inst/doc/mboost.R

In mboost: Model-Based Boosting

### R code from vignette source 'mboost.Rnw'

###################################################
### code chunk number 1: options
###################################################
options(prompt = "R> ", continue = "+  ", digits = 4)
set.seed(290875)
## use old degrees of freedom for reproducibility
options(mboost_dftraceS = TRUE)

### store result of crossvalidation; this takes too long for CRAN checks
cvm <-
structure(c(3.7463373531230646, 5.0294654135338313, 3.805863095238093, 
4.0915440115440198, 5.1818741137894335, 5.6048850574712619, 5.2657919254658365, 
4.1252366863905303, 4.2108424908424871, 3.4747760210803671, 4.5522090909090878, 
4.4596816751392012, 5.1701923076923046, 4.424523809523806, 3.9238333333333304, 
4.3438666666666634, 4.8396938775510163, 3.8774999999999973, 3.7093367346938746, 
4.3919333333333439, 4.1541777777777744, 4.3980769230769203, 4.9424999999999963, 
4.6229999999999958, 3.6159329832728822, 3.574058441558436, 4.8180117794486161, 
3.6206845238095191, 3.899367140795722, 4.9901047943991443, 5.4433908045976969, 
5.0412267080745305, 3.9449336961115762, 4.0259312482389351, 3.3079070205157133, 
4.356518181818176, 4.2569038973614264, 5.0051923076923028, 4.2553551832255474, 
3.7495476190476134, 4.1373333333333253, 4.6329081632653004, 3.7192857142857085, 
3.5133843537414919, 4.1956666666666784, 3.998399999999994, 4.2201923076923018, 
4.7508522727272666, 4.429666666666658, 3.44752503653981, 3.4019495980210186, 
4.6070429882398241, 3.4566898148148089, 3.7071902700474246, 4.8124456329084584, 
5.2882915360501501, 4.8397774327122089, 3.7917743554522323, 3.8386161594815364, 
3.1379841897233165, 4.1716999999999906, 4.0624594529169835, 4.840299027895175, 
4.0819890260630896, 3.5818778409090837, 3.9384833333333229, 4.4339413265306042, 
3.5746712018140512, 3.3205782312925103, 4.0190000000000108, 3.8489079365079277, 
4.0440442890442805, 4.5600090718105344, 4.2369999999999877, 3.2842925485844137, 
3.2335992578849617, 4.4171326585694963, 3.3115509259259182, 3.5150133992991268, 
4.6380473409829905, 5.1300943845271245, 4.6912267080745256, 3.6424336961115702, 
3.6598601078408697, 2.9680613589309197, 3.990118181818171, 3.8705446623093813, 
4.6808294590025268, 3.9093636096413737, 3.4082482413419815, 3.7629833333333211, 
4.2474362244897845, 3.4366326530612161, 3.1263775510203997, 3.8423333333333427, 
3.7046222222222127, 3.8943648018647932, 4.3663158899923493, 4.0682087028824689, 
3.1244711200129829, 3.0742965367965245, 4.227222328899173, 3.179189814814805, 
3.3295031952174958, 4.4650235527456896, 4.9741897461611275, 4.5426759834368422, 
3.4880761684336616, 3.4939384653807695, 2.8017905581204734, 3.8279818181818062, 
3.6884458968772833, 4.5146460750787565, 3.7236936605917941, 3.2488683712121103, 
3.6087148148148036, 4.0630229591836615, 3.2990157312925072, 2.9474829931972697, 
3.6656666666666746, 3.5526507936507863, 3.7456812496446572, 4.1744563858601147, 
3.8945966371027212, 2.9733356658313079, 2.9387438157080901, 4.0454702409870889, 
3.0547974537036922, 3.1757463376357555, 4.2929216105195209, 4.8278532368519658, 
4.3941252587991588, 3.3367983501421161, 3.3414672456423458, 2.64042775212851, 
3.6659764193660673, 3.5063471314451848, 4.3580648197955778, 3.5347423965807985, 
3.1030148809523705, 3.4660851851851748, 3.9083351818988348, 3.1574624433106466, 
2.7676417989652324, 3.4890000000000065, 3.4198523476523444, 3.5984821885431568, 
3.9970288597464134, 3.7078709540630412, 2.8384955631235571, 2.8140839517625156, 
3.8705626055191034, 2.9309259259259122, 3.0278090982238646, 4.1186823904573169, 
4.691715488440007, 4.2448498964803152, 3.2270024718433374, 3.188079167374462, 
2.4806360093444382, 3.5168724893093071, 3.3242483660130864, 4.2394602918793245, 
3.3892916898397698, 2.9790863095238023, 3.3197878306878215, 3.7743661911607984, 
3.0144139739228906, 2.6039711306358675, 3.3123333333333385, 3.2930530469530481, 
3.4540103212054372, 3.8316212881908354, 3.5284583208534079, 2.7120669916949875, 
2.6984261943413701, 3.6998914232530917, 2.8099016203703573, 2.8876000343742509, 
3.9437145386921024, 4.5540584078893724, 4.0797004399585735, 3.1276223325318497, 
3.0489138455168319, 2.3192732033524743, 3.3846249577248755, 3.1615940450254323, 
4.1280798757693793, 3.2703982413467338, 2.8596834733893539, 3.1667402116402066, 
3.6451909743645023, 2.8796988378684696, 2.4658579803923173, 3.1430606060606108, 
3.1881767768866887, 3.3156223733856431, 3.6842355466895045, 3.3536097426096156, 
2.5768737014648804, 2.5991220560193766, 3.5414583198048217, 2.7031423611110985, 
2.7393213289526908, 3.7871326420994742, 4.4229490669989859, 3.9173091356107461, 
3.0222554035035936, 2.9181232659041387, 2.1894680556025574, 3.2612682875751067, 
3.0033733624817138, 3.9896342890979843, 3.1434632517179302, 2.7594873949579841, 
3.0365898799285778, 3.5181783767727941, 2.773944431560492, 2.3403254436596761, 
2.9948787878787932, 3.0897343362863547, 3.1961282691681197, 3.5435355834319751, 
3.1937917014718677, 2.4508880811945457, 2.4956852646361605, 3.3897897483762569, 
2.6047580180576424, 2.6042440253039598, 3.6520316977946927, 4.3124076593811145, 
3.7738988095237875, 2.9263081938505029, 2.8026044818036269, 2.0869735358680153, 
3.1384941421802757, 2.8461719804033367, 3.8542947351086352, 3.0292550181432323, 
2.6593067486253799, 2.9116990056841452, 3.3940772428887209, 2.6565834667112092, 
2.2146206807785114, 2.8450285204991155, 3.0017738581679856, 3.087116917303582, 
3.4028274253661297, 3.0304819310278388, 2.3367616372824371, 2.4004412539884257, 
3.2386011769476921, 2.5284267954713511, 2.4976300857177769, 3.545552820450605, 
4.2135993538905581, 3.6517899963010039, 2.842455771505048, 2.6937801280197604, 
1.9906758256850399, 3.0130309387170757, 2.6950490795521764, 3.7421198386798453, 
2.9171725331814948, 2.5608180049797755, 2.7906042160535276, 3.2860897228804262, 
2.5469436280813076, 2.1091655565589913, 2.7132101307189633, 2.9324891078306097, 
2.9699543918652984, 3.2582142475888172, 2.8862986253050704, 2.2353903306846497, 
2.3165689089484642, 3.0864840947195797, 2.4492355050654657, 2.3960831939624536, 
3.4392619311073949, 4.1062587190153073, 3.5399382139124671, 2.7659794920490146, 
