bleu      0.6369644 -0.1733670  0.031740956
#>
#> , , 16
#>
#>                  F1           F2          F3
#> marron   -0.4995219 -0.018118054  0.06886520
#> noisette -0.3871333  0.168166619 -0.09159875
#> vert      0.0915638  0.271941656  0.16359099
#> bleu      0.5566087  0.008611832  0.03284469
#>
#> , , 17
#>
#>                   F1          F2         F3
#> marron   -0.49560397 -0.08958042 0.02124663
#> noisette -0.21605482  0.14936315 0.01398777
#> vert      0.03792371  0.40342426 0.28317595
#> bleu      0.66280894 -0.07338752 0.04194923
#>
#> , , 18
#>
#>                  F1          F2          F3
#> marron   -0.5063867 -0.11129252  0.06136288
#> noisette -0.1786158  0.25948802 -0.16069921
#> vert      0.2096213  0.35650565  0.03092348
#> bleu      0.5962728 -0.03636342  0.03077159
#>
#> , , 19
#>
#>                  F1          F2          F3
#> marron   -0.4722995 -0.10358887 -0.03592057
#> noisette -0.2457857  0.19896146 -0.06533668
#> vert      0.2707471  0.37943749 -0.05915964
#> bleu      0.3037658  0.03886311 -0.16988001
#>
#> , , 20
#>
#>                  F1          F2          F3
#> marron   -0.3968674 -0.02113082 -0.10163432
#> noisette -0.2664539  0.22388959 -0.36791876
#> vert      0.1137417  0.30431192  0.01229836
#> bleu      0.5330735 -0.02388479  0.08693941
#>
#> , , 21
#>
#>                  F1          F2          F3
#> marron   -0.5142415 -0.20147680 -0.03580960
#> noisette -0.1614675  0.28064614 -0.13868540
#> vert      0.1329746  0.43497052  0.07973258
#> bleu      0.4984402 -0.09704152 -0.07472603
#>
#> , , 22
#>
#>                   F1          F2           F3
#> marron   -0.50199731 -0.11941160  0.012276199
#> noisette -0.32135814 -0.08652371 -0.005533253
#> vert      0.09343504  0.24511623 -0.012088451
#> bleu      0.48233881 -0.10897452  0.083188745
#>
#> , , 23
#>
#>                  F1          F2          F3
#> marron   -0.5063608 -0.20189570  0.01815830
#> noisette -0.1990184  0.30297308 -0.04461261
#> vert      0.1368976  0.35598442  0.20222171
#> bleu      0.4367196 -0.07462164  0.04315444
#>
#> , , 24
#>
#>                  F1         F2          F3
#> marron   -0.4656598 -0.1464057 -0.00686596
#> noisette -0.2164907  0.2731396 -0.06514263
#> vert      0.1586176  0.2205339 -0.06825168
#> bleu      0.6612424 -0.1110803  0.04296612
#>
#> , , 25
#>
#>                   F1          F2           F3
#> marron   -0.49175020 -0.03554677 -0.111346975
#> noisette -0.10275958  0.17709523 -0.199828225
#> vert     -0.01271032  0.25078139 -0.003267128
#> bleu      0.55077929 -0.05778111 -0.103824950
#>
#> , , 26
#>
#>                   F1          F2           F3
#> marron   -0.49726317 -0.11633750  0.003577148
#> noisette -0.15663524  0.23494492 -0.087567341
#> vert     -0.04337431  0.36987134  0.040765420
#> bleu      0.58803058 -0.02735104  0.034038865
#>
#> , , 27
#>
#>                   F1          F2           F3
#> marron   -0.45476114 -0.06607246 -0.094070271
#> noisette -0.07745407  0.24723342 -0.001522229
#> vert      0.18696197  0.19056501  0.035341403
#> bleu      0.62871984 -0.07295266 -0.050086284
#>
#> , , 28
#>
#>                   F1         F2          F3
#> marron   -0.55666875 -0.1549199  0.02823233
#> noisette -0.06938401  0.2769595 -0.26627861
#> vert      0.27283738  0.2991760  0.27496736
#> bleu      0.47951271 -0.1061164 -0.05738948
#>
#> , , 29
#>
#>                  F1          F2          F3
#> marron   -0.5389254 -0.27419032 -0.02987881
#> noisette -0.2258271  0.03922894 -0.12298783
#> vert      0.1229234  0.32547954  0.11642078
#> bleu      0.4931448 -0.06385428 -0.04511109
#>
#> , , 30
#>
#>                  F1         F2          F3
#> marron   -0.5312066 -0.1001550  0.02764545
#> noisette -0.1679850  0.1533494 -0.08249576
#> vert      0.1616451  0.3717303  0.24085748
#> bleu      0.5199715 -0.1395455  0.10521657
#>
get_replications(Y, margin = 2)
#> , , 1
#>
#>                  F1          F2           F3
