Performs stability selection based on gradient boosting.

stabsel(formula, data, family = "gaussian",
  q, maxit, B = 100, thr = .9, fraction = 0.5, seed = NULL, ...)

## Plot selection frequencies.
# S3 method for stabsel
plot(x, show = NULL,
  pal = function(n) gray.colors(n, start = 0.9, end = 0.3), ...)

Arguments

formula

A formula or extended formula.

data

A data.frame.

family

A bamlss.family object.

q

An integer specifying how many terms to select in each boosting run.

maxit

An integer specifying the maximum number of boosting iterations. See opt_boost. Either choose q or maxit as hyper-parameter for regularization.

B

An integer. The boosting is run B times.

thr

Cut-off threshold of relative frequencies (between 0 and 1) for selection.

fraction

Numeric between 0 and 1. The fraction of data to be used in each boosting run.

seed

A seed to be set before the stability selection.

x

A object of class stabsel.

show

Number of terms to be shown.

pal

Color palette for different model terms.

...

Not used yet in stabsel.

Value

A object of class stabsel.

Details

stabsel performs stability selection based on gradient boosting (opt_boost): The boosting algorithm is run B times on a randomly drawn fraction of the data. Each boosting run is stopped either when q terms have been selected, or when maxit iterations have been performed, i.e. either q or maxit can be used to tune the regularization of the boosting. After the boosting the relative selection frequencies are evaluated. Terms with a relative selection frequency larger then thr are suggested for a final regression model.

If neither q nor maxit has been specified, q will be set to the square root of the number of columns in data.

Gradient boosting does not depend on random numbers. Thus, the individual boosting runs differ only in the subset of data which is used.

Author

Thorsten Simon

Examples

if (FALSE) ## Simulate some data.
set.seed(111)
d <- GAMart()
n <- nrow(d)

## Add some noise variables.
for(i in 4:9)
  d[[paste0("x",i)]] <- rnorm(n)

f <- paste0("~ ", paste("s(x", 1:9, ")", collapse = "+", sep = ""))
f <- paste(f, "+ te(lon,lat)")
f <- as.formula(f)
f <- list(update(f, num ~ .), f)

## Run stability selection.
sel <- stabsel(f, data = d, q = 6, B = 10)
#> Stability selection boosting run 1 / 10 

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#> 
#>  elapsed time:  0.36sec
#> Stability selection boosting run 2 / 10 

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#> 
#>  elapsed time:  0.47sec
#> Stability selection boosting run 3 / 10 

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#> 
#>  elapsed time:  0.38sec
#> Stability selection boosting run 4 / 10 

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#> logLik  32.2054 eps 0.0478 iteration    59 qsel 4
#> logLik  34.6044 eps 0.0442 iteration    60 qsel 4
#> logLik  35.5558 eps 0.0052 iteration    61 qsel 4
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#> logLik  37.8948 eps 0.0468 iteration    64 qsel 4
#> logLik  39.0071 eps 0.0512 iteration    65 qsel 4
#> logLik  41.0981 eps 0.0359 iteration    66 qsel 4
#> logLik  42.0046 eps 0.0050 iteration    67 qsel 4
#> logLik  42.7489 eps 0.0044 iteration    68 qsel 4
#> logLik  43.4363 eps 0.0347 iteration    69 qsel 5
#> logLik  44.0883 eps 0.0504 iteration    70 qsel 5
#> logLik  44.7660 eps 0.0042 iteration    71 qsel 5
#> logLik  45.4241 eps 0.6254 iteration    72 qsel 5
#> logLik  46.4627 eps 0.0258 iteration    73 qsel 5
#> logLik  48.3165 eps 0.0579 iteration    74 qsel 5
#> logLik  49.0506 eps 0.0043 iteration    75 qsel 5
#> logLik  49.6524 eps 0.0039 iteration    76 qsel 5
#> logLik  50.3026 eps 0.0029 iteration    77 qsel 6
#> 
#>  elapsed time:  0.34sec
#> Stability selection boosting run 5 / 10 