2.5702043852780507, 1.9134996542069129, 2.8874638391499792, 2.5768441590976789, 
3.63511679104501, 2.8092585820786939, 2.4662011691811312, 2.6999296546500222, 
3.1809283365680039, 2.450075473921089, 2.0188504308701263, 2.5675918113912308, 
2.847781600849761, 2.8529563657952313, 3.1165783688720938, 2.7353894192591928, 
2.1423193356766475, 2.2382408669728791, 2.9468994793349679, 2.3674040716517308, 
2.3027531906324512, 3.3282799963754663, 4.001186937716497, 3.4464281008371418, 
2.6790544427393508, 2.4489026101301259, 1.8359962118314224, 2.774522662679396, 
2.4754235667668714, 3.5258353608382955, 2.6988035449982735, 2.3740387193473991, 
2.6075717599131836, 3.0813902066054117, 2.3547859070782016, 1.9319853204183544, 
2.4529687102798206, 2.744473676375494, 2.7271024801871664, 2.992477567712474, 
2.5810082087804238, 2.0504163376064009, 2.1566747920388072, 2.807167611203103, 
2.2840638070491388, 2.2206945694744626, 3.217078697674173, 3.8911786622140414, 
3.3422062743547643, 2.6002458257775114, 2.3313735722164801, 1.7705406822633007, 
2.6630443409095905, 2.3811544220019689, 3.4227582040142845, 2.5876924338871663, 
2.2882656017767879, 2.5152138651763449, 2.9827694218457959, 2.2620694775596091, 
1.8430083154121566, 2.3501796888648059, 2.6602898396338195, 2.6034463967769037, 
2.8767101291752306, 2.4429232945979535, 1.9533100317832062, 2.0804871128250655, 
2.6707426396229543, 2.2005611340320126, 2.1519169547496424, 3.1058773989728805, 
3.7907173069526809, 3.2403088869280814, 2.5213572618234563, 2.2547923756352768, 
1.7241207636167404, 2.5680073661196765, 2.2967941386948802, 3.325513897771597, 
2.4764521238096502, 2.2103298644680156, 2.4225046932079675, 2.8816516724162606, 
2.1692787334667019, 1.7595266568085914, 2.2444462543297039, 2.5651158242159355, 
2.4816867090961661, 2.767799691354945, 2.2882324840534922, 1.8629990404427716, 
1.9990599879098692, 2.5431160680648239, 2.1190459790341625, 2.0858144003992942, 
2.9946761002715876, 3.6888258403602738, 3.1401692165918655, 2.446964549272852, 
2.1895812142476365, 1.6730586898454856, 2.4629216812487607, 2.2228299757056269, 
3.236831961281855, 2.3694407799030781, 2.1323920751128358, 2.3409697115229888, 
2.7870535776817991, 2.0757635353131225, 1.6857220727597273, 2.1217026743170551, 
2.4764306984360207, 2.3564062001314494, 2.6673492409044992, 2.1616998097988382, 
1.8020325215815214, 1.916191407624646, 2.4177026669262238, 2.0369466710978172, 
2.0139658721221965, 2.8834748015702951, 3.5979256569294296, 3.045075534923293, 
2.3801542543046526, 2.1476939754599518, 1.6197261982634636, 2.3632078563457752, 
2.1488658127163731, 3.1464461245341693, 2.2831813315174641, 2.0464659136572663, 
2.2802609203141975, 2.6975862682574641, 1.9910183884551633, 1.629269947096915, 
2.0312596264468397, 2.3882786516523939, 2.2478801217573365, 2.566591665146928, 
2.0259588709784366, 1.7303252433525091, 1.8334798336921772, 2.2964852233573758, 
1.955976713498661, 1.9421458338735875, 2.7722735028690022, 3.5022657292134687, 
2.9312228611859372, 2.3300554624190477, 2.12736782724919, 1.5768021748153662, 
2.2850512541542916, 2.0749016497271193, 3.0583874862796829, 2.2130488863291737, 
1.9750811259245211, 2.2244402243435051, 2.6131982712339812, 1.9342578518248774, 
1.5891969429500283, 1.9458863410432163, 2.354113466475285, 2.1304238804235922, 
2.4658340893893569, 1.8971709921905635, 1.6582684490040336, 1.7673466893617162, 
2.1790270154091913, 1.8756233287033808, 1.874012294311477, 2.6610722041677097, 
3.4073027446572643, 2.8088061194423379, 2.288499094501788, 2.1143366116698945, 
1.5357767144914201, 2.1989524141826724, 2.0028786240592011, 2.9720513832536115, 
2.1376831654658606, 1.9059468740255658, 2.1859525869808687, 2.5268860451595834, 
1.9046412338279686, 1.56476109319978, 1.8584090185380875, 2.3074603810530578, 
2.0492118592811326, 2.3770979527541853, 1.8271419574685965, 1.6151717995970674, 
1.7115042576920805, 2.0730725200451152, 1.8027896397512666, 1.8152107446108243, 
2.553678813244904, 3.3098483898576805, 2.6928979932632235, 2.2572775618698677, 
2.1124460022792695, 1.4998637397104242, 2.1289946217691793, 1.9291858036091318, 
2.8828618637313719, 2.053959316521889, 1.8557830020749331, 2.1310234110604296, 
2.4457780911033327, 1.8662775934021731, 1.5343748128135, 1.7735990945567002, 
2.26880600000535, 1.9841740589273407, 2.299300749956986, 1.7748532540131317, 
1.5583275893207451, 1.663839585762702, 1.9680880172834998, 1.7244242639879868, 
1.7745319911204942, 2.4809649752847163, 3.2133875495410771, 2.5868617460364982, 
2.2301752390952778, 2.1253664151996818, 1.4522535014330313, 2.0669658330026861, 
1.8584731597682298, 2.803117801367228, 1.9613667239292998, 1.8160537619997632, 
2.0663354069937037, 2.3724770908613428, 1.8284265555511365, 1.5071246120338879, 
1.6826529778714521, 2.2205508369684503, 1.9176296339272925, 2.2215035471597875, 
1.7479015069524071, 1.4912469346660084, 1.6179795696145829, 1.859243040594641, 
1.6603848682494551, 1.7615141048048233, 2.4154012994915939, 3.1085468797369908, 
2.4784158928322566, 2.1915795220934333, 2.1357839031171695, 1.4029409654985403, 
1.9877051375921406, 1.7924485307761795, 2.7257966697040481, 1.8752556128181896, 
1.7741577084409197, 1.982883424425893, 2.2988080580308234, 1.7935953153627548, 
1.4800253335829316, 1.6021495721363044, 2.198124956125115, 1.8495773468249224, 
2.1437063443625886, 1.6969890640750542, 1.4254285367373714, 1.5685481436146087, 
1.7773307824063744, 1.6025721016606826, 1.7249840596709738, 2.35338078443516, 
3.0074764660519895, 2.3780442262244796, 2.1500865662056801, 2.1227173750506401, 
1.3830092573851405, 1.9168319793194006, 1.7356692466558983, 2.6480860885849604, 
1.8192530586390543, 1.732688980463472, 1.9125017710652501, 2.2260687899097862, 
1.7587640751743734, 1.4375153068449653, 1.5645411397806699, 2.1746366158943333, 
1.7894529245004436, 2.0798725835608747, 1.6458344580091966, 1.3694775463933613, 
1.5169462528583044, 1.6964141111197142, 1.5525447661887013, 1.6936538973861837, 
2.2877057290570817, 2.9076941959604685, 2.2862647225480863, 2.1147536597437666, 
2.0938430786153654, 1.3683545259273426, 1.8473038938873998, 1.6740106807957549, 
2.5682834722721677, 1.7776106335262956, 1.6890391390258415, 1.8451442349843092, 
