WAPLS: Weighted averaging partial least squares (WAPLS) regression...

Description Usage Arguments Details Value Author(s) References See Also Examples

View source: R/WAPLS.r

Description

Functions for reconstructing (predicting) environmental values from biological assemblages using weighted averaging partial least squares (WAPLS) regression and calibration.

Usage

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WAPLS(y, x, npls=5, iswapls=TRUE, standx=FALSE, lean=FALSE,
      check.data=TRUE, ...)

WAPLS.fit(y, x, npls=5, iswapls=TRUE, standx=FALSE, lean=FALSE)

## S3 method for class 'WAPLS'
 predict(object, newdata=NULL, sse=FALSE, nboot=100,
      match.data=TRUE, verbose=TRUE, ...)

## S3 method for class 'WAPLS'
crossval(object, cv.method="loo", verbose=TRUE, ngroups=10, 
      nboot=100, h.cutoff=0, h.dist=NULL, ...)

## S3 method for class 'WAPLS'
performance(object, ...)

## S3 method for class 'WAPLS'
rand.t.test(object, n.perm=999, ...)

## S3 method for class 'WAPLS'
screeplot(x, rand.test=TRUE, ...)

## S3 method for class 'WAPLS'
print(x, ...)

## S3 method for class 'WAPLS'
summary(object, full=FALSE, ...)

## S3 method for class 'WAPLS'
plot(x, resid=FALSE, xval=FALSE, npls=1, 
      xlab="", ylab="", ylim=NULL, xlim=NULL, add.ref=TRUE,
      add.smooth=FALSE, ...)

## S3 method for class 'WAPLS'
residuals(object, cv=FALSE, ...)

## S3 method for class 'WAPLS'
coef(object, ...)

## S3 method for class 'WAPLS'
fitted(object, ...)

Arguments

y

a data frame or matrix of biological abundance data.

x, object

a vector of environmental values to be modelled or an object of class wa.

newdata

new biological data to be predicted.

iswapls

logical logical to perform WAPLS or PLS. Defaults to TRUE = WAPLS.

standx

logical to standardise x-data in PLS, defaults to FALSE.

npls

number of pls components to extract.

check.data

logical to perform simple checks on the input data.

match.data

logical indicate the function will match two species datasets by their column names. You should only set this to FALSE if you are sure the column names match exactly.

lean

logical to exclude some output from the resulting models (used when cross-validating to speed calculations).

full

logical to show head and tail of output in summaries.

resid

logical to plot residuals instead of fitted values.

xval

logical to plot cross-validation estimates.

xlab, ylab, xlim, ylim

additional graphical arguments to plot.wa.

add.ref

add 1:1 line on plot.

add.smooth

add loess smooth to plot.

cv.method

cross-validation method, either "loo", "lgo", "bootstrap" or "h-block".

verbose

logical show feedback during cross-validation.

nboot

number of bootstrap samples.

ngroups

number of groups in leave-group-out cross-validation, or a vector contain leave-out group menbership.

h.cutoff

cutoff for h-block cross-validation. Only training samples greater than h.cutoff from each test sample will be used.

h.dist

distance matrix for use in h-block cross-validation. Usually a matrix of geographical distances between samples.

sse

logical indicating that sample specific errors should be calculated.

rand.test

logical to perform a randomisation t-test to test significance of cross validated components.

n.perm

number of permutations for randomisation t-test.

cv

logical to indicate model or cross-validation residuals.

...

additional arguments.

Details

Function WAPLS performs partial least squares (PLS) or weighted averaging partial least squares (WAPLS) regression. WAPLS was first described in ter Braak and Juggins (1993) and ter Braak et al. (1993) and has since become popular in palaeolimnology for reconstructing (predicting) environmental values from sub-fossil biological assemblages, given a training dataset of modern species and envionmental data. Prediction errors and model complexity (number of components) can be estimated by cross-validation using crossval which implements leave-one out, leave-group-out, or bootstrapping. With leave-group out one may also supply a vector of group memberships for more carefully designed cross-validation experiments.

Function predict predicts values of the environemntal variable for newdata or returns the fitted (predicted) values from the original modern dataset if newdata is NULL. Variables are matched between training and newdata by column name (if match.data is TRUE). Use compare.datasets to assess conformity of two species datasets and identify possible no-analogue samples.

WAPLS has methods fitted and rediduals that return the fitted values (estimates) and residuals for the training set, performance, which returns summary performance statistics (see below), coef which returns the species coefficients, and print and summary to summarise the output. WAPLS also has a plot method that produces scatter plots of predicted vs observed measurements for the training set.

Function rand.t.test performs a randomisation t-test to test the significance of the cross-validated components after van der Voet (1994).

Function screeplot displays the RMSE of prediction for the training set as a function of the number of components and is useful for estimating the optimal number for use in prediction. By default screeplot will also carry out a randomisation t-test and add a line to scree plot indicating percentage change in RMSE with each component annotate with the p-value from the randomisation test.

Value

Function WAPLS returns an object of class WAPLS with the following named elements:

coefficients

species coefficients (the updated "optima").

meanY

weighted mean of the environmental variable.

iswapls

logical indicating whether analysis was WAPLS (TRUE) or PLS (FALSE).