#> logLik -84.5410 eps 0.0620 iteration     2 qsel 1
#> logLik -77.9757 eps 0.0581 iteration     3 qsel 1
#> logLik -71.7559 eps 0.0587 iteration     4 qsel 2
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#> logLik  58.4812 eps 0.0425 iteration    64 qsel 4
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#> logLik  61.9714 eps 0.0490 iteration    66 qsel 4
#> logLik  63.2054 eps 0.0056 iteration    67 qsel 4
#> logLik  64.2209 eps 0.0050 iteration    68 qsel 4
#> logLik  65.1332 eps 0.0535 iteration    69 qsel 5
#> logLik  66.0220 eps 0.0046 iteration    70 qsel 5
#> logLik  66.9858 eps 0.0040 iteration    71 qsel 6
#> 
#>  elapsed time:  0.30sec
#> Stability selection boosting run 6 / 10 

#> logLik -88.1342 eps 0.0532 iteration     2 qsel 1
#> logLik -82.4361 eps 0.0533 iteration     3 qsel 1
#> logLik -77.1654 eps 0.0498 iteration     4 qsel 2
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#> logLik -44.5228 eps 0.0115 iteration    14 qsel 3
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#> logLik  38.3441 eps 7.5094 iteration    59 qsel 4
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#> logLik  62.0397 eps 1.0834 iteration    79 qsel 4
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#> logLik  63.8694 eps 0.0044 iteration    81 qsel 4
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#> logLik  65.1145 eps 0.0248 iteration    83 qsel 4
#> logLik  65.6949 eps 0.0036 iteration    84 qsel 4
#> logLik  66.4899 eps 0.0041 iteration    85 qsel 5
#> logLik  67.0318 eps 0.0148 iteration    86 qsel 5
#> logLik  68.6377 eps 0.0224 iteration    87 qsel 5
#> logLik  69.5666 eps 0.0200 iteration    88 qsel 5
#> logLik  70.2226 eps 0.0038 iteration    89 qsel 5
#> logLik  70.7600 eps 0.0034 iteration    90 qsel 5
#> logLik  71.4128 eps 0.0036 iteration    91 qsel 5
#> logLik  71.8968 eps 0.0171 iteration    92 qsel 5
#> logLik  73.2988 eps 0.0893 iteration    93 qsel 5
#> logLik  73.8488 eps 0.0034 iteration    94 qsel 5
#> logLik  74.2989 eps 0.0031 iteration    95 qsel 5
#> logLik  74.8509 eps 0.0032 iteration    96 qsel 5
#> logLik  75.3190 eps 0.0264 iteration    97 qsel 6
#> 
#>  elapsed time:  0.41sec
#> Stability selection boosting run 7 / 10 

#> logLik -87.3456 eps 0.0461 iteration     2 qsel 1
#> logLik -81.1418 eps 0.0470 iteration     3 qsel 2
#> logLik -75.9629 eps 0.0460 iteration     4 qsel 2
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#> logLik -66.7355 eps 0.0422 iteration     6 qsel 3
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#> logLik  44.1973 eps 0.0061 iteration    60 qsel 4
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#> logLik  59.6627 eps 0.0206 iteration    74 qsel 5
#> logLik  60.5006 eps 0.0045 iteration    75 qsel 5
#> logLik  61.1984 eps 0.0150 iteration    76 qsel 6
#> 
#>  elapsed time:  0.58sec
#> Stability selection boosting run 8 / 10 

