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:  0.27sec
#> Stability selection boosting run 2 / 10 

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#> 
#>  elapsed time:  0.23sec
#> Stability selection boosting run 3 / 10 

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#> 
#>  elapsed time:  0.25sec
#> Stability selection boosting run 4 / 10 

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#> logLik  42.4339 eps 0.0584 iteration   100 qsel 5
#> logLik  42.8779 eps 0.1313 iteration   101 qsel 6
#> 
#>  elapsed time:  0.27sec
#> Stability selection boosting run 5 / 10 

#> logLik -107.777 eps 0.1842 iteration     2 qsel 1
#> logLik -102.541 eps 0.2629 iteration     3 qsel 2
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#> logLik  28.5353 eps 0.0280 iteration    79 qsel 6
#> 
#>  elapsed time:  0.22sec
#> Stability selection boosting run 6 / 10 

#> logLik -125.209 eps 0.1975 iteration     2 qsel 1
#> logLik -118.872 eps 0.7340 iteration     3 qsel 1
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#> logLik  20.8832 eps 0.0407 iteration    79 qsel 6
#> 
#>  elapsed time:  0.21sec
#> Stability selection boosting run 7 / 10 

#> logLik -120.464 eps 0.5589 iteration     2 qsel 1
#> logLik -114.199 eps 0.7678 iteration     3 qsel 2
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#> logLik  25.1071 eps 0.0223 iteration    86 qsel 6
#> 
#>  elapsed time:  0.25sec
#> Stability selection boosting run 8 / 10 

#> logLik -110.594 eps 0.2761 iteration     2 qsel 1
#> logLik -104.450 eps 0.6843 iteration     3 qsel 2
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#> logLik -21.2179 eps 0.1249 iteration    34 qsel 3
#> logLik -19.5300 eps 0.0087 iteration    35 qsel 3
#> logLik -17.8993 eps 0.0585 iteration    36 qsel 3
#> logLik -14.9454 eps 0.1315 iteration    37 qsel 4
#> logLik -13.1584 eps 0.0088 iteration    38 qsel 4
#> logLik -11.6830 eps 0.0078 iteration    39 qsel 4
#> logLik -10.2057 eps 0.2674 iteration    40 qsel 4
#> logLik  -8.6925 eps 0.0846 iteration    41 qsel 4
#> logLik  -7.2457 eps 0.0076 iteration    42 qsel 4
#> logLik  -5.8151 eps 0.0685 iteration    43 qsel 4
#> logLik  -2.8444 eps 0.0932 iteration    44 qsel 4
#> logLik  -1.3077 eps 0.0077 iteration    45 qsel 4
#> logLik  -0.0138 eps 0.0736 iteration    46 qsel 4
#> logLik   1.3523 eps 0.0071 iteration    47 qsel 4
#> logLik   2.5745 eps 0.1309 iteration    48 qsel 4
#> logLik   3.8537 eps 0.0528 iteration    49 qsel 4
#> logLik   6.7359 eps 0.0885 iteration    50 qsel 4
#> logLik   8.2759 eps 0.0075 iteration    51 qsel 4
#> logLik   9.5455 eps 0.0067 iteration    52 qsel 4
#> logLik  10.7186 eps 0.0587 iteration    53 qsel 4
#> logLik  11.8437 eps 0.0062 iteration    54 qsel 4
#> logLik  12.8976 eps 14.100 iteration    55 qsel 4
#> logLik  13.8897 eps 0.0057 iteration    56 qsel 4
#> logLik  14.9062 eps 0.0374 iteration    57 qsel 4
#> logLik  17.8441 eps 0.1737 iteration    58 qsel 4
#> logLik  18.9154 eps 0.0352 iteration    59 qsel 4
#> logLik  20.0516 eps 0.0061 iteration    60 qsel 4
#> logLik  20.9860 eps 0.0054 iteration    61 qsel 4
#> logLik  21.8654 eps 0.0290 iteration    62 qsel 4
#> logLik  24.6659 eps 0.1550 iteration    63 qsel 4
#> logLik  25.6546 eps 0.0055 iteration    64 qsel 4
#> logLik  26.5436 eps 0.0425 iteration    65 qsel 4
#> logLik  27.4598 eps 0.0369 iteration    66 qsel 4
#> logLik  28.3800 eps 0.0052 iteration    67 qsel 4
#> logLik  29.1398 eps 0.0376 iteration    68 qsel 4
#> logLik  31.7046 eps 0.1007 iteration    69 qsel 4
#> logLik  32.6571 eps 0.0053 iteration    70 qsel 4
#> logLik  33.4393 eps 0.0047 iteration    71 qsel 4
#> logLik  34.1882 eps 0.0235 iteration    72 qsel 4
#> logLik  34.9744 eps 0.0479 iteration    73 qsel 4
#> logLik  35.6959 eps 0.0044 iteration    74 qsel 4
#> logLik  36.3671 eps 0.0203 iteration    75 qsel 4
#> logLik  37.1758 eps 0.0378 iteration    76 qsel 5
#> logLik  39.5225 eps 0.0507 iteration    77 qsel 5
#> logLik  40.3144 eps 0.0046 iteration    78 qsel 5
#> logLik  41.0630 eps 0.0170 iteration    79 qsel 6
#> 
#>  elapsed time:  0.22sec
#> Stability selection boosting run 9 / 10 