T

sample scores.

P

variable (species) scores.

npls

number of pls components extracted.

fitted.values

fitted values for the training set.

call

original function call.

x

environmental variable used in the model.

standx, meanT sdx

additional information returned for a PLS model.

Function crossval also returns an object of class WAPLS and adds the following named elements:

predicted

predicted values of each training set sample under cross-validation.

residuals.cv

prediction residuals.

If function predict is called with newdata=NULL it returns the fitted values of the original model, otherwise it returns a list with the following named elements:

fit

predicted values for newdata.

If sample specific errors were requested the list will also include:

fit.boot

mean of the bootstrap estimates of newdata.

v1

standard error of the bootstrap estimates for each new sample.

v2

root mean squared error for the training set samples, across all bootstram samples.

SEP

standard error of prediction, calculated as the square root of v1^2 + v2^2.

Function performance returns a matrix of performance statistics for the WAPLS model. See performance, for a description of the summary.

Function rand.t.test returns a matrix of performance statistics together with columns indicating the p-value and percentage change in RMSE with each higher component (see van der Veot (1994) for details).

Author(s)

Steve Juggins

References

ter Braak, C.J.F. & Juggins, S. (1993) Weighted averaging partial least squares regression (WA-PLS): an improved method for reconstructing environmental variables from species assemblages. Hydrobiologia, 269/270, 485-502.

ter Braak, C.J.F., Juggins, S., Birks, H.J.B., & Voet, H., van der (1993). Weighted averaging partial least squares regression (WA-PLS): definition and comparison with other methods for species-environment calibration. In Multivariate Environmental Statistics (eds G.P. Patil & C.R. Rao), pp. 525-560. Elsevier Science Publishers.

van der Voet, H. (1994) Comparing the predictive accuracy of models uing a simple randomization test. Chemometrics and Intelligent Laboratory Systems, 25, 313-323.

See Also

WA, MAT, performance, and compare.datasets for diagnostics.

Examples

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data(IK)
spec <- IK$spec
SumSST <- IK$env$SumSST
core <- IK$core

fit <- WAPLS(spec, SumSST)
fit
# cross-validate model
fit.cv <- crossval(fit, cv.method="loo")
# How many components to use?
rand.t.test(fit.cv)
screeplot(fit.cv)

#predict the core
pred <- predict(fit, core, npls=2)

#plot predictions - depths are in rownames
depth <- as.numeric(rownames(core))
plot(depth, pred$fit[, 2], type="b", ylab="Predicted SumSST", las=1)

# predictions with sample specific errors
## Not run: 
pred <- predict(fit, core, npls=2, sse=TRUE, nboot=1000)
pred

## End(Not run)

Example output

This is rioja 0.9-15

Method : Weighted Averaging Partial Least Squares
Call   : WAPLS(y = spec, x = SumSST) 

No. samples        : 61 
No. species        : 22 
No. components     : 5 
Cross val.         : none 


Performance:
          RMSE      R2  Avg.Bias  Max.Bias    Skill
Comp01  2.0342  0.9161   -0.0272    4.3510  91.6025
Comp02  1.6956  0.9417   -0.0041    3.7135  94.1653
Comp03  1.5807  0.9493   -0.0080    3.7599  94.9296
Comp04  1.5077  0.9539   -0.0101    3.6533  95.3869
Comp05  1.4672  0.9563   -0.0071    3.6361  95.6318

Cross-validating:

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           RMSE        R2     Avg.Bias Max.Bias    Skill delta.RMSE     p
Comp01 2.223843 0.8997053 -0.038122418 4.834263 89.96416 -68.320601 0.001
Comp02 1.898230 0.9268972 -0.029250935 4.544696 92.68788 -14.641893 0.036
Comp03 1.872352 0.9289024 -0.024634606 4.593223 92.88589  -1.363257 0.352
Comp04 1.943207 0.9234816 -0.021386351 4.483557 92.33726   3.784256 0.877
Comp05 2.032738 0.9164191 -0.004121857 4.470094 91.61489   4.607386 0.961
Bootstrapping for SSE:

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$fit
       Comp01   Comp02   Comp03   Comp04   Comp05
0    26.78117 27.50267 26.80464 26.66463 26.55504
10   26.77837 27.48634 26.73384 26.59153 26.42024
20   26.52282 27.18974 26.68634 26.71219 27.13506
30   26.15825 26.77552 26.65750 27.24597 27.98245
40   26.14461 26.70910 26.44604 26.20876 26.31273
50   26.12850 26.70861 26.49125 26.32658 26.58580
60   25.87182 26.34495 26.14529 25.95815 26.33049
70   26.00850 26.56813 26.50372 26.68609 27.26150
80   26.26466 26.91566 26.83726 27.02950 27.80388
90   25.64232 26.10081 26.23855 26.92838 28.06304
100  26.09793 26.77005 27.04452 28.07576 29.60997
110  25.59963 26.07028 26.19927 27.58743 28.93216
120  25.80343 26.39794 26.59310 27.60523 28.85912
130  25.74047 26.23833 26.33551 27.34205 28.71149
140  25.74024 26.17401 25.92995 26.31271 26.77818
150  25.96067 26.47148 26.21548 25.98740 26.05205
160  25.83166 26.27752 25.96036 25.49608 25.41950
170  26.16484 26.77187 26.67776 26.81090 27.14472
180  25.97464 26.50793 26.40061 26.72299 27.32843
190  26.46027 27.22310 27.28499 28.42575 29.71404
200  26.39448 27.11637 27.14814 28.02109 28.79860
210  26.47913 27.29425 27.26914 27.94139 28.73402
220  26.71430 27.55458 27.55632 28.76589 29.84401
230  26.74288 27.51521 27.13257 27.69562 28.30796
240  26.79038 27.61923 27.44147 28.00558 28.07806
250  26.05970 26.62050 26.39939 26.86158 27.25837
260  26.37014 27.03014 26.79377 27.07583 26.99720
270  26.34664 27.04314 26.97463 27.84326 27.78365
280  26.14412 26.77072 26.66539 27.39996 27.80129
290  26.36302 26.95629 26.40833 26.52226 26.73350
300  26.24859 26.85405 26.60564 26.46418 27.15834
310  25.83478 26.30470 26.08493 26.29262 27.43984
320  25.99296 26.55896 26.53787 27.14087 28.16197
330  25.38198 25.65623 25.39210 25.25599 25.48839
340  26.03421 26.60550 26.59850 26.60208 27.14461
350  26.25781 26.89035 26.72082 26.74226 27.17320
360  26.25042 26.87221 26.66115 26.91304 27.61743
370  26.64786 27.50017 27.67568 28.55492 29.67283
380  26.67308 27.52204 27.60187 28.78772 30.27366
390  26.23706 26.90543 26.89289 27.51871 28.59241
400  25.50448 25.86401 25.63540 26.14455 27.00007
410  26.69774 27.61933 27.83990 29.21358 31.02554
420  26.57004 27.38973 27.38436 28.33279 29.54978
430  26.54720 27.36225 27.51094 28.93554 30.67787
440  26.20876 26.87752 26.86202 28.09014 29.56224
450  26.79348 27.55825 27.04329 27.12381 26.88712
460  26.72094 27.43593 26.85360 26.53421 25.81059
470  26.22041 26.82986 26.59529 26.65592 26.48486
480  25.41950 25.75944 25.48327 25.89824 26.12530
490  26.74907 27.54739 27.23181 27.78251 27.91083
500  26.75355 27.54724 27.19088 27.80198 28.23139
510  26.21582 26.85539 26.70454 27.41093 28.40886
520  25.75537 26.24390 26.07987 26.94359 27.94975
530  25.81597 26.27871 26.04691 26.01003 26.91954
540  25.55364 25.95136 25.88799 25.65782 26.25934
550  24.97841 25.14224 24.99376 24.99400 24.84638
560  25.30453 25.53990 25.06774 25.57203 25.61592
570  25.34477 25.60631 25.13554 25.52134 25.45126
580  25.35531 25.66104 25.39141 25.90047 25.83850
590  26.51984 27.24947 27.09320 27.04966 27.63572
600  26.10133 26.66741 26.41653 26.93084 27.62950
610  26.12522 26.73817 26.72815 27.59648 28.54687
620  26.09084 26.66136 26.53147 26.71936 27.21383
630  25.79888 26.24160 25.89059 26.36882 26.88158
640  26.35150 26.98661 26.58161 26.80854 26.91546
650  26.29893 26.91206 26.53814 26.80538 27.08780
660  26.06453 26.61202 26.34599 26.24376 26.50015
670  24.51132 25.22708 25.09017 25.65222 26.26937
680  25.27238 26.09717 26.41737 27.49072 28.50347
690  26.62665 27.42619 27.39044 27.28354 28.10887
700  26.26620 26.86893 26.58547 26.58605 26.71560
710  26.45078 27.31765 27.37072 27.74891 28.29680
720  26.03472 26.71063 27.15991 28.23281 29.41323
730  26.06413 26.76812 26.85790 27.81241 28.88175
740  26.12348 26.68988 26.32821 26.60721 26.57972
750  25.98283 26.58050 26.41324 27.01719 27.50195
760  26.31953 26.92669 26.49001 26.35132 26.19553
770  26.66863 27.49908 27.46561 28.06825 29.05239
780  27.03407 28.00599 27.99383 28.99676 29.74810
790  26.96861 27.83302 27.45475 27.98349 28.52783
800  26.81975 27.60675 27.14707 27.19499 27.56892
810  26.44039 27.13071 26.86543 27.14532 27.45478
820  25.49531 25.87561 25.50486 25.54755 25.53217
830  25.83012 26.28821 26.09843 25.92053 26.15682
840  26.09881 26.64943 26.42132 26.20876 26.61859
850  26.25086 26.88085 26.62654 27.13197 28.36332
860  25.60322 26.03309 25.94890 26.37968 27.12587
870  26.15962 26.80818 26.84345 27.40369 28.31315
880  25.77586 26.26442 26.26640 27.24981 28.51863
890  24.15751 24.12329 24.25466 25.38347 27.02193
900  24.41673 24.61320 24.75665 26.33962 28.35365
910  24.96332 25.16890 25.27444 25.88884 27.00926
920  25.43630 25.91586 26.40476 28.23191 30.69133
930  26.20058 26.92622 27.27994 28.77826 30.45434
940  26.41312 27.15564 27.22807 27.98199 29.07072
950  26.29578 26.91752 26.66006 27.23891 28.24878
960  26.10632 26.68057 26.47318 26.96620 27.68595
970  26.17554 26.76105 26.49299 26.49368 26.97129
980  25.80513 26.30920 26.25789 27.30057 28.61997
990  25.73468 26.17197 25.93433 26.69263 27.67055
1000 25.84942 26.34912 26.24495 27.00154 28.02538
1010 24.83355 24.90397 24.59001 25.34127 26.15739
1020 24.09225 23.96673 23.96153 24.93489 26.47424
1030 24.48485 24.43795 24.04766 24.59867 25.27788
1040 24.19237 24.06971 23.63795 24.43474 25.42447
1050 25.61900 26.02674 25.89751 26.53081 27.74046
1060 25.15548 25.39543 25.24340 26.40056 27.77679
1070 24.82225 24.92975 24.69255 24.74926 25.21685
1080 25.97002 26.46571 26.16253 26.55513 27.26448
1090 25.66224 26.07333 25.86296 26.04551 26.39564