#> logLik -74.2076 eps 0.0491 iteration     2 qsel 1
#> logLik -67.9870 eps 0.0480 iteration     3 qsel 2
#> logLik -62.7213 eps 0.0465 iteration     4 qsel 3
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#> logLik  52.1328 eps 0.0052 iteration    59 qsel 4
#> logLik  52.9708 eps 0.0046 iteration    60 qsel 4
#> logLik  53.8290 eps 0.5306 iteration    61 qsel 4
#> logLik  54.8655 eps 0.0267 iteration    62 qsel 4
#> logLik  55.6577 eps 0.0318 iteration    63 qsel 4
#> logLik  57.8267 eps 0.1525 iteration    64 qsel 4
#> logLik  58.7964 eps 0.0050 iteration    65 qsel 4
#> logLik  59.5929 eps 0.0044 iteration    66 qsel 4
#> logLik  60.3411 eps 0.0547 iteration    67 qsel 4
#> logLik  61.2443 eps 0.0280 iteration    68 qsel 4
#> logLik  61.9848 eps 0.0042 iteration    69 qsel 4
#> logLik  62.6507 eps 0.2887 iteration    70 qsel 4
#> logLik  64.6045 eps 0.0458 iteration    71 qsel 4
#> logLik  65.3471 eps 0.0042 iteration    72 qsel 4
#> logLik  66.0025 eps 0.0386 iteration    73 qsel 4
#> logLik  66.7969 eps 0.0414 iteration    74 qsel 4
#> logLik  68.4754 eps 0.0478 iteration    75 qsel 4
#> logLik  69.2482 eps 0.0042 iteration    76 qsel 4
#> logLik  69.8820 eps 0.0038 iteration    77 qsel 4
#> logLik  70.4650 eps 0.0387 iteration    78 qsel 4
#> logLik  71.0106 eps 0.0035 iteration    79 qsel 4
#> logLik  71.6688 eps 0.0034 iteration    80 qsel 5
#> logLik  72.2145 eps 0.0239 iteration    81 qsel 5
#> logLik  72.8173 eps 0.0182 iteration    82 qsel 6
#> 
#>  elapsed time:  0.36sec
#> Stability selection boosting run 9 / 10 