2.1502227348801073, 1.7207950224771591, 1.3936841380137983, 1.5508943292966098, 
2.1378386369686693, 1.737091588109358, 2.0289908555923564, 1.6600315036798012, 
1.3224534572296294, 1.4773151740171, 1.6225661729058092, 1.5202339386147177, 
1.6670848816949169, 2.2101737154966488, 2.8107092945728551, 2.1930182695975593, 
2.0936532323933381, 2.1153745951549228, 1.3454528314757295, 1.770848580610469, 
1.6230709995939634, 2.4892876157734873, 1.751058202686177, 1.6529529868059687, 
1.8143801787281841, 2.0863097887492721, 1.6793958587623379, 1.3615465021193442, 
1.5463488747511551, 2.112072722762727, 1.6922276002397267, 1.9753897107689224, 
1.6528134591052726, 1.2800440882902802, 1.4402528507245715, 1.5456110480934577, 
1.4898170504346731, 1.6452414901878563, 2.1598661447551541, 2.7148466391658661, 
2.1131285219796854, 2.0673681937541648, 2.1085706309402439, 1.3173264900602779, 
1.7197572623287667, 1.5771964659284674, 2.4085450820213956, 1.7224863664733812, 
1.6275363201393021, 1.8062280289983779, 2.0238509992311191, 1.6247223274184197, 
1.3536933087855609, 1.5398411560547571, 2.0800465423821812, 1.6579833268494584, 
1.9347658075351808, 1.667738779916158, 1.2352985985355147, 1.4041377507187864, 
1.5143491731626271, 1.4594130179418265, 1.623542226030263, 2.1164992854920515, 
2.6521149292544273, 2.037138183815439, 2.0545622662599099, 2.0989696976110661, 
1.2954012603763507, 1.6783426992211057, 1.5413928430546888, 2.3159681578858238, 
1.6900963327635148, 1.6106767460616398, 1.8162280144886298, 1.9638324846365514, 
1.5775202976326403, 1.3596038467207667, 1.5140952264006666, 2.0635402234488898, 
1.6427770853775976, 1.8887173196437745, 1.6821780604078629, 1.1805827003267961, 
1.3693645605956262, 1.4841086740900378, 1.4304682463050942, 1.6001950443901438, 
2.0680005640783214, 2.57696592933616, 1.9622595588827039, 2.0390248822440888, 
2.0954045127958807, 1.271876220478483, 1.6408241120812628, 1.5099415278079187, 
2.2431135320333744, 1.6706992710715876, 1.6037973621942718, 1.8353189235795386, 
1.9192997917587664, 1.5465741117472478, 1.3759530181307849, 1.4883492967465761, 
2.0272920636554872, 1.640970393251755, 1.8433544394379331, 1.689663264347647, 
1.1248982818566109, 1.3477706578004685, 1.4494305419701694, 1.4011107840087129, 
1.578407486690776, 2.0366797108957884, 2.5148438538810285, 1.9050593769259991, 
2.0290486305927606, 2.0942618280996239, 1.2536186294036833, 1.6186606003207322, 
1.4885811816638712, 2.1698167791418514, 1.6411121185159545, 1.6085352490483695, 
1.8239126971674215, 1.8659512815916381, 1.5138791174462749, 1.3954603907396976, 
1.4757374710093376, 2.0285936763235326, 1.6302728984524573, 1.8135613351393423, 
1.7027567714514162, 1.0791705848491813, 1.3365238713138707, 1.4188513338827391, 
1.3668138587144956, 1.5721714148097221, 2.0136476030784265, 2.4893148895283832, 
1.8554753748223793, 2.015144548842041, 2.0766632766925004, 1.2411392148344262, 
1.6127183942551868, 1.475874830575262, 2.0948173263820524, 1.6110012061896413, 
1.6171150416812099, 1.8187101673843489, 1.827090371320343, 1.4900805079374106, 
1.4081729683148443, 1.4555600067188685, 2.014595386929523, 1.6201973412042148, 
1.7917233155194587, 1.7012517671042886, 1.038905244464625, 1.3228449158781272, 
1.3975733874192855, 1.3491221702064358, 1.5633088849475461, 1.9981440042936744, 
2.453518264187589, 1.8229452329754725, 2.0060080968222112, 2.0566117334468883, 
1.2289962181093119, 1.6122522714685537, 1.4588051805826869, 2.0197164816578232, 
1.5834760626384752, 1.6198865063276739, 1.8136323151976661, 1.7963027798854267, 
1.4757994954328411, 1.4192880320973902, 1.4500085486722711, 2.0283205878702417, 
1.6160929225667608, 1.7692687623009711, 1.6966144996098815, 1.0104149157436111, 
1.3258470235709638, 1.3662245523502754, 1.3304154974134363, 1.5597614758272906, 
1.9871165995999718, 2.3967198265051222, 1.7994026804007572, 1.9964303082783739, 
2.0428891461844882, 1.228651507272924, 1.6051626477116081, 1.4401455162266885, 
1.9586636376397248, 1.5565996808257863, 1.6151263717511744, 1.8052480837524545, 
1.7743557166716981, 1.4609871898859623, 1.4268350484157828, 1.4517849511193963, 
2.0385160655392904, 1.6168270770773783, 1.7503045267939976, 1.6954810061695875, 
0.98006250011437313, 1.3085574950453847, 1.3598410688473799, 
1.3060022212188787, 1.5544521033701857, 1.9766818289628367, 2.3400515124400916, 
1.7679635492242312, 1.9767126963669208, 2.0231634003708026, 1.22514936890291, 
1.6020043943547682, 1.4343516132597058, 1.8942830357832976, 1.5351134343339521, 
1.6131198368114079, 1.8006197386132454, 1.7513526753822828, 1.4458341586001549, 
1.427813133732416, 1.4623278140266798, 2.0374384980100597, 1.6279740949372052, 
1.7258662097990218, 1.6741267213031461, 0.95427175004278608, 
1.2957133628552948, 1.3475361841113063, 1.2796755731502278, 1.5267841862747769, 
1.9665599822361421, 2.3032715714961887, 1.7476161345317569, 1.9640343172202956, 
2.0002811209380083, 1.2193810716230871, 1.5981806361520841, 1.4472358817878497, 
1.8449061855658924, 1.5159060670472679, 1.611916143473531, 1.7903951909245381, 
1.7302821092513747, 1.4357442351991818, 1.4190609339501594, 1.4706113536833356, 
2.0526516657351839, 1.6326177932935264, 1.7128799565722623, 1.6366267213031482, 
0.94594092668302798, 1.2992271952985244, 1.3357776621087738, 
1.2544211905965132, 1.5008920772008547, 1.9396520446512235, 2.2681737782641433, 
1.7230315105544485, 1.9585696821787844, 1.9763807291541913, 1.2143577617817454, 
1.5968749113557836, 1.46209328416678, 1.8208578086416272, 1.5038925550816713, 
1.6041497557008, 1.7736758764916214, 1.7239157460609353, 1.4253743585674579, 
1.4131948750190357, 1.4799620628884642, 2.0419183436162816, 1.6338240470500893, 
1.6944518913724567, 1.6050018365014522, 0.93301235774223179, 
1.3061257558915877, 1.3324897846441723, 1.238709022536655, 1.4891997028034791, 
1.9340572441872066, 2.2296416451857262, 1.7182534280636552, 1.9456752028029962, 
1.9601722215262143, 1.2079128388397777, 1.5997316998822833, 1.4776152557685651, 
1.777478829807843, 1.489400128769103, 1.5912687687945379, 1.7591383978603301, 
1.7228826789226781, 1.4161296681985933, 1.4101805946742965, 1.4812572925144818, 
2.0364431907779394, 1.6318296014550302, 1.7016197246315565, 1.5758351698347872, 
0.93816714985827399, 1.3162231263183382, 1.3191029438808066, 