#> logLik -125.595 eps 0.3992 iteration     2 qsel 1
#> logLik -119.793 eps 0.7282 iteration     3 qsel 1
#> logLik -114.758 eps 0.7832 iteration     4 qsel 2
#> logLik -110.010 eps 0.2769 iteration     5 qsel 2
#> logLik -105.887 eps 58.563 iteration     6 qsel 2
#> logLik -102.002 eps 0.2570 iteration     7 qsel 2
#> logLik -98.6247 eps 0.3091 iteration     8 qsel 2
#> logLik -95.4447 eps 0.1572 iteration     9 qsel 2
#> logLik -92.1143 eps 0.3855 iteration    10 qsel 3
#> logLik -89.3596 eps 0.3979 iteration    11 qsel 3
#> logLik -86.8114 eps 0.1706 iteration    12 qsel 3
#> logLik -84.1389 eps 0.2030 iteration    13 qsel 3
#> logLik -81.8385 eps 0.0134 iteration    14 qsel 3
#> logLik -79.4766 eps 0.7750 iteration    15 qsel 3
#> logLik -77.3290 eps 0.2032 iteration    16 qsel 3
#> logLik -74.9568 eps 0.0133 iteration    17 qsel 3
#> logLik -72.5803 eps 1.7943 iteration    18 qsel 3
#> logLik -70.3728 eps 0.0125 iteration    19 qsel 3
#> logLik -68.2445 eps 0.5178 iteration    20 qsel 3
#> logLik -66.2108 eps 0.0116 iteration    21 qsel 3
#> logLik -64.2180 eps 0.3582 iteration    22 qsel 3
#> logLik -62.1080 eps 0.1271 iteration    23 qsel 3
#> logLik -60.0350 eps 0.0115 iteration    24 qsel 3
#> logLik -58.1266 eps 0.1530 iteration    25 qsel 3
#> logLik -56.2346 eps 0.0107 iteration    26 qsel 3
#> logLik -54.4794 eps 0.2160 iteration    27 qsel 3
#> logLik -52.6043 eps 0.0985 iteration    28 qsel 3
#> logLik -50.7122 eps 0.0104 iteration    29 qsel 3
#> logLik -49.0066 eps 0.1487 iteration    30 qsel 3
#> logLik -47.2940 eps 0.0097 iteration    31 qsel 3
#> logLik -45.7529 eps 0.2509 iteration    32 qsel 3
#> logLik -44.2126 eps 0.0090 iteration    33 qsel 3
#> logLik -42.6945 eps 0.3272 iteration    34 qsel 3
#> logLik -40.9640 eps 0.0835 iteration    35 qsel 3
#> logLik -39.4357 eps 0.0088 iteration    36 qsel 3
#> logLik -38.0901 eps 0.0734 iteration    37 qsel 3
#> logLik -36.7271 eps 0.0081 iteration    38 qsel 3
#> logLik -35.3847 eps 0.0983 iteration    39 qsel 3
#> logLik -33.8520 eps 0.0768 iteration    40 qsel 3
#> logLik -32.5180 eps 0.0079 iteration    41 qsel 3
#> logLik -31.3473 eps 0.0695 iteration    42 qsel 3
#> logLik -30.1666 eps 0.0073 iteration    43 qsel 3