#> logLik -83.9094 eps 0.0514 iteration     2 qsel 1
#> logLik -78.3498 eps 0.0501 iteration     3 qsel 1
#> logLik -73.3469 eps 0.0476 iteration     4 qsel 2
#> logLik -68.9256 eps 0.0532 iteration     5 qsel 2
#> logLik -64.9424 eps 0.0511 iteration     6 qsel 2
#> logLik -61.1025 eps 0.0542 iteration     7 qsel 3
#> logLik -57.6085 eps 0.2368 iteration     8 qsel 3
#> logLik -54.4916 eps 0.0828 iteration     9 qsel 3
#> logLik -51.4290 eps 0.0961 iteration    10 qsel 3
#> logLik -48.6637 eps 0.0783 iteration    11 qsel 3
#> logLik -46.2216 eps 0.1216 iteration    12 qsel 3
#> logLik -43.7708 eps 0.1282 iteration    13 qsel 3
#> logLik -41.5786 eps 0.4908 iteration    14 qsel 3
#> logLik -39.2153 eps 0.0115 iteration    15 qsel 3
#> logLik -37.2012 eps 0.1354 iteration    16 qsel 3
#> logLik -35.0401 eps 0.0107 iteration    17 qsel 3
#> logLik -32.8699 eps 0.1458 iteration    18 qsel 3
#> logLik -30.8736 eps 0.0100 iteration    19 qsel 3
#> logLik -28.8653 eps 0.1098 iteration    20 qsel 3
#> logLik -27.0321 eps 0.0094 iteration    21 qsel 3
#> logLik -25.2183 eps 0.1190 iteration    22 qsel 3
#> logLik -23.3058 eps 0.0915 iteration    23 qsel 3
#> logLik -21.4600 eps 0.0093 iteration    24 qsel 3
#> logLik -19.7177 eps 0.0742 iteration    25 qsel 3
#> logLik -18.0426 eps 0.0086 iteration    26 qsel 3
#> logLik -16.3389 eps 0.0842 iteration    27 qsel 3
#> logLik -14.8051 eps 0.0443 iteration    28 qsel 3
#> logLik -13.1522 eps 0.0084 iteration    29 qsel 3
#> logLik -11.6456 eps 0.0768 iteration    30 qsel 3
#> logLik -10.1606 eps 0.0078 iteration    31 qsel 3
#> logLik  -8.6628 eps 0.0809 iteration    32 qsel 3
#> logLik  -7.3260 eps 0.0073 iteration    33 qsel 3
#> logLik  -5.9657 eps 0.0469 iteration    34 qsel 3
#> logLik  -2.5467 eps 0.0947 iteration    35 qsel 4
#> logLik  -1.0861 eps 0.0075 iteration    36 qsel 4
#> logLik   0.2634 eps 0.1054 iteration    37 qsel 4
#> logLik   3.2905 eps 0.0546 iteration    38 qsel 4
#> logLik   4.8385 eps 0.0076 iteration    39 qsel 4
#> logLik   6.1147 eps 0.0068 iteration    40 qsel 4
#> logLik   7.3849 eps 0.0357 iteration    41 qsel 4
#> logLik   8.7486 eps 0.0448 iteration    42 qsel 4
#> logLik   9.9846 eps 0.0066 iteration    43 qsel 4
#> logLik  11.1907 eps 0.0454 iteration    44 qsel 4
#> logLik  14.0864 eps 0.0393 iteration    45 qsel 4
#> logLik  15.3950 eps 0.0067 iteration    46 qsel 4
#> logLik  16.5025 eps 0.0256 iteration    47 qsel 4
#> logLik  17.6993 eps 0.0264 iteration    48 qsel 4
#> logLik  18.9404 eps 0.0064 iteration    49 qsel 4
#> logLik  19.9770 eps 0.0285 iteration    50 qsel 4
#> logLik  22.6076 eps 0.0404 iteration    51 qsel 4
#> logLik  23.8881 eps 0.0064 iteration    52 qsel 4
#> logLik  24.9420 eps 0.0057 iteration    53 qsel 4
#> logLik  25.9448 eps 0.0527 iteration    54 qsel 4
#> logLik  27.0452 eps 0.0277 iteration    55 qsel 4
#> logLik  28.0426 eps 0.0055 iteration    56 qsel 4
#> logLik  28.9588 eps 0.0278 iteration    57 qsel 4
#> logLik  31.3949 eps 0.0384 iteration    58 qsel 4
#> logLik  32.4222 eps 0.0055 iteration    59 qsel 4
#> logLik  33.2995 eps 0.0314 iteration    60 qsel 4
#> logLik  34.2871 eps 0.0273 iteration    61 qsel 4
#> logLik  35.2455 eps 0.0052 iteration    62 qsel 4
#> logLik  36.0326 eps 0.0047 iteration    63 qsel 4
#> logLik  36.8351 eps 0.0219 iteration    64 qsel 4
#> logLik  39.0610 eps 0.0537 iteration    65 qsel 4
#> logLik  39.8700 eps 0.0047 iteration    66 qsel 4
#> logLik  40.6595 eps 0.0265 iteration    67 qsel 4
#> logLik  41.5817 eps 0.0217 iteration    68 qsel 4
#> logLik  42.3367 eps 0.0045 iteration    69 qsel 4
#> logLik  43.0162 eps 0.0188 iteration    70 qsel 4
#> logLik  44.9795 eps 0.0583 iteration    71 qsel 4
#> logLik  45.7368 eps 0.0044 iteration    72 qsel 4
#> logLik  46.4283 eps 0.0241 iteration    73 qsel 4
#> logLik  47.2762 eps 0.0207 iteration    74 qsel 4
#> logLik  47.9760 eps 0.0042 iteration    75 qsel 4
#> logLik  48.7932 eps 0.0040 iteration    76 qsel 5
#> logLik  49.4061 eps 0.0039 iteration    77 qsel 5
#> logLik  50.1373 eps 0.0039 iteration    78 qsel 6
#> 
#>  elapsed time:  0.37sec
#> Stability selection boosting run 10 / 10 