$fit.boot
       Comp01   Comp02   Comp03   Comp04   Comp05
0    26.81142 27.49388 26.74032 26.74046 26.67863
10   26.80778 27.47535 26.66512 26.70077 26.62509
20   26.55339 27.19061 26.67142 26.78491 27.06663
30   26.18837 26.78568 26.69403 27.21162 27.68833
40   26.17509 26.71444 26.42444 26.23902 26.20068
50   26.15896 26.71751 26.49330 26.38326 26.49273
60   25.90549 26.36512 26.17377 26.02206 26.16129
70   26.03898 26.58054 26.53490 26.67709 26.99153
80   26.29529 26.92531 26.85422 27.03860 27.49836
90   25.67238 26.12194 26.29925 26.90400 27.64163
100  26.12778 26.78892 27.13253 27.99531 29.01444
110  25.63446 26.11376 26.37503 27.63702 28.64377
120  25.83630 26.42896 26.70571 27.59918 28.47106
130  25.77305 26.26643 26.43170 27.34748 28.31190
140  25.77448 26.20085 25.99741 26.40236 26.73848
150  25.98973 26.47906 26.21381 26.04394 26.00493
160  25.85942 26.28127 25.92369 25.57702 25.47422
170  26.19867 26.79234 26.72585 26.84224 27.00811
180  26.00882 26.53439 26.48455 26.77479 27.11048
190  26.48915 27.23442 27.37007 28.39301 29.27766
200  26.42471 27.12788 27.20979 27.94863 28.43417
210  26.50537 27.29130 27.27331 27.83721 28.32791
220  26.74536 27.56455 27.61797 28.69425 29.45771
230  26.77338 27.51473 27.11729 27.70031 28.16151
240  26.81633 27.60579 27.37464 27.85014 27.88701
250  26.08945 26.62955 26.41266 26.82749 27.06618
260  26.39916 27.03080 26.77564 27.01638 26.90445
270  26.37393 27.04311 26.98168 27.68388 27.57384
280  26.17139 26.77689 26.70099 27.32342 27.55264
290  26.39625 26.96555 26.40270 26.62820 26.78914
300  26.27790 26.85604 26.58025 26.49413 26.86378
310  25.86233 26.31095 26.08803 26.34365 27.04199
320  26.02311 26.57416 26.58375 27.15720 27.87002
330  25.41244 25.67161 25.39135 25.30548 25.37613
340  26.06427 26.61576 26.60453 26.61112 26.91212
350  26.28606 26.89296 26.70755 26.75941 26.99425
360  26.28351 26.88840 26.70368 26.96365 27.40746
370  26.67430 27.49855 27.68277 28.45429 29.23468
380  26.69934 27.52001 27.62894 28.66959 29.71845
390  26.26078 26.90059 26.88619 27.45401 28.18650
400  25.52946 25.86459 25.61854 26.07401 26.64076
410  26.72300 27.61857 27.89367 29.09018 30.36122
420  26.59893 27.39505 27.42229 28.28581 29.16924
430  26.57699 27.37478 27.59638 28.85395 30.11436
440  26.23571 26.88377 26.91518 28.02991 29.11543
450  26.81904 27.53620 26.92721 27.04226 26.85818
460  26.74785 27.41876 26.74317 26.54202 26.01875
470  26.24881 26.83005 26.56476 26.61583 26.42999
480  25.44302 25.75697 25.45870 25.76756 25.82355
490  26.77328 27.52820 27.15561 27.66578 27.77017
500  26.77922 27.53173 27.12769 27.73543 28.10236
510  26.24179 26.85420 26.69837 27.38766 28.09750
520  25.78036 26.24696 26.08795 26.87456 27.57816
530  25.84395 26.28219 26.01983 26.03138 26.57943
540  25.58211 25.96276 25.87585 25.67520 25.95545
550  25.00654 25.15685 24.96626 24.95454 24.71015
560  25.33393 25.55208 25.07114 25.52857 25.49027
570  25.36966 25.60566 25.09030 25.47542 25.41752
580  25.38459 25.67873 25.43324 25.85635 25.72768
590  26.54871 27.24791 27.06368 27.03970 27.36214
600  26.12843 26.66472 26.38848 26.84188 27.26417
610  26.15551 26.75270 26.78490 27.52305 28.12551
620  26.11451 26.65057 26.45834 26.62877 26.89926
630  25.83022 26.25796 25.92480 26.39936 26.71694
640  26.37824 26.98220 26.55526 26.81506 26.85372
650  26.32788 26.91192 26.51518 26.78357 26.91774
660  26.09050 26.60614 26.27621 26.24960 26.42353
670  24.53514 25.24561 25.14251 25.67037 26.11352
680  25.29311 26.10434 26.45676 27.34050 28.05887
690  26.65318 27.42056 27.35991 27.20212 27.55798
700  26.29328 26.86392 26.53482 26.54378 26.53859
710  26.47386 27.30702 27.34175 27.60195 27.87188
720  26.06189 26.72046 27.19766 27.99736 28.71110
730  26.08898 26.76885 26.86285 27.68465 28.40968
740  26.14834 26.68148 26.28166 26.56156 26.52731
750  26.01116 26.58651 26.42724 26.93604 27.21260
760  26.34484 26.91255 26.39482 26.32859 26.20409
770  26.69563 27.49440 27.44747 27.96038 28.61294
780  27.05839 27.98993 27.96264 28.82012 29.32346
790  26.99663 27.82151 27.40760 27.94630 28.34875
800  26.84606 27.59113 27.07984 27.20379 27.44770
810  26.46771 27.12661 26.85042 27.08287 27.18560
820  25.52064 25.87635 25.48522 25.50734 25.31776
830  25.85722 26.29112 26.06923 25.95803 26.03247
840  26.12539 26.64438 26.35783 26.25830 26.53000
850  26.27603 26.87367 26.60121 27.10022 27.91345
860  25.62947 26.04155 25.97281 26.31602 26.75062
870  26.18733 26.81304 26.85687 27.31899 27.93040
880  25.80434 26.27985 26.33029 27.24397 28.15698
890  24.18191 24.14715 24.32254 25.28780 26.36790
900  24.43891 24.63217 24.84499 26.22441 27.62753
910  24.99490 25.20270 25.36165 25.90821 26.63231
920  25.46169 25.93619 26.51128 28.09731 29.83135
930  26.22867 26.93917 27.36036 28.61024 29.73862
940  26.44172 27.16267 27.26701 27.93691 28.65642
950  26.33085 26.94073 26.73975 27.33176 28.01980
960  26.13757 26.69412 26.51943 26.97611 27.42326
970  26.20421 26.76224 26.46888 26.51445 26.80549
980  25.83559 26.32771 26.33620 27.24791 28.13028
990  25.76341 26.18394 25.98450 26.68426 27.32208
1000 25.88005 26.36793 26.31500 27.00693 27.68211
1010 24.86740 24.93800 24.67793 25.37793 25.89485
1020 24.11734 23.99099 24.00717 24.89677 25.93573
1030 24.51582 24.47018 24.11886 24.68382 25.14209
1040 24.21059 24.06891 23.62422 24.35360 25.06456
1050 25.64684 26.03897 25.92743 26.55772 27.42581
1060 25.17987 25.40161 25.24647 26.32392 27.32466
1070 24.84777 24.94278 24.69306 24.76755 25.01623
1080 25.99917 26.47286 26.16994 26.58933 27.04644
1090 25.68976 26.07957 25.85828 26.01784 26.17114