1.2332003156732076, 1.4822551087604874, 1.9229199553525831, 2.200002849884755, 
1.7067245379274412, 1.9327211429739359, 1.9355774074533056, 1.2001870361901974, 
1.6009307375813606, 1.4840810344186361, 1.7581033161229629, 1.4773772380907919, 
1.5776343067717005, 1.7462663240778371, 1.7237497476604144, 1.4106365221935502, 
1.3997554341634231, 1.4920576852313743, 2.0385943037387211, 1.6308367403914292, 
1.7081804699019791, 1.5466685031681222, 0.94786978201458838, 
1.3283914428277737, 1.3013755343257032, 1.2288353252166497, 1.4651487457467567, 
1.923489755798345, 2.176508488054441, 1.694645696374919, 1.9175809148607657, 
1.9235829082442797, 1.1916906593746692, 1.5964686605549565, 1.4826858586013028, 
1.7478727289387643, 1.4708193285997058, 1.5703763624762388, 1.7289379014983703, 
1.7163077659354826, 1.4077294999672785, 1.4013593451719226, 1.498781254944431, 
2.0312815616917699, 1.6241936105016184, 1.7121155095076461, 1.5339596462850908, 
0.96096191195524583, 1.3251639644238276, 1.2933393626649456, 
1.2230015368710934, 1.4475134070864304, 1.9255604625253098, 2.149850460167495, 
1.6821523476843425, 1.9041204630158985, 1.912437687927786, 1.1859916104444701, 
1.5937318728281931, 1.4781521319820714, 1.7521131179146254, 1.4679239089353322, 
1.5588217373623734, 1.7125383337480458, 1.7148843750455181, 1.4053826168197043, 
1.4046762052004484, 1.5149556848551926, 2.0263178723170854, 1.6105039258750653, 
1.7266708210247268, 1.5209753098703434, 0.97223988705135533, 
1.3176520260820581, 1.2793915002001297, 1.2136500518196767, 1.4418036124658309, 
1.9131760720372721, 2.1462991006912135, 1.6843706095600917, 1.8921314378291993, 
1.9095501134296349, 1.1827364484650522, 1.5907582592831289, 1.4765623500974305, 
1.7349807995072621, 1.4623892896744632, 1.5522270642954032, 1.6883661030136985, 
1.7210486458721956, 1.4048054958896208, 1.4073160819805703, 1.5326367874944595, 
2.0163814985952229, 1.6065234431763993, 1.7319698952961886, 1.5156637289104176, 
0.98505261324084836, 1.3132135132234313, 1.2615349213248572, 
1.2047316067760405, 1.4380066908857403, 1.8976806124348655, 2.1510724641035082, 
1.6804911351739229, 1.8785997485182166, 1.892493825349995, 1.1828379241528735, 
1.5868909006858445, 1.4766155061514312, 1.7157816170285214, 1.4573798284199897, 
1.5455908785097248, 1.6728864316833687, 1.7191770633271646, 1.4032547065475296, 
1.4106666488937705, 1.5399895903469103, 2.0069958798576097, 1.6018436222909662, 
1.7412970765640088, 1.5158959703320081, 0.98711603566285844, 
1.316290979426247, 1.2481115173280504, 1.1928153749462285, 1.4397660381653217, 
1.8841760007338106, 2.1481748187893714, 1.6746346836522863, 1.8679962914763204, 
1.8843516512473881, 1.181423823958345, 1.5817399830717647, 1.4813117406681673, 
1.7098050947945558, 1.4493604512403306, 1.5352436357604722, 1.653840840775924, 
1.7189725078188531, 1.3949990072199363, 1.4161010103900218, 1.5477876619491067, 
1.9884090434440591, 1.5873798018935157, 1.7505072313799681, 1.5013404602352705, 
0.97676166135499576, 1.320122977018561, 1.2302456377749345, 1.1835710905762264, 
1.443431974635929, 1.882556047966953, 2.1402725576773665, 1.6711606555216163, 
1.8556691537702663, 1.8850565620921647, 1.1786869434908982, 1.5762039677923854, 
1.4819289623284182, 1.7010167394386158, 1.4440810095945389, 1.5319074141017768, 
1.6552924277945686, 1.721969464903303, 1.3933974290189792, 1.414546618532859, 
1.559557582160451, 1.9776724350308093, 1.5784325410567317, 1.7641524508321049, 
1.4856017586521582, 0.98164663070934111, 1.3290712370181654, 
1.2213793989558468, 1.1769387112966163, 1.4424268122865047, 1.8716213959680328, 
2.1284040037670704, 1.666774980901677, 1.8512968599401491, 1.8801475362041553, 
1.1889729827458573, 1.5680505749438651, 1.4920589259870116, 1.6758959334356724, 
1.4300180729174832, 1.5250798501171619, 1.6422594080124184, 1.7351128255382309, 
1.3924698758493048, 1.4121990328554372, 1.5689674824521997, 1.9721947981577008, 
1.5765968880054992, 1.7614564518179869, 1.4844101792447626, 0.99181683587985348, 
1.3361261085524423, 1.221698106653843, 1.1832666402614862, 1.4499311694480481, 
1.8688944628696029, 2.1211369018213975, 1.6790719746488618, 1.8524846637942598, 
1.8741654502378902, 1.1912154234566592, 1.5676907853546047, 1.4960517293657429, 
1.6712948624440453, 1.4239734758087335, 1.5210947915376394, 1.636084481408475, 
1.7410074424826216, 1.3864037387297032, 1.4139264129361517, 1.5732030697588786, 
1.9706174048422707, 1.5697275605730492, 1.7683872268382836, 1.4860705452949761, 
1.0040816540705879, 1.3546873308819194, 1.2141090680236284, 1.1903125939262871, 
1.4545358520790248, 1.8661441376611747, 2.1120110291339897, 1.6852390516333557, 
1.8400782559388522, 1.8625661262173372, 1.1917669432855476, 1.5616517973863706, 
1.4937852287300151, 1.6602467233132634, 1.4194904675859124, 1.5233742238286403, 
1.6295434797090442, 1.749421155587084, 1.3854018978260767, 1.415435592035214, 
1.5882879045104679, 1.9619462783337263, 1.5648745589009629, 1.7762114593047007, 
1.4784101565534935, 1.0123196648556387, 1.3805383617023335, 1.2101251949243172, 
1.1957681959145117, 1.4501912309395588, 1.8645832718443967, 2.1100916854108309, 
1.6845482411190615, 1.8258011906214193, 1.8579733819554085, 1.2011976379059872, 
1.5616319603397175, 1.5048881965945005, 1.6509904286375263, 1.4139868535721039, 
1.5185964558054885, 1.6204110156952636, 1.7611085846123307, 1.3904371514082767, 
1.4135967093734172, 1.5911532275516385, 1.955160644602068, 1.5610841459982407, 
1.7785253545915269, 1.4697840359265133, 1.0311906238724124, 1.4054953815916289, 
1.2076563551830046, 1.1985702569533954, 1.4387527535653906, 1.8554912418591931, 
2.1042389510503172, 1.6825243398730865, 1.8183630812484535, 1.8492646315487442, 
1.2034564813948163, 1.5458299187017486, 1.5076399017965629, 1.6353676591785555, 
1.4160726100142598, 1.5139822548679818, 1.6199948211240121, 1.7699958447374142, 
1.3896809870627287, 1.403015161316566, 1.6032751351949583, 1.9399439562038676, 
1.5566571177530013, 1.7784467887832769, 1.465395236655425, 1.0467472575941714, 
1.4230542249854481, 1.2124137572458216, 1.1971568943531141, 1.4385947049728531, 
1.8551788988697109, 2.1018860550190106, 1.6819691029820023, 1.8117842279993288, 