#> brun    -0.59269891 -0.27204877  0.007852403
#> chatain -0.27281028  0.04681004 -0.002172651
#> roux    -0.07894285  0.31193899  0.098088424
#> blond    0.91046920 -0.10867858  0.052481630
#>
#> , , 2
#>
#>                  F1          F2           F3
#> brun    -0.59663951 -0.31518789  0.069082406
#> chatain -0.16170474  0.06547917 -0.020619830
#> roux    -0.09568452  0.27202671  0.169957965
#> blond    0.73789742 -0.08217788  0.003462903
#>
#> , , 3
#>
#>                 F1          F2          F3
#> brun    -0.6722810 -0.27229639  0.14893530
#> chatain -0.2670570 -0.06685766 -0.07957773
#> roux    -0.1326102  0.16561042  0.15924910
#> blond    0.8750771 -0.20363343  0.01772279
#>
#> , , 4
#>
#>                  F1          F2          F3
#> brun    -0.44080207 -0.14841907 -0.01139760
#> chatain -0.21371308  0.07253944 -0.09943133
#> roux    -0.03550838  0.41751186  0.30373907
#> blond    0.80193880  0.07894975  0.11453392
#>
#> , , 5
#>
#>                  F1         F2          F3
#> brun    -0.56746420 -0.2535260  0.11515772
#> chatain -0.16416613  0.0387354 -0.08483334
#> roux    -0.03139334  0.5370875 -0.05586640
#> blond    0.76855654 -0.1082736 -0.05868684
#>
#> , , 6
#>
#>                 F1          F2          F3
#> brun    -0.5759453 -0.15372011  0.06638289
#> chatain -0.1806496 -0.05234133 -0.15630344
#> roux     0.0620854  0.32812748  0.25824293
#> blond    0.8783074 -0.11191292 -0.06920610
#>
#> , , 7
#>
#>                  F1         F2           F3
#> brun    -0.44163968 -0.2550011  0.009631931
#> chatain -0.03437326  0.1489022  0.085702965
#> roux    -0.10025730  0.1704124 -0.017817128
#> blond    0.96966902 -0.1823600  0.048389341
#>
#> , , 8
#>
#>                  F1         F2          F3
#> brun    -0.54753857 -0.3425506 -0.01580713
#> chatain -0.07088389  0.0990347  0.00787293
#> roux    -0.02587502  0.3516112  0.11746743
#> blond    0.90995830 -0.0568574  0.16221455
#>
#> , , 9
#>
#>                 F1          F2          F3
#> brun    -0.5273692 -0.39199947  0.10806708
#> chatain -0.1626601 -0.02809348 -0.06711148
#> roux    -0.1358804  0.33392208  0.11022104
#> blond    0.9157005 -0.14530349 -0.03999555
#>
#> , , 10
#>
#>                 F1          F2          F3
#> brun    -0.5784176 -0.25454316  0.06633064
#> chatain -0.1106519  0.07867519 -0.11933827
#> roux    -0.1275282  0.35497775  0.10121385
#> blond    0.8299634 -0.07856896  0.05536390
#>
#> , , 11
#>
#>                 F1         F2          F3
#> brun    -0.6194985 -0.2495996  0.14073623
#> chatain -0.2114464  0.1975855 -0.18902804
#> roux    -0.1375554  0.1407045 -0.17317934
#> blond    0.8341036 -0.1324184 -0.08543657
#>
#> , , 12
#>
#>                 F1          F2          F3
#> brun    -0.4116441 -0.22430509  0.07717900
#> chatain -0.2201247  0.02831498 -0.08138473
#> roux    -0.1894939  0.30188537  0.01618851
#> blond    0.8947725 -0.20746209 -0.02547889
#>
#> , , 13
#>
#>                 F1          F2          F3
#> brun    -0.4046455 -0.04333794  0.03514153
#> chatain -0.1377127  0.02174883 -0.09827104
#> roux    -0.1241763  0.40782474  0.04116631
#> blond    0.8197239 -0.05931764  0.03160987
#>
#> , , 14
#>
#>                  F1          F2           F3
#> brun    -0.53234455 -0.18867796  0.005517542
#> chatain -0.09873327  0.02976044  0.024497595
#> roux    -0.14348834  0.33223669  0.084524031
#> blond    0.83258143 -0.01170232 -0.005895072
#>
#> , , 15
#>
#>                 F1          F2          F3
#> brun    -0.5163777 -0.24237766  0.10358194
#> chatain -0.1564821  0.08166781 -0.11748283
#> roux    -0.2267366  0.24557530 -0.05278090
#> blond    0.8494555 -0.14158647  0.01553918
#>
#> , , 16
#>
#>                  F1          F2          F3
#> brun    -0.48318379 -0.04148297 -0.01736949
#> chatain -0.09889756  0.06885155 -0.13361032
#> roux    -0.04492404  0.22275668  0.02967480
#> blond    0.94854826 -0.15808658  0.08831282
#>
#> , , 17
#>