$v1.boot
        Comp01    Comp02    Comp03    Comp04    Comp05
0    0.2985636 0.1993996 0.2659706 0.3338606 0.4692956
10   0.2992106 0.2018243 0.3076484 0.4318632 0.6234108
20   0.2741364 0.1963373 0.2270529 0.3198915 0.4935309
30   0.2445429 0.1875823 0.2505319 0.3875620 0.4856456
40   0.2479425 0.1925550 0.2549689 0.3666549 0.5525040
50   0.2417198 0.1991202 0.2640445 0.3935013 0.5504859
60   0.2377733 0.2141432 0.3341849 0.5079653 0.7141081
70   0.2391519 0.1995372 0.3019161 0.4627145 0.6040926
80   0.2538670 0.2007072 0.2599072 0.4319314 0.6183460
90   0.2158417 0.1949602 0.3075046 0.6130711 0.9925053
100  0.2323272 0.1955619 0.3187676 0.5915207 0.8705347
110  0.2212001 0.2389796 0.4899309 0.7799406 1.1265876
120  0.2226724 0.2133926 0.3711734 0.6494509 0.9887779
130  0.2203915 0.2033808 0.3258756 0.6044229 0.9651938
140  0.2426024 0.2388551 0.3495117 0.5633400 0.9095069
150  0.2388807 0.2017579 0.2729864 0.3752722 0.5121463
160  0.2422930 0.2246598 0.3618560 0.5107037 0.7032792
170  0.2512767 0.2080458 0.2904696 0.3885238 0.4982777
180  0.2579303 0.2394243 0.4031172 0.6184349 0.8995720
190  0.2639428 0.2176836 0.4671556 0.8583855 1.2697638
200  0.2710656 0.2173379 0.4081714 0.6788786 0.9684372
210  0.2893194 0.2224815 0.3119125 0.5291992 0.7922429
220  0.2858216 0.2038958 0.3384941 0.6040422 0.9694920
230  0.2975090 0.2174183 0.2850974 0.4756771 0.7973659
240  0.3187055 0.2598485 0.4127850 0.7109559 0.9827263
250  0.2539103 0.2201284 0.2996075 0.4461246 0.7248910
260  0.2747335 0.2318181 0.3771034 0.6227522 0.8795563
270  0.2721436 0.2615254 0.5544557 0.9935543 1.4137397
280  0.2454047 0.2296360 0.4325048 0.7821855 1.1859617
290  0.2716499 0.2333636 0.3407265 0.5339816 0.8349946
300  0.2604647 0.2059670 0.3001202 0.4757402 0.7366377
310  0.2298258 0.2281008 0.4404671 0.7755011 1.1062935
320  0.2288188 0.1861061 0.2496136 0.4873555 0.7489133
330  0.2422321 0.2292234 0.3180768 0.4690862 0.7363635
340  0.2439862 0.1984572 0.2477498 0.4168946 0.6470319
350  0.2631331 0.2198601 0.3276247 0.5080152 0.7460127
360  0.2636445 0.2157011 0.3116699 0.4660432 0.6784204
370  0.2988541 0.2529333 0.3148730 0.5790280 0.9153897
380  0.2931416 0.2192221 0.3104116 0.5872224 0.9735277
390  0.2584564 0.2211045 0.3100285 0.5812356 0.9240892
400  0.2247893 0.2046928 0.2827901 0.4802348 0.7577563
410  0.3082165 0.2484614 0.4273273 0.8153577 1.2973488
420  0.2885673 0.2161103 0.2872297 0.5519767 0.9376718
430  0.2742065 0.2054369 0.3690442 0.6896091 1.1139234
440  0.2492654 0.1988048 0.3156600 0.6044549 0.9869083
450  0.3166671 0.2322595 0.3711392 0.5339453 0.7383687
460  0.3086515 0.2412063 0.4260281 0.6009081 0.7572447
470  0.2524462 0.1933010 0.2238170 0.3104729 0.5185233
480  0.2113270 0.2029175 0.2897819 0.4553144 0.6647483
490  0.3121417 0.2320878 0.3254083 0.4837865 0.6970752
500  0.3133878 0.2372983 0.3239823 0.4891406 0.7512554
510  0.2588806 0.2204829 0.3141576 0.5697693 0.9340414
520  0.2241092 0.2249692 0.3052100 0.5167261 0.8087835
530  0.2177419 0.1990095 0.2667427 0.3859910 0.4993657