1.8520345006933177, 1.2046774570453596, 1.5391052810612209, 1.5216223426055391, 
1.6346396618813088, 1.4093005048340079, 1.5102602904423597, 1.6143626224911625, 
1.7834111134036241, 1.3817894368242281, 1.4086716305607543, 1.6014767752817374, 
1.9390390059407649, 1.5626308718601469, 1.7884725975831657, 1.4687603336445627, 
1.0682209760760009, 1.435330164866693, 1.2172953789098835, 1.1988877981986665, 
1.4399878733513141, 1.8448367367695477, 2.0920164292307102, 1.6793168544641721, 
1.8154419054191619, 1.8465651345273169, 1.2052028540433419, 1.5280292844106134, 
1.5278810657325632, 1.6380679338447619, 1.4139987161184639, 1.5094966725182131, 
1.6082258731236991, 1.7876490841337735, 1.3832365216920659, 1.4090996841205066, 
1.6064900186046218, 1.9416677197759491, 1.5599772046515776, 1.8004896048901933, 
1.4482264259795035, 1.0811118280942686, 1.4405353811189214, 1.2075017428715489, 
1.2042000421524657, 1.4302175212403438, 1.8434597705528855, 2.0725664778813084, 
1.6793061181334061, 1.8113405249816323, 1.8428174543414024, 1.2053389770186178, 
1.527588545296968, 1.5319886773758209, 1.6259771074006169, 1.4081664901892199, 
1.5135859094045891, 1.5990659289234797, 1.8009115441281947, 1.3786771164808751, 
1.4032376205371555, 1.6060758923486285, 1.9463001440183731, 1.5565091661868835, 
1.7975492752696731, 1.4564087851161747, 1.0982609638431551, 1.4628590248643503, 
1.1987909466031272, 1.2062019657919623, 1.4266998044747243, 1.8307869252288214, 
2.0542711083180616, 1.6742169571314531, 1.8017265418549799, 1.8410301047936701, 
1.2031720766937879, 1.5250575774040231, 1.5309966205025598, 1.6145067180937518, 
1.4019205725228705, 1.4969976876704116, 1.5894526814818177, 1.8129621342941675, 
1.3738556348075142, 1.3981234357511199, 1.6060595924783039, 1.9522271137153422, 
1.5580150583925039, 1.7959953423828636, 1.4629226303326552, 1.1082034257493047, 
1.4817868896047977, 1.1888067042554362, 1.200812661584673, 1.4252618113150706, 
1.8281096915113955, 2.0577942028057827, 1.6757541281514248, 1.7966561214123424, 
1.8331051907557527, 1.2035969625550573, 1.5202938764571647, 1.5333806278131741, 
1.6155414400627142, 1.3964604849008153, 1.4878770550295224, 1.5846013916133097, 
1.8091275811965646, 1.368601586596824, 1.4049849968867829, 1.6028770756625479, 
1.9568595379577658, 1.5523311889601028, 1.7946693125887085, 1.4529981628000594, 
1.109164511859362, 1.5018433690147397, 1.1826866172791031, 1.2014889721158921, 
1.4244266080184715, 1.8236831513327452, 2.0475925810184719, 1.6731295595199855, 
1.7954672755683474, 1.8352253327897623, 1.2029282779494046, 1.5235645960631639, 
1.5329522631308552, 1.6022018450038449, 1.4018760786265285, 1.4821412429113578, 
1.5857422094218641, 1.8096325407890728, 1.3604389905499732, 1.3994318501365051, 
1.6043120697877868, 1.9613319622001897, 1.5528585028914184, 1.7997792280554548, 
1.4510868075533152, 1.1041878334441857, 1.5158268228520202, 1.1771416366971559, 
1.2087454010181642, 1.4289007476704103, 1.8236915171523864, 2.0295897265768565, 
1.6655074625922912, 1.8038292589602607, 1.8262466515340721, 1.2024349128799658, 
1.523726015611611, 1.5416084065505629, 1.6101400518880653, 1.3992442685290998, 
1.4793525188358705, 1.5875313762303325, 1.8058876761903946, 1.3599498292043728, 
1.4004406735503068, 1.6132927491684668, 1.9651583258365528, 1.5474023354620625, 
1.794868621161303, 1.4610427323296618, 1.1059942551469601, 1.5312163264474175, 
1.1613219124541168, 1.2105290635112926, 1.4206022027562266, 1.8226047660194353, 
2.0150116564681544, 1.6673154983712397, 1.8157888766209993, 1.8207212360275997, 
1.2092909647530095, 1.5266046499812231, 1.5402184224077073, 1.6082083128307438, 
1.4008473512442505, 1.4785191740760557, 1.5895057498806373, 1.8062493953776193, 
1.3532526636920861, 1.3898490172088063, 1.6152266293528839, 1.9556502454345286, 
1.5444804707416255, 1.8009455297322641, 1.4662197415599521, 1.1076961416427011, 
1.5267767569133102, 1.1586027914180257, 1.2202052517412172, 1.4286308572293982, 
1.8135342310711873, 2.0074273315453643, 1.6631887193201063, 1.8181414474856132, 
1.8148091847493173, 1.2004803640202517, 1.5226540439513072, 1.5393930500612376, 
1.6102606256104341, 1.4007591678227345, 1.4776858407427227, 1.5926358443780757, 
1.8015276838412995, 1.3488430272954441, 1.3802070692390338, 1.6119480335481413, 
1.9551116420089683, 1.5417547493062769, 1.8087293424167981, 1.4622472104095323, 
1.1093694204658793, 1.5322538080333257, 1.1526395677196257, 1.2162018032940938, 
1.4315451568824886, 1.8069880319418223, 2.010368855855087, 1.6661429963273968, 
1.8219341517505196, 1.8101894199335757, 1.202264936365776, 1.519108394509173, 
1.5446939930986305, 1.6107973290186668, 1.4008919400085591, 1.472990813547695, 
1.6004083410867274, 1.7972662892516647, 1.3494098883027201, 1.3844667938834954, 
1.6168459553937617, 1.9533083921187617, 1.5450405157404177, 1.8138584511243736, 
1.466050051599842, 1.1234236361777046, 1.535939816112931, 1.1571523622104447, 
1.2136059605043321, 1.4301302729171861, 1.8071669239332009, 2.0100724773567396, 
1.6651124025489961, 1.8222479130666023, 1.80854167005963, 1.2030009101019119, 
1.5189013486185834, 1.5435117199831039, 1.609857465937605, 1.3983397132688675, 
1.4659432793825118, 1.5987895149383915, 1.7888810861898696, 1.3506588143420812, 
1.385012631683052, 1.6192537451200117, 1.9526364553598683, 1.5417899196531277, 
1.8190710325487884, 1.4695567248617478, 1.1266450739639966, 1.5424085027037633, 
1.1517604851108612, 1.2108055467521524, 1.4401831323386349, 1.7994613899004419, 
2.0101279637422769, 1.6624070205118386, 1.8254047887868796, 1.8020502118111161, 
1.2044495735347527, 1.522080293295065, 1.5435437993775922, 1.6160336067114907, 
1.4053639038580152, 1.4610193661420214, 1.6027666236708398, 1.7694895135224924, 
1.3454719951520804, 1.3836646768347982, 1.6179289418807346, 1.9513549446000966, 
1.5466573446556291, 1.8192113672486221, 1.453377861945288, 1.127362223456897, 
1.5517581106150879, 1.1551951027801806, 1.2046741917876396, 1.4405607396322122, 
1.7958554241773961, 2.01083588963421, 1.6577680756779143, 1.8290632586769244, 
1.8043108774533156, 1.2066583528469845, 1.5224473142263752, 1.5491550199148076, 
1.6238701736333532, 1.4069594487766888, 1.4585143156369704, 1.612461092745312, 