#> logLik -28.9848 eps 0.0913 iteration    44 qsel 3
#> logLik -25.5366 eps 0.1061 iteration    45 qsel 4
#> logLik -24.2131 eps 0.1476 iteration    46 qsel 4
#> logLik -22.8151 eps 0.0078 iteration    47 qsel 4
#> logLik -21.6635 eps 0.0070 iteration    48 qsel 4
#> logLik -20.5967 eps 0.1281 iteration    49 qsel 4
#> logLik -19.5809 eps 0.0064 iteration    50 qsel 4
#> logLik -18.5395 eps 0.0663 iteration    51 qsel 4
#> logLik -15.1929 eps 0.1720 iteration    52 qsel 4
#> logLik -13.9992 eps 0.1061 iteration    53 qsel 4
#> logLik -12.7992 eps 0.0069 iteration    54 qsel 4
#> logLik -11.8120 eps 0.0061 iteration    55 qsel 4
#> logLik -10.8490 eps 0.0572 iteration    56 qsel 4
#> logLik  -9.9614 eps 0.0791 iteration    57 qsel 4
#> logLik  -6.9215 eps 0.1145 iteration    58 qsel 4
#> logLik  -5.7996 eps 0.0065 iteration    59 qsel 4
#> logLik  -4.8771 eps 0.0058 iteration    60 qsel 4
#> logLik  -4.0268 eps 0.0393 iteration    61 qsel 4
#> logLik  -2.9155 eps 0.0603 iteration    62 qsel 4
#> logLik  -0.2107 eps 0.0663 iteration    63 qsel 4
#> logLik   0.8313 eps 0.0061 iteration    64 qsel 4
#> logLik   1.6875 eps 0.0054 iteration    65 qsel 4
#> logLik   2.4743 eps 0.0467 iteration    66 qsel 4
#> logLik   3.2194 eps 0.0050 iteration    67 qsel 4
#> logLik   3.9771 eps 0.0257 iteration    68 qsel 4
#> logLik   4.9925 eps 0.0368 iteration    69 qsel 4
#> logLik   7.4315 eps 0.1914 iteration    70 qsel 4
#> logLik   8.2689 eps 0.0052 iteration    71 qsel 4
#> logLik   8.9560 eps 0.0047 iteration    72 qsel 4
#> logLik   9.6473 eps 0.0265 iteration    73 qsel 4
#> logLik  10.3006 eps 0.0275 iteration    74 qsel 4
#> logLik  11.2103 eps 0.0515 iteration    75 qsel 4
#> logLik  11.8844 eps 0.0046 iteration    76 qsel 4
#> logLik  12.5144 eps 0.0249 iteration    77 qsel 5
#> logLik  14.6735 eps 0.0543 iteration    78 qsel 5
#> logLik  15.3635 eps 0.0046 iteration    79 qsel 5
#> logLik  15.9566 eps 0.0243 iteration    80 qsel 5
#> logLik  16.5502 eps 0.0042 iteration    81 qsel 5
#> logLik  17.1236 eps 0.0181 iteration    82 qsel 5
#> logLik  17.9470 eps 0.0515 iteration    83 qsel 5
#> logLik  18.5053 eps 0.0221 iteration    84 qsel 6
#> 
#>  elapsed time:  0.24sec
#> Stability selection boosting run 10 / 10 

