Stability selection.
stabsel.RdPerforms 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.familyobject.- 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 chooseqormaxitas 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.
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
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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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#> Stability selection boosting run 5 / 10
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#> elapsed time: 0.30sec
#> Stability selection boosting run 6 / 10
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#>
#> elapsed time: 0.41sec
#> Stability selection boosting run 7 / 10
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#>
#> elapsed time: 0.58sec
#> Stability selection boosting run 8 / 10
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#>
#> elapsed time: 0.36sec
#> Stability selection boosting run 9 / 10
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#> 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)