1.7583345685283576, 1.3443756375497316, 1.3849601088565482, 1.6220232783932855, 
1.9506830078412027, 1.5553690929176864, 1.8218090737983801, 1.4429521904075981, 
1.1327062592891952, 1.553099018709809, 1.1605577365068762, 1.1999086828988748, 
1.4436842621990325, 1.7805894664681594, 2.0104506376745372, 1.6556118534204696, 
1.8253581406954913, 1.8064639509174598, 1.2071777239684269, 1.5262302805895138, 
1.5469127519706907, 1.6285979150033538, 1.4042054893172093, 1.4589175611672196, 
1.6115644970335723, 1.7518479621604832, 1.3438617278012628, 1.3852966458992964, 
1.6208960848725997, 1.9481679627790636, 1.5599424328157132, 1.8250493243028649, 
1.4386170396824944, 1.1316722652061004, 1.5593839729834909, 1.1566453898697009, 
1.1933960671256785, 1.4456993188807392, 1.780701883042997, 2.0099971201293685, 
1.6586672966119433, 1.8160798365011241, 1.8016919804839351, 1.2124127675911862, 
1.5263772466010466, 1.5430712338237034, 1.6282599778405782, 1.4088045699259977, 
1.4592458439955027, 1.6201221989120169, 1.7259407073873099, 1.3409315433952382, 
1.3839067016318662, 1.6214892845128059, 1.946364712888857, 1.5642787291711098, 
1.8224089976485365, 1.4364656451558349, 1.1482140817520015, 1.5613758244263634, 
1.1566665574763773, 1.189326723731601, 1.449234266466809, 1.7663566464050642, 
2.0118882678984265, 1.6512739844292883, 1.8151338849251224, 1.7987967032359764, 
1.2077162323368078, 1.5274074267190039, 1.5369747868268371, 1.6332461989107516, 
1.4128420526601386, 1.4608519046015636, 1.6203315224290704, 1.7166720898662817, 
1.3390099634907564, 1.3850697314424469, 1.6247902842504813, 1.9445614629986505, 
1.5659428484761162, 1.8268011170574534, 1.4317738241972209, 1.1538711462843136, 
1.5714994815208345, 1.160139046458299, 1.1913769404169161, 1.4459323204691228, 
1.7716855831558065, 2.013789126500269, 1.6552970431047032, 1.8220770150674943, 
1.8037142924988709, 1.2149950256646525, 1.5250569370115779, 1.5399759030095352, 
1.6372497391987144, 1.4143265863317511, 1.4621801874298463, 1.6180269781435419, 
1.7072269249388021, 1.3423361797300255, 1.3848497926183234, 1.6320638908726175, 
1.9438895262397571, 1.5743604379600182, 1.8323368575227392, 1.4417491563686093, 
1.1618241852335578, 1.5657585077918807, 1.1590159270940037, 1.1921710934175249, 
1.4403873225656549, 1.7717193797753066, 2.0100271453645915, 1.6485397909112176, 
1.8314737541429511, 1.7976342585144935, 1.2164335807685258, 1.5309979075304845, 
1.5310251460204582, 1.631674295851502, 1.4125238182574809, 1.4627862480359071, 
1.6272480661081625, 1.7084536722598429, 1.341771859146397, 1.3908767069464552, 
1.6347946609582997, 1.9420862763495506, 1.5751811662653827, 1.8309771157547425, 
1.4364225570420117, 1.1577839532919012, 1.5813028056609506, 1.159097179203104, 
1.1863668923527824, 1.4445185576519843, 1.7625236553568047, 2.0173495555673462, 
1.6428087106318607, 1.8294569491814867, 1.7913985158970966, 1.2162776347544417, 
1.5337442786920525, 1.5250979249699239, 1.6333673482411488, 1.4210028569726874, 
1.462783722783382, 1.6316482590312145, 1.6999519965698939, 1.3408953897585805, 
1.3961144154372249, 1.6335224602831573, 1.9402830264593443, 1.5746203951841382, 
1.8280947724036489, 1.4377760827980464, 1.1682393160858049, 1.5836070353123313, 
1.1560818142083253, 1.1884083237519134, 1.4394866015847148, 1.7574567625029318, 
2.0142599966333607, 1.641670948988645, 1.8376488595145151, 1.7897328223212079, 
1.22085087668631, 1.5311743499527626, 1.5254713696814903, 1.633682656910038, 
1.4177552107482878, 1.4614503894500488, 1.6303612943534658, 1.7000927190785295, 
1.3418348164206397, 1.3951380238461284, 1.630120981142023, 1.9396110897004504, 
1.5691310115980659, 1.8261134938782526, 1.4350575321146539, 1.1707025265675821, 
1.5903558869388588, 1.1587407940261591, 1.1949908115895342, 1.4344585461250314, 
1.7357876932213301, 2.0141822073100446, 1.6422141995618798, 1.8358538163041773, 
1.7920333204706487, 1.2246603191878869, 1.5360897922623911, 1.5234926200865024, 
1.6317414349285277, 1.4173596625205149, 1.4617837227833816, 1.6287233574127751, 
1.7059632361552752, 1.3401943044591835, 1.3912997295375382, 1.627909204934936, 
1.9394608920719918, 1.5757923213028537, 1.8246153325229726, 1.435143594791159, 
1.1760350585555048, 1.5951980986664094, 1.1704974977621547, 1.1930426289348286, 
1.4336297113045851, 1.7328528376475949, 2.0135628999399668, 1.6403237628014546, 
1.8343571905031864, 1.7897005989037231, 1.2274624914316878, 1.5369758703076815, 
1.5213802588775036, 1.6402412655243439, 1.4190044399460031, 1.4604503894500487, 
1.631867254916167, 1.7057634913470177, 1.3413456308642613, 1.3918654331005293, 
1.6293912424345995, 1.9376576421817853, 1.5759386749492077, 1.8254984080210936, 
1.4282934996700263, 1.187803061358125, 1.5859773970938218, 1.1676977483340041, 
1.1900664384586366, 1.4296315775371906, 1.7296925204973708, 2.0047969234621195, 
1.6257448187886183, 1.8318427523435046, 1.7902651010052215, 1.2276854483862691, 
1.5342394032747404, 1.5232927845734932, 1.6495239719012649, 1.4221853224354506, 
1.4603329652076242, 1.6311854483748447, 1.6992004965563521, 1.3416558876254947, 
1.400605032701667, 1.6273617885570184, 1.9372544801264491, 1.5759731404836737, 
1.8227316604588912, 1.4247226146986174, 1.1936665206637918, 1.5857201513383765, 
1.1770546276346248, 1.1870902479824448, 1.4182954810939503, 1.7215601361434518, 
2.0057172902863352, 1.6248113141483955, 1.8276637438027177, 1.7863099133886355, 
1.231045219664012, 1.5377236237849876, 1.525997191734241, 1.6539175528440415, 
1.4261623647730499, 1.4603329652076242, 1.6302508574385939, 1.6974167905955839, 
1.3427529680988746, 1.398729618484585, 1.6288980578608758, 1.9372544801264491, 
1.5756579556684893, 1.8159036709604472, 1.4289068815087385, 1.2021895985700752, 
1.5856815644750601, 1.1811321918396622, 1.1841140575062528, 1.4139077981769805, 
1.7157928549774937, 2.0001570043661121, 1.6247227189971185, 1.8285424097170484, 
1.7876167078495062, 1.2311390924985957, 1.5416983275141209, 1.5184950145985638, 
1.6526709857283197, 1.4312832825358657, 1.4603329652076242, 1.630549943391209, 
1.694014870394901, 1.3409293439261127, 1.3977939512696611, 1.6312219589597772, 
1.9372544801264491, 1.5756924212029551, 1.8163059419854497, 1.4330527955853207, 