#>                 F1          F2          F3
#> brun    -0.5636659 -0.08611450  0.07687446
#> chatain -0.2370838  0.02937827 -0.01580499
#> roux    -0.1134973  0.47490608  0.15868144
#> blond    0.8317807 -0.08237761 -0.01346469
#>
#> , , 18
#>
#>                  F1          F2           F3
#> brun    -0.59922543 -0.32243102  0.123487752
#> chatain -0.16292227  0.03906659 -0.084685748
#> roux    -0.08872457  0.21934736  0.007324563
#> blond    0.85286612 -0.10605186 -0.000924499
#>
#> , , 19
#>
#>                  F1           F2          F3
#> brun    -0.56795655 -0.276891586 -0.04356517
#> chatain -0.02607463 -0.008921548 -0.04491184
#> roux    -0.05985666  0.313750345 -0.04866088
#> blond    0.74113333  0.048811590  0.08068146
#>
#> , , 20
#>
#>                  F1          F2          F3
#> brun    -0.40621518 -0.23812614  0.11264511
#> chatain -0.23377642  0.08431617 -0.11761991
#> roux     0.02862494  0.16997076  0.09701370
#> blond    0.80210101 -0.15907429  0.07108569
#>
#> , , 21
#>
#>                  F1          F2           F3
#> brun    -0.57188450 -0.32359253  0.161653144
#> chatain -0.15040018  0.03231398 -0.005517225
#> roux    -0.07578767  0.59690153  0.096270049
#> blond    0.80768318 -0.03244748  0.024497874
#>
#> , , 22
#>
#>                  F1          F2          F3
#> brun    -0.42588402 -0.12637937 -0.08040199
#> chatain -0.20720144  0.03686945  0.01005777
#> roux    -0.07575059  0.16708763  0.12349757
#> blond    0.83299148 -0.09070656  0.01060690
#>
#> , , 23
#>
#>                   F1          F2          F3
#> brun    -0.429003553 -0.22855922  0.12555614
#> chatain -0.144193729  0.04396478 -0.07019129
#> roux     0.008980427  0.50144763 -0.02727208
#> blond    0.784751572 -0.01336707  0.04307175
#>
#> , , 24
#>
#>                 F1          F2          F3
#> brun    -0.5295646 -0.21008775  0.11278127
#> chatain -0.1833138  0.13556901  0.02086187
#> roux    -0.1077644  0.37929143 -0.08297452
#> blond    0.8113060 -0.06337545  0.07058767
#>
#> , , 25
#>
#>                 F1          F2          F3
#> brun    -0.5369188 -0.14360603  0.23964367
#> chatain -0.1428582  0.02511217  0.07650986
#> roux    -0.1415312  0.33963835  0.21323621
#> blond    0.8712755 -0.07346265 -0.03620212
#>
#> , , 26
#>
#>                 F1          F2          F3
#> brun    -0.5490216 -0.25372342  0.12327074
#> chatain -0.1523089 -0.02117028 -0.04869329
#> roux    -0.0189157  0.20330619 -0.03596923
#> blond    0.8828647 -0.24208431 -0.11218509
#>
#> , , 27
#>
#>                 F1            F2          F3
#> brun    -0.5734908 -0.1307679903  0.05285589
#> chatain -0.2097141  0.0206665511 -0.07507213
#> roux    -0.1963413  0.3805453640 -0.24167375
#> blond    0.7414199  0.0008124745 -0.09777576
#>
#> , , 28
#>
#>                 F1          F2          F3
#> brun    -0.5050929 -0.31971389  0.23883374
#> chatain -0.1423565 -0.01289670 -0.16935324
#> roux    -0.1470608  0.40217121  0.07552330
#> blond    0.8297251  0.04805687 -0.02872387
#>
#> , , 29
#>
#>                  F1           F2           F3
#> brun    -0.51606001 -0.196506577  0.055839675
#> chatain -0.07723371 -0.006013988 -0.041895825
#> roux     0.14301315  0.460882233  0.148864353
#> blond    0.85722496 -0.087894418 -0.001393031
#>
#> , , 30
#>
#>                  F1          F2           F3
#> brun    -0.39199683 -0.20562793  0.082352500
#> chatain -0.22404812  0.04025555 -0.050761391
#> roux    -0.08660588  0.41098261  0.166909451
#> blond    0.84403054  0.01123001  0.004460793
#>
# }

## Plot with ellipses
plot_rows(Y) +
ggplot2::stat_ellipse()

plot_columns(Y) +
ggplot2::stat_ellipse()

## Partial bootstrap on PCA
## Compute principal components analysis
data(iris)
X <- pca(iris)
#> 1 qualitative variable was removed: Species.

## Plot results
plot_columns(X) +
ggrepel::geom_label_repel()

## Bootstrap (30 replicates)
Y <- bootstrap(X, n = 30)

## Plot with ellipses
plot_columns(Y) +
ggplot2::stat_ellipse()