540  0.2021987 0.2070040 0.2939554 0.4589366 0.6289446
550  0.2199654 0.2297675 0.3638412 0.6184100 0.9369544
560  0.2490545 0.2681550 0.3435256 0.4394268 0.5914698
570  0.2250148 0.2247589 0.2959005 0.4318441 0.6207377
580  0.2238926 0.2285065 0.3027472 0.3721396 0.5061747
590  0.2832978 0.2216673 0.2800901 0.3962106 0.5271499
600  0.2556116 0.2020411 0.2674152 0.4773421 0.8301765
610  0.2528406 0.2000157 0.3313935 0.5540452 0.8788716
620  0.2688247 0.2336776 0.3754893 0.6704466 1.0897726
630  0.2481579 0.2401185 0.3115694 0.4363213 0.7124344
640  0.2656252 0.2033656 0.2657354 0.4149674 0.6875049
650  0.2615665 0.1965586 0.2477863 0.3821957 0.6579696
660  0.2601285 0.2519098 0.4231929 0.6529702 0.9163235
670  0.2458586 0.2103489 0.2757022 0.4317084 0.6800509
680  0.2687264 0.2631780 0.3982809 0.7290009 1.1461909
690  0.3030064 0.2516946 0.4212004 0.7583015 1.2375529
700  0.2610140 0.1887020 0.2735174 0.4607371 0.7961152
710  0.3085356 0.2422591 0.3553651 0.6344487 0.9966044
720  0.2568116 0.2422686 0.4058534 0.7740450 1.2580683
730  0.2775036 0.2453025 0.3835981 0.7428216 1.2190274
740  0.2553915 0.2170092 0.3117445 0.4817013 0.7143641
750  0.2523207 0.1899182 0.2596532 0.4080239 0.6609948
760  0.2848710 0.2349963 0.3836113 0.5904079 0.9151814
770  0.3048566 0.2570632 0.3444045 0.5978973 0.9440094
780  0.3390711 0.3057920 0.5394874 0.9483693 1.3450376
790  0.3197799 0.2433906 0.3474721 0.5652178 0.8710713
800  0.3094325 0.2272337 0.3238176 0.4947673 0.7950072
810  0.2713941 0.2062121 0.3190548 0.5617464 0.8476109
820  0.2273913 0.2277059 0.4308421 0.7751838 1.1153498
830  0.2232005 0.1974383 0.3037780 0.4803726 0.6906602
840  0.2446506 0.2101797 0.3132849 0.4039026 0.5926799
850  0.2567089 0.2017596 0.3096303 0.6003013 1.0260740
860  0.2238874 0.2017937 0.3105741 0.5184324 0.7256763
870  0.2503435 0.2167640 0.3128956 0.5436429 0.7952501
880  0.2152817 0.1776960 0.3253825 0.6707774 1.0679483
890  0.2135983 0.1982204 0.3723266 0.6976165 1.0195261
900  0.1826401 0.1988973 0.4876108 0.8893984 1.2715612
910  0.2048894 0.2028007 0.3141054 0.5704825 0.8045519
920  0.1920606 0.2127867 0.4647721 0.8962206 1.3422419
930  0.2438634 0.2031616 0.3983821 0.7129741 1.0511449
940  0.2593874 0.2043575 0.2919604 0.5311513 0.7544375
950  0.2665635 0.2297744 0.3658338 0.6214596 0.9379506
960  0.2399535 0.1977780 0.3156792 0.5376092 0.6978422
970  0.2448498 0.1854848 0.1980391 0.2871259 0.4117051
980  0.2252045 0.1961681 0.3502580 0.5944040 0.8265008
990  0.2374479 0.2114956 0.3728766 0.7004385 1.0889132
1000 0.2307903 0.2081661 0.3490469 0.6115756 0.9010724
1010 0.2930231 0.3443377 0.5042358 0.7399587 1.0694280
1020 0.2364576 0.2194743 0.3600548 0.7074453 1.1023308
1030 0.2703774 0.3020329 0.3829748 0.5878307 0.9056800
1040 0.2216002 0.2440060 0.3746394 0.6321166 1.0016932
1050 0.2106578 0.1808593 0.2540089 0.5607954 0.9792076
1060 0.2001571 0.1878337 0.3428643 0.6631000 1.0951358
1070 0.2124488 0.2164259 0.2874816 0.4364617 0.5978907
1080 0.2402708 0.2018391 0.3027019 0.5435595 0.8648495
1090 0.2231126 0.1933533 0.2547277 0.4168466 0.6577175