1.2062422593791504, 1.5858616365038714, 1.1806344446746102, 1.1811378670300607, 
1.4218812110729941, 1.7141716039560528, 1.9909243507490928, 1.6143647283923308, 
1.8317349893090282, 1.7865381637595428, 1.2367140331082829, 1.5357703665062237, 
1.5209611030209642, 1.6582630209887408, 1.4359191914803395, 1.4603329652076242, 
1.6336543143428983, 1.6849274519630111, 1.3368904846816207, 1.396995761268865, 
1.6336619112298154, 1.9372544801264491, 1.5758387748493092, 1.8130178749565742, 
1.4362410544808961, 1.2158510878815196, 1.5853857318562983, 1.1842274461999029, 
1.1781616765538689, 1.417706164577839, 1.7209045657647219, 1.9876859342188375, 
1.6140197919075527, 1.8203003214274036, 1.7728293746201549, 1.2325079391191145, 
1.5442587410389723, 1.5198454485591766, 1.6570226681442664, 1.441040109243156, 
1.4603329652076242, 1.6355294368461337, 1.6803401420439734, 1.3338806361823292, 
1.396995761268865, 1.6344134396760486, 1.9372544801264491, 1.575873240383775, 
1.8089379587534962, 1.4363654341662497, 1.2120681713568093, 1.5857844627772379, 
1.1771511668771106, 1.1751854860776769, 1.4216078665682441, 1.7132843773244215, 
1.9826405070423305, 1.6116651014483607, 1.8186989501876565, 1.7720663066651694, 
1.2381991955094496, 1.5366166110175714, 1.5170706823075197, 1.6611397316837819, 
1.44567601818763, 1.4603329652076242, 1.6336366099459809, 1.6742209619862487, 
1.3280637592850124, 1.396995761268865, 1.6372021315723873, 1.9372544801264491, 
1.5759077059182411, 1.8077814063789892, 1.4372290705298842, 1.2240759768406764, 
1.5861831936981778, 1.1731751152013121, 1.1736673445509429, 1.4291826706486117, 
1.7135812873116854, 1.9774953084731643, 1.612658268325776, 1.8207569648508592, 
1.7700835348720665, 1.2363197240534458, 1.5357611757299283, 1.5135854776012001, 
1.6605158372970301, 1.4512819447687884, 1.4603329652076242, 1.6302203772700379, 
1.6784415623478726, 1.3287366213197456, 1.396995761268865, 1.6375668972415012, 
1.9372544801264491, 1.5755925211030566, 1.7980568476052115, 1.4383432195387678, 
1.2215531026539661, 1.5850513123742194, 1.1752536000805882, 1.1736673445509425, 
1.445730363083231, 1.7134570395229305, 1.9596901837145455, 1.6139043652319955, 
1.8143991303256908, 1.768546755479786, 1.2444501194677959, 1.5436120232713872, 
1.5125433073884891, 1.6568062075981105, 1.4564028625316041, 1.4603329652076242, 
1.63269633845277, 1.6747856871849769, 1.3267675172119791, 1.396995761268865, 
1.6369157397033871, 1.9372544801264491, 1.5760885250990608, 1.7942836401034903, 
1.4420278006113738, 1.2219074980313067, 1.5858873610794155, 1.1772959830802479, 
1.1736673445509422, 1.4580700581582831, 1.7036841329819141, 1.9613481787106495, 
1.6202521999393091, 1.8133944143317113, 1.7699732264319432, 1.2419663379320318, 
1.5444766921599782, 1.5035924574928261, 1.6588360537924502, 1.4620087891127624, 
1.4603329652076242, 1.6333093097951537, 1.6802835964958864, 1.3319093791815144, 
1.396995761268865, 1.6387415100115104, 1.9372544801264491, 1.5756414721520082, 
1.7955601357845514, 1.4379864607818256, 1.2288075295799163, 1.5855985201719316, 
1.171278569010946, 1.1746763716425102, 1.4565349745222231, 1.6985354104395352, 
1.9579493087435944, 1.6258525378515802, 1.8089946360227815, 1.7710802565548105, 
1.256336299559659, 1.5394030068975035, 1.4980981707569219, 1.6565029935151041, 
1.4671297068755789, 1.4603329652076242, 1.632429973445229, 1.6801695350914534, 
1.3266993555741691, 1.396995761268865, 1.6362413232701474, 1.9372544801264491, 
1.5739393686999048, 1.7885724052768892, 1.4443295612004512, 1.2278474291880557, 
1.6010601188770228, 1.1749194762781585, 1.1703868723847124, 1.461296311938219, 
1.6945936251509477, 1.9617190206768, 1.6215984853901424, 1.8051484821766277, 
1.7724791750682343, 1.2518017547795908, 1.544696467919823, 1.4974378080184176, 
1.6580669362622968, 1.4722506246383946, 1.4603329652076242, 1.6334839704286384, 
1.6826958055249528, 1.3308908438480753, 1.396995761268865, 1.6374095462236635, 
1.9372544801264491, 1.5743256634396472, 1.7765453690703743, 1.4504759091165205, 
1.2400953744410725, 1.604702953037735, 1.1841396616451041, 1.1710432595698614, 
1.4636724265911616, 1.6913373098975302, 1.9623382793737869, 1.6250644133410719, 
1.8000972001253457, 1.7722829346950415, 1.2570135747519682, 1.5374448935238292, 
1.4939536887909119, 1.6552219585800605, 1.477371542401211, 1.4603329652076242, 
1.6322969417710218, 1.6789214125108083, 1.3296837302638014, 1.396995761268865, 
1.6400040520973185, 1.9372544801264491, 1.5735581120255437, 1.7566296965076427, 
1.4507496728998426, 1.2475568547596951, 1.6106850761082996, 1.1800268472339119, 
1.1831893913361471, 1.4666433292643128, 1.6852387248456768, 1.9577264239711818, 
1.6230500610491427, 1.8002776783329146, 1.7720397870380995, 1.256209807426554, 
1.5440002460137165, 1.4875487615675131, 1.6559909502169234, 1.481217513538204, 
1.4603329652076242, 1.632750938754431, 1.6815757589268683, 1.3251541104193012, 
1.396995761268865, 1.6403485547494432, 1.9372544801264491, 1.5739444067652864, 
1.7637389718201304, 1.4503454917151744, 1.2568892177134636, 1.6201195569713516, 
1.1843559561948664, 1.184371884249712, 1.4620060386063247, 1.6782073484990876, 
1.9656618854899002, 1.6245599522133711, 1.8043674219226582, 1.7724376650221834, 
1.2565279751788858, 1.5492277149019109, 1.4873098893642089, 1.652553233922085, 
1.4874848157807379, 1.4603329652076242, 1.6339639100968144, 1.6775234414203586, 
1.3200569502331123, 1.396995761268865, 1.6396115347053135, 1.9372544801264491, 
1.5743307015050287, 1.7638653818908432, 1.4503454917151744, 1.2565513016520571, 
1.6274278421805473, 1.181553468227849, 1.1809537579886049, 1.4645723847840086, 
1.6746837423671563, 1.9612117704515524, 1.630177853778676, 1.8090981911534276, 
1.7705035364375783, 1.2553933908122126, 1.5479279279854563, 1.4790054140771305, 
1.6528363858381885, 1.4902572273694548, 1.4603329652076242, 1.6295693854945206, 
1.6789340919969895, 1.3162153340710676, 1.396995761268865, 1.6456187098830768, 
1.9372544801264491, 1.5745180572527291, 1.7645840222372406, 1.4503454917151744, 
1.2637347049305379, 1.637756580964626, 1.1788610492749796, 1.1820135285880011, 
1.4668242354989569, 1.6736136100846963, 1.9600141728052751, 1.6325142910372008, 