#> logLik -124.376 eps 0.2020 iteration     2 qsel 1
#> logLik -118.987 eps 0.5100 iteration     3 qsel 2
#> logLik -113.866 eps 0.6241 iteration     4 qsel 2
#> logLik -109.470 eps 0.6343 iteration     5 qsel 2
#> logLik -105.293 eps 0.7178 iteration     6 qsel 2
#> logLik -101.705 eps 0.6067 iteration     7 qsel 2
#> logLik -98.2963 eps 0.8038 iteration     8 qsel 2
#> logLik -94.7609 eps 0.3064 iteration     9 qsel 3
#> logLik -91.8834 eps 0.2975 iteration    10 qsel 3
#> logLik -89.1459 eps 2.7590 iteration    11 qsel 3
#> logLik -86.3403 eps 0.2020 iteration    12 qsel 3
#> logLik -84.0302 eps 0.2105 iteration    13 qsel 3
#> logLik -81.8280 eps 0.2773 iteration    14 qsel 3
#> logLik -79.5039 eps 0.0134 iteration    15 qsel 3
#> logLik -77.1583 eps 0.1994 iteration    16 qsel 3
#> logLik -74.9976 eps 0.0125 iteration    17 qsel 3
#> logLik -72.9517 eps 0.2246 iteration    18 qsel 3
#> logLik -70.9681 eps 0.0117 iteration    19 qsel 3
#> logLik -68.9214 eps 0.2521 iteration    20 qsel 3
#> logLik -66.8672 eps 0.1343 iteration    21 qsel 3
#> logLik -64.8421 eps 0.0115 iteration    22 qsel 3
#> logLik -63.0387 eps 0.1115 iteration    23 qsel 3
#> logLik -61.1993 eps 0.0107 iteration    24 qsel 3
#> logLik -59.3917 eps 1.0918 iteration    25 qsel 3
#> logLik -57.5930 eps 0.1030 iteration    26 qsel 3
#> logLik -55.7527 eps 0.0105 iteration    27 qsel 3
#> logLik -54.1679 eps 0.0611 iteration    28 qsel 3
#> logLik -52.5117 eps 0.0097 iteration    29 qsel 3
#> logLik -50.9194 eps 0.2067 iteration    30 qsel 3
#> logLik -49.3459 eps 0.0956 iteration    31 qsel 3
#> logLik -47.7168 eps 0.0094 iteration    32 qsel 3
#> logLik -46.3297 eps 0.0508 iteration    33 qsel 3
#> logLik -44.8754 eps 0.0087 iteration    34 qsel 3
#> logLik -43.4776 eps 0.0830 iteration    35 qsel 3
#> logLik -39.4144 eps 0.1214 iteration    36 qsel 4
#> logLik -37.7792 eps 0.0091 iteration    37 qsel 4
#> logLik -36.3660 eps 0.1503 iteration    38 qsel 4
#> logLik -34.9042 eps 0.0084 iteration    39 qsel 4
#> logLik -33.6987 eps 0.0693 iteration    40 qsel 4
#> logLik -32.4044 eps 0.0077 iteration    41 qsel 4
#> logLik -31.1368 eps 0.0492 iteration    42 qsel 4
#> logLik -27.2140 eps 0.0991 iteration    43 qsel 4
#> logLik -25.7622 eps 0.0081 iteration    44 qsel 4
#> logLik -24.4921 eps 0.0538 iteration    45 qsel 4
#> logLik -23.2016 eps 0.0075 iteration    46 qsel 4
#> logLik -22.1183 eps 0.0368 iteration    47 qsel 4
#> logLik -20.9814 eps 0.0069 iteration    48 qsel 4
#> logLik -19.8790 eps 0.0321 iteration    49 qsel 4
#> logLik -16.2228 eps 0.1847 iteration    50 qsel 4
#> logLik -14.9614 eps 0.0072 iteration    51 qsel 4
#> logLik -13.8200 eps 0.0425 iteration    52 qsel 4
#> logLik -12.7042 eps 0.0066 iteration    53 qsel 4
#> logLik -11.7390 eps 0.0416 iteration    54 qsel 4
#> logLik -10.7607 eps 0.0061 iteration    55 qsel 4
#> logLik  -9.8037 eps 0.0352 iteration    56 qsel 4
#> logLik  -6.4734 eps 0.4235 iteration    57 qsel 4
#> logLik  -5.4018 eps 0.0063 iteration    58 qsel 4
#> logLik  -4.3775 eps 0.0460 iteration    59 qsel 4
#> logLik  -3.3362 eps 0.0586 iteration    60 qsel 5
#> logLik  -2.3253 eps 0.0060 iteration    61 qsel 5
#> logLik  -1.4666 eps 0.0740 iteration    62 qsel 5
#> logLik  -0.5850 eps 0.0056 iteration    63 qsel 5
#> logLik   0.3035 eps 0.0438 iteration    64 qsel 6
#> 
#>  elapsed time:  0.18sec
#> 
plot(sel)