$v2.boot
[1] 2.225480 1.895848 1.874993 1.923715 1.977098

$SEP.boot
       Comp01   Comp02   Comp03   Comp04   Comp05
0    2.245418 1.906305 1.893763 1.952471 2.032032
10   2.245504 1.906560 1.900065 1.971595 2.073055
20   2.242301 1.905987 1.888691 1.950131 2.037766
30   2.238876 1.905105 1.891657 1.962367 2.035871
40   2.239249 1.905602 1.892250 1.958345 2.052846
50   2.238569 1.906276 1.893494 1.963549 2.052304
60   2.238146 1.907904 1.904542 1.989651 2.102110
70   2.238293 1.906320 1.899145 1.978582 2.067328
80   2.239913 1.906443 1.892921 1.971610 2.071538
90   2.235923 1.905846 1.900042 2.019044 2.212235
100  2.237574 1.905908 1.901897 2.012605 2.160266
110  2.236446 1.910851 1.937945 2.075810 2.275548
120  2.236592 1.907820 1.911379 2.030386 2.210565
130  2.236367 1.906726 1.903101 2.016435 2.200117
140  2.238664 1.910835 1.907291 2.004503 2.176263
150  2.238264 1.906553 1.894761 1.959977 2.042354
160  2.238631 1.909113 1.909591 1.990352 2.098456
170  2.239621 1.907229 1.897359 1.962558 2.038921
180  2.240377 1.910907 1.917838 2.020679 2.172130
190  2.241078 1.908304 1.932313 2.106539 2.349727
200  2.241928 1.908265 1.918907 2.039990 2.201542
210  2.244208 1.908858 1.900760 1.995177 2.129922
220  2.243760 1.906781 1.905302 2.016320 2.202006
230  2.245278 1.908274 1.896544 1.981653 2.131832
240  2.248185 1.913573 1.919893 2.050887 2.207865
250  2.239918 1.908585 1.898780 1.974768 2.105798
260  2.242374 1.909968 1.912539 2.022004 2.163917
270  2.242058 1.913801 1.955255 2.165140 2.430551
280  2.238970 1.909705 1.924230 2.076655 2.305520
290  2.241998 1.910157 1.905700 1.996451 2.146190
300  2.240671 1.907003 1.898860 1.981668 2.109870
310  2.237316 1.909521 1.926035 2.074146 2.265569
320  2.237213 1.904961 1.891535 1.984489 2.114187
330  2.238624 1.909655 1.901781 1.980082 2.109775
340  2.238815 1.906207 1.891290 1.968370 2.080281
350  2.240982 1.908554 1.903401 1.989663 2.113162
360  2.241042 1.908079 1.900720 1.979363 2.090256
370  2.245457 1.912646 1.901248 2.008969 2.178728
380  2.244704 1.908481 1.900514 2.011346 2.203786
390  2.240438 1.908698 1.900452 2.009606 2.182397
400  2.236804 1.906866 1.896199 1.982752 2.117336
410  2.246722 1.912060 1.923072 2.089375 2.364748
420  2.244111 1.908126 1.896866 2.001339 2.188183
430  2.242310 1.906946 1.910966 2.043586 2.269304
440  2.239396 1.906243 1.901379 2.016444 2.209730
450  2.247897 1.910022 1.911372 1.996442 2.110475
460  2.246782 1.911131 1.922784 2.015384 2.117153
470  2.239753 1.905677 1.888304 1.948608 2.043963
480  2.235491 1.906676 1.897254 1.976864 2.085859
490  2.247264 1.910001 1.903021 1.983616 2.096385
500  2.247437 1.910641 1.902778 1.984928 2.115018
510  2.240487 1.908626 1.901130 2.006320 2.186630
520  2.236736 1.909149 1.899672 1.991905 2.136129
530  2.236107 1.906265 1.893872 1.962058 2.039187
540  2.234647 1.907116 1.897896 1.977702 2.074726