#> logLik -88.7509 eps 0.0704 iteration     2 qsel 1
#> logLik -83.1333 eps 0.0662 iteration     3 qsel 2
#> logLik -77.8415 eps 0.0856 iteration     4 qsel 2
#> logLik -73.1818 eps 1.1861 iteration     5 qsel 3
#> logLik -68.8271 eps 0.2091 iteration     6 qsel 3
#> logLik -64.6851 eps 0.2255 iteration     7 qsel 3
#> logLik -61.0240 eps 0.1154 iteration     8 qsel 3
#> logLik -57.6444 eps 0.1277 iteration     9 qsel 3
#> logLik -54.4007 eps 0.2465 iteration    10 qsel 3
#> logLik -51.5141 eps 0.2015 iteration    11 qsel 3
#> logLik -48.8881 eps 0.1580 iteration    12 qsel 3
#> logLik -46.3464 eps 0.2272 iteration    13 qsel 3
#> logLik -43.9955 eps 0.0117 iteration    14 qsel 3
#> logLik -41.5937 eps 2.5035 iteration    15 qsel 3
#> logLik -39.4029 eps 0.0110 iteration    16 qsel 3
#> logLik -37.1498 eps 0.1100 iteration    17 qsel 3
#> logLik -34.9523 eps 0.0974 iteration    18 qsel 3
#> logLik -32.6921 eps 0.0109 iteration    19 qsel 3
#> logLik -30.5880 eps 0.1782 iteration    20 qsel 3
#> logLik -28.5096 eps 0.0102 iteration    21 qsel 3
#> logLik -26.5782 eps 0.0649 iteration    22 qsel 3
#> logLik -24.6793 eps 0.0095 iteration    23 qsel 3
#> logLik -22.6972 eps 0.1846 iteration    24 qsel 3
#> logLik -20.8551 eps 0.0585 iteration    25 qsel 3
#> logLik -18.9377 eps 0.0094 iteration    26 qsel 3
#> logLik -17.2902 eps 0.0535 iteration    27 qsel 3
#> logLik -15.5605 eps 0.0087 iteration    28 qsel 3
#> logLik -13.8640 eps 0.0477 iteration    29 qsel 3
#> logLik  -9.5869 eps 0.0661 iteration    30 qsel 4
#> logLik  -7.6254 eps 0.0092 iteration    31 qsel 4
#> logLik  -5.9806 eps 0.0553 iteration    32 qsel 4
#> logLik  -4.2122 eps 0.0085 iteration    33 qsel 4
#> logLik  -2.7525 eps 0.0075 iteration    34 qsel 4
#> logLik  -1.2420 eps 0.0750 iteration    35 qsel 4
#> logLik   2.8843 eps 0.0677 iteration    36 qsel 4
#> logLik   4.5406 eps 0.0080 iteration    37 qsel 4
#> logLik   5.9971 eps 0.0486 iteration    38 qsel 4
#> logLik   7.4808 eps 0.0074 iteration    39 qsel 4
#> logLik   9.0130 eps 0.0650 iteration    40 qsel 4
#> logLik  10.3515 eps 0.0069 iteration    41 qsel 4
#> logLik  11.6791 eps 0.0368 iteration    42 qsel 4
#> logLik  15.4981 eps 0.1164 iteration    43 qsel 4
#> logLik  16.9905 eps 0.0072 iteration    44 qsel 4
#> logLik  18.2243 eps 0.0339 iteration    45 qsel 4
#> logLik  19.5547 eps 0.0310 iteration    46 qsel 4
#> logLik  20.9827 eps 0.0069 iteration    47 qsel 4
#> logLik  22.1591 eps 0.0061 iteration    48 qsel 4
#> logLik  23.3303 eps 0.0299 iteration    49 qsel 4
#> logLik  26.8049 eps 0.0493 iteration    50 qsel 4
#> logLik  28.0969 eps 0.0064 iteration    51 qsel 4
#> logLik  29.1604 eps 0.0057 iteration    52 qsel 4
#> logLik  30.2335 eps 0.0343 iteration    53 qsel 4
#> logLik  31.4855 eps 0.0291 iteration    54 qsel 4
#> logLik  34.4898 eps 0.4261 iteration    55 qsel 4
#> logLik  35.7200 eps 0.0061 iteration    56 qsel 4
#> logLik  36.7618 eps 0.0633 iteration    57 qsel 4
#> logLik  39.3312 eps 0.0431 iteration    58 qsel 4
#> logLik  40.5972 eps 0.0061 iteration    59 qsel 4
#> logLik  41.6391 eps 0.0054 iteration    60 qsel 4
#> logLik  42.5573 eps 0.0237 iteration    61 qsel 4
#> logLik  43.7038 eps 0.0272 iteration    62 qsel 4
#> logLik  44.6879 eps 0.0052 iteration    63 qsel 4
#> logLik  45.5576 eps 0.0222 iteration    64 qsel 4
#> logLik  47.8626 eps 0.0601 iteration    65 qsel 4
#> logLik  48.8658 eps 0.0052 iteration    66 qsel 4
#> logLik  49.6900 eps 0.0046 iteration    67 qsel 4
#> logLik  50.4985 eps 0.1127 iteration    68 qsel 4
#> logLik  51.5626 eps 0.1756 iteration    69 qsel 4
#> logLik  52.3400 eps 0.0044 iteration    70 qsel 4
#> logLik  53.0626 eps 0.0640 iteration    71 qsel 4
#> logLik  55.1169 eps 0.0461 iteration    72 qsel 4
#> logLik  55.9025 eps 0.0044 iteration    73 qsel 4
#> logLik  56.5938 eps 0.0270 iteration    74 qsel 4
#> logLik  57.5622 eps 0.1826 iteration    75 qsel 4
#> logLik  58.2934 eps 0.0042 iteration    76 qsel 4
#> logLik  58.9199 eps 0.0142 iteration    77 qsel 5
#> logLik  59.5502 eps 0.0039 iteration    78 qsel 5
#> logLik  60.1462 eps 0.0881 iteration    79 qsel 5
#> logLik  60.7260 eps 0.0246 iteration    80 qsel 5
#> logLik  62.5334 eps 0.1716 iteration    81 qsel 5
#> logLik  63.4209 eps 0.0226 iteration    82 qsel 5
#> logLik  64.1260 eps 0.0041 iteration    83 qsel 5
#> logLik  64.7039 eps 0.0036 iteration    84 qsel 5
#> logLik  65.2222 eps 0.0154 iteration    85 qsel 5
#> logLik  65.7285 eps 0.0338 iteration    86 qsel 5
#> logLik  67.3055 eps 0.0273 iteration    87 qsel 5
#> logLik  68.1295 eps 0.0237 iteration    88 qsel 5
#> logLik  68.7605 eps 0.0038 iteration    89 qsel 5
#> logLik  69.2774 eps 0.0034 iteration    90 qsel 5
#> logLik  69.7532 eps 0.0199 iteration    91 qsel 5
#> logLik  70.1953 eps 0.0031 iteration    92 qsel 5
#> logLik  70.8737 eps 0.0032 iteration    93 qsel 6
#> 
#>  elapsed time:  0.45sec
#> 
plot(sel)