## Estimate selected model.
nf <- formula(sel)
b <- bamlss(nf, data = d)
#> AICc -123.239 logPost  69.3283 logLik  93.6099 edf 30.006 eps 0.5816 iteration   1
#> AICc -263.907 logPost 149.7018 logLik 164.6302 edf 30.610 eps 0.2569 iteration   2
#> AICc -287.393 logPost 162.0310 logLik 180.4552 edf 34.172 eps 0.1674 iteration   3
#> AICc -290.935 logPost 147.4173 logLik 183.1285 edf 34.952 eps 0.1033 iteration   4
#> AICc -293.177 logPost -89.8766 logLik 183.5869 edf 34.380 eps 0.0116 iteration   5
#> AICc -293.821 logPost -2574.92 logLik 183.6353 edf 34.143 eps 0.0040 iteration   6
#> AICc -293.824 logPost -2574.92 logLik 183.6394 edf 34.145 eps 0.0007 iteration   7
#> AICc -293.824 logPost -2574.92 logLik 183.6400 edf 34.145 eps 0.0000 iteration   8
#> AICc -293.824 logPost -2574.92 logLik 183.6400 edf 34.145 eps 0.0000 iteration   8
#> elapsed time:  0.26sec
#> Starting the sampler...
#> 
#> |                    |   0%  4.64sec
#> |*                   |   5%  4.50sec  0.24sec
#> |**                  |  10%  4.34sec  0.48sec
#> |***                 |  15%  4.05sec  0.72sec
#> |****                |  20%  3.89sec  0.97sec
#> |*****               |  25%  3.69sec  1.23sec
#> |******              |  30%  3.49sec  1.50sec
#> |*******             |  35%  3.26sec  1.76sec
#> |********            |  40%  3.07sec  2.05sec
#> |*********           |  45%  2.84sec  2.33sec
#> |**********          |  50%  2.60sec  2.60sec
#> |***********         |  55%  2.34sec  2.86sec
#> |************        |  60%  2.09sec  3.13sec
#> |*************       |  65%  1.83sec  3.41sec
#> |**************      |  70%  1.58sec  3.68sec
#> |***************     |  75%  1.32sec  3.95sec
#> |****************    |  80%  1.05sec  4.22sec
#> |*****************   |  85%  0.79sec  4.48sec
#> |******************  |  90%  0.53sec  4.78sec
#> |******************* |  95%  0.27sec  5.06sec
#> |********************| 100%  0.00sec  5.34sec
plot(b)