stabsel.Rd
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), ...)
A formula or extended formula.
A data.frame
.
A bamlss.family
object.
An integer specifying how many terms to select in each boosting run.
An integer specifying the maximum number of boosting iterations.
See opt_boost
. Either choose q
or maxit
as hyper-parameter
for regularization.
An integer. The boosting is run B times.
Cut-off threshold of relative frequencies (between 0 and 1) for selection.
Numeric between 0 and 1. The fraction of data to be used in each boosting run.
A seed to be set before the stability selection.
A object of class stabsel.
Number of terms to be shown.
Color palette for different model terms.
Not used yet in stabsel
.
A object of class stabsel.
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.
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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#>
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#> 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 -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)