## Estimate selected model.
nf <- formula(sel)
b <- bamlss(nf, data = d)
#> AICc -233.934 logPost 128.8045 logLik 149.6334 edf 30.601 eps 0.8488 iteration   1
#> AICc -373.546 logPost 209.4583 logLik 220.1280 edf 31.206 eps 0.1952 iteration   2
#> AICc -399.814 logPost 221.9233 logLik 238.1983 edf 35.496 eps 0.1279 iteration   3
#> AICc -402.053 logPost 222.3120 logLik 241.5083 edf 37.374 eps 0.2640 iteration   4
#> AICc -402.290 logPost 222.2838 logLik 241.9305 edf 37.633 eps 0.0088 iteration   5
#> AICc -402.323 logPost 222.2714 logLik 241.9633 edf 37.647 eps 0.0010 iteration   6
#> AICc -402.326 logPost 222.2713 logLik 241.9648 edf 37.647 eps 0.0000 iteration   7
#> AICc -402.326 logPost 222.2713 logLik 241.9648 edf 37.647 eps 0.0000 iteration   7
#> elapsed time:  0.40sec
#> Starting the sampler...
#> 
#> |                    |   0%  9.04sec
#> |*                   |   5%  7.73sec  0.41sec
#> |**                  |  10%  7.31sec  0.81sec
#> |***                 |  15%  8.31sec  1.47sec
#> |****                |  20%  7.52sec  1.88sec
#> |*****               |  25%  7.00sec  2.33sec
#> |******              |  30%  6.47sec  2.77sec
#> |*******             |  35%  5.93sec  3.19sec
#> |********            |  40%  5.44sec  3.63sec
#> |*********           |  45%  4.97sec  4.06sec
#> |**********          |  50%  4.54sec  4.54sec
#> |***********         |  55%  4.22sec  5.16sec
#> |************        |  60%  3.79sec  5.69sec
#> |*************       |  65%  3.31sec  6.15sec
#> |**************      |  70%  2.84sec  6.62sec
#> |***************     |  75%  2.36sec  7.08sec
#> |****************    |  80%  1.88sec  7.53sec
#> |*****************   |  85%  1.41sec  7.98sec
#> |******************  |  90%  0.94sec  8.43sec
#> |******************* |  95%  0.47sec  8.94sec
#> |********************| 100%  0.00sec  9.48sec
plot(b)