550  2.236325 1.909721 1.909968 2.020671 2.187876
560  2.239373 1.914718 1.906203 1.973266 2.063675
570  2.236827 1.909124 1.898198 1.971591 2.072253
580  2.236714 1.909569 1.899277 1.959380 2.040865
590  2.243439 1.908763 1.895798 1.964094 2.046168
600  2.240112 1.906583 1.893967 1.982054 2.144320
610  2.239797 1.906370 1.904054 2.001911 2.163639
620  2.241658 1.910195 1.912222 2.037199 2.257548
630  2.239273 1.910994 1.900704 1.972576 2.101542
640  2.241276 1.906724 1.893730 1.967963 2.093222
650  2.240799 1.906010 1.891295 1.961315 2.083709
660  2.240632 1.912511 1.922158 2.031515 2.179120
670  2.239020 1.907482 1.895155 1.971561 2.090786
680  2.241646 1.914028 1.916827 2.057213 2.285316
690  2.246013 1.912483 1.921720 2.067777 2.332478
700  2.240734 1.905216 1.894838 1.978120 2.131365
710  2.246766 1.911264 1.908372 2.025637 2.214077
720  2.240249 1.911265 1.918415 2.073602 2.343428
730  2.242715 1.911652 1.913830 2.062151 2.322702
740  2.240087 1.908228 1.900732 1.983108 2.102197
750  2.239738 1.905337 1.892886 1.966511 2.084666
760  2.243639 1.910357 1.913833 2.012278 2.178640
770  2.246264 1.913197 1.906361 2.014488 2.190906
780  2.251162 1.920351 1.951063 2.144781 2.391243
790  2.248338 1.911408 1.906918 2.005032 2.160482
800  2.246889 1.909417 1.902750 1.986322 2.130951
810  2.241967 1.907030 1.901945 2.004056 2.151130
820  2.237067 1.909474 1.923857 2.074028 2.270005
830  2.236645 1.906101 1.899442 1.982786 2.094261
840  2.238887 1.907463 1.900986 1.965660 2.064022
850  2.240237 1.906554 1.900387 2.015203 2.227498
860  2.236714 1.906557 1.900541 1.992349 2.106068
870  2.239517 1.908200 1.900922 1.999057 2.131042
880  2.235869 1.904157 1.903017 2.037308 2.247094
890  2.235707 1.906182 1.911603 2.046302 2.224489
900  2.232962 1.906253 1.937360 2.119366 2.350699
910  2.234892 1.906664 1.901121 2.006522 2.134531
920  2.233752 1.907752 1.931738 2.122238 2.389672
930  2.238801 1.906702 1.916848 2.051588 2.239157
940  2.240546 1.906830 1.897588 1.995696 2.116151
950  2.241388 1.909721 1.910349 2.021607 2.188303
960  2.238379 1.906136 1.901382 1.997425 2.096640
970  2.238909 1.904900 1.885423 1.945025 2.019509
980  2.236846 1.905970 1.907428 2.013454 2.142900
990  2.238112 1.907608 1.911710 2.047265 2.257133
1000 2.237415 1.907242 1.907205 2.018590 2.172751
1010 2.244688 1.926865 1.941611 2.061121 2.247797
1020 2.238007 1.908510 1.909251 2.049673 2.263637
1030 2.241844 1.919756 1.913705 2.011523 2.174666
1040 2.236486 1.911486 1.912055 2.024908 2.216372
1050 2.235428 1.904455 1.892120 2.003790 2.206301
1060 2.234463 1.905130 1.906084 2.034793 2.260142
1070 2.235598 1.908161 1.896904 1.972607 2.065524
1080 2.238413 1.906562 1.899270 1.999034 2.157981
1090 2.236636 1.905682 1.892217 1.968360 2.083629

rioja documentation built on Oct. 28, 2020, 5:07 p.m.

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