1.8132648578200943, 1.7694161879455095, 1.2588215870706769, 1.5457305250414917, 
1.4704766986802231, 1.6443350191919188, 1.4931641803723936, 1.4603329652076242, 
1.6295693854945206, 1.6797836540003199, 1.3217736113759422, 1.396995761268865, 
1.6559782336926003, 1.9372544801264491, 1.5737505058386256, 1.7586817786474975, 
1.4503454917151744, 1.263857031550951, 1.6405939746376674, 1.1793014177496075, 
1.1852599710785563, 1.4629109743964543, 1.6597775856153636, 1.9561682635978139, 
1.6342040257320067, 1.8179956270508635, 1.7679668069547334, 1.2573623133976106, 
1.5445285923299241, 1.4719609547568027, 1.6414985299566429, 1.4931641803723936, 
1.4603329652076242, 1.6295693854945206, 1.682818164086666, 1.3190562973480817, 
1.396995761268865, 1.672474387538754, 1.9372544801264491, 1.5739378615863258, 
1.7629917384018454, 1.4503454917151744, 1.2573384697916088, 1.6479423570341269, 
1.1815397135457901, 1.1822992673987105, 1.4693441184119371, 1.6580034166943289, 
1.9538257388989686, 1.6356436953447342, 1.8206411502317923, 1.7668757667629507, 
1.2549337007127563, 1.5522851363764005, 1.4649228683308464, 1.6391471464781375, 
1.4931641803723936, 1.4603329652076242, 1.6295693854945206, 1.6801359263221585, 
1.3159499498837899, 1.396995761268865, 1.6845659626303291, 1.9372544801264491, 
1.5741252173340261, 1.7474320533732248, 1.4503454917151744, 1.2576640966099275, 
1.6469189447540393, 1.1904719334122733, 1.1816896060862534, 1.463404886608799, 
1.6460402075171559, 1.9562569656021411, 1.6316081499904074, 1.8210485429375629, 
1.7630388257914653, 1.2644922190697343, 1.5515553855459674, 1.464132785408675, 
1.6351517809659448, 1.4931641803723936, 1.4603329652076242, 1.6295693854945206, 
1.6802376574283551, 1.3133353219856561, 1.396995761268865, 1.6960613838757501, 
1.9372544801264491, 1.5745115120737685, 1.7437527902711312, 1.4503454917151744, 
1.26058629588787, 1.6623720507857358, 1.1913491469040942, 1.1752787914458864, 
1.4673294391710376, 1.640380343140043, 1.9542636646447396, 1.6261365840693516, 
1.8271601243045577, 1.760286116732896, 1.2694965434650243, 1.5644846983506637, 
1.4640556391985986, 1.6372883285642841, 1.4931641803723936, 1.4603329652076242, 
1.6295693854945206, 1.6755548922768404, 1.311638002445682, 1.396995761268865, 
1.6992802483446143, 1.9372544801264491, 1.5735450216676226, 1.7414847810661114, 
1.4503454917151744, 1.2730936778025517, 1.6571411606051949, 1.1909695536681457, 
1.1728722298540135, 1.4638552313965574, 1.6285488470415275, 1.9499603437166473, 
1.6288934619086881, 1.8279038337244451, 1.756118245130813, 1.2726958432676758, 
1.5701078928070109, 1.4689579309793943, 1.6381643271857729, 1.4931641803723936, 
1.4603329652076242, 1.6295693854945206, 1.6730594592950356, 1.3094510358064286, 
1.396995761268865, 1.6994467300999974, 1.9372544801264491, 1.5743918472558274, 
1.7401885979789891, 1.4503454917151744, 1.2746735038848946, 1.6528150006540361, 
1.1863580228905588, 1.1758010760371727, 1.4661764273287325, 1.6300763511284757, 
1.9516010736496801, 1.6275660405342891, 1.8306592291453563, 1.7511948790232359, 
1.2720347333940547, 1.5727629280701272, 1.4641853580775799, 1.6367999029282325, 
1.4931641803723936, 1.4603329652076242, 1.6295693854945206, 1.6720305497203114, 
1.3030144684605318, 1.396995761268865, 1.6968800034325264, 1.9372544801264491, 
1.5743918472558274, 1.73651651027967, 1.4503454917151744, 1.2690655092114058, 
1.6514817181957535, 1.1875116201771951, 1.1787584426397359, 1.4705209662548597, 
1.6285766780305533, 1.9490563488832249, 1.6151705600787349, 1.8344639190368228, 
1.7470270074211531, 1.2767613860455216, 1.5823696861245258, 1.4720899064801136, 
1.6394406107458908, 1.4931641803723936, 1.4603329652076242, 1.6295693854945206, 
1.6682474035775818, 1.3025426701317826, 1.396995761268865, 1.6955213600728751, 
1.9372544801264491, 1.5743918472558274, 1.7330362577804015, 1.4503454917151744, 
1.2612791272014214, 1.6513443555583909, 1.1921238649860497, 1.1767584847595913, 
1.469071675448649, 1.6255443164204233, 1.950889891174745, 1.6177556456565323, 
1.8242494648436112, 1.7428591358190704, 1.2782403361423349, 1.5812521776415662, 
1.4646971077273661, 1.63808197485855, 1.4931641803723936, 1.4603329652076242, 
1.6295693854945206, 1.6603915940660088, 1.3004591758628543, 1.396995761268865, 
1.6948691798762185, 1.9372544801264491, 1.5743918472558274, 1.7299045690134691, 
1.4503454917151744, 1.2598879989507648, 1.6514817181957528, 1.1929099633483398, 
1.1789592557843755, 1.4761513235856816, 1.6276322898187954, 1.9496332047410776, 
1.616116521144972, 1.8279940621854098, 1.7386912642169878, 1.2822157061532025, 
1.588624451568347, 1.4605272837484264, 1.638511582348412, 1.4931641803723936, 
1.4603329652076242, 1.6295693854945206, 1.6623520740850151, 1.2985826766237474, 
1.396995761268865, 1.6955806560811735, 1.9372544801264491, 1.5743918472558274, 
1.7355771550907939, 1.4503454917151744, 1.255004627193897, 1.65134435555839, 
1.1951762967100694, 1.1804473510224704, 1.4760737338044212, 1.6243792210894961, 
1.940663516705198, 1.6208480163765322, 1.8257981521555959, 1.735971615444708, 
1.2820772513190954, 1.5923551572224539, 1.4578757457328069, 1.639404244578015, 
1.4931641803723936, 1.4603329652076242, 1.6295693854945206, 1.6624546810087431, 
1.2958956934637684, 1.396995761268865, 1.6916964050119454, 1.9372544801264491, 
1.5743918472558274, 1.7323351932618858, 1.4503454917151744, 1.2583118891791516, 
1.6514817181957524, 1.1882699097078779, 1.1819354462605656, 1.4713625840551803, 
1.6257002183218408, 1.9441464681096337, 1.6216754267743627, 1.827561545301619, 
1.7417454585391048, 1.2880841939225187, 1.6116368279020146, 1.448242519639191, 
1.6401849281421066, 1.4931641803723936, 1.4603329652076242, 1.6295693854945206, 
1.6626034905325522, 1.2937903774815571, 1.396995761268865, 1.6893712952031352, 
1.9372544801264491, 1.5743918472558274, 1.7299995920924056, 1.4503454917151744, 
1.2601165110278922, 1.6513443555583893, 1.1894057267087343, 1.1834235414986605, 
1.4747535083918191, 1.6209552104060283, 1.9332816579892755, 1.6260987893478973, 
1.8274306666937472, 1.740798975224203, 1.3057416872037924, 1.6123091960090554, 
1.4459486348555755, 1.6405205377506573, 1.4931641803723936, 1.4603329652076242, 
1.6295693854945206, 1.6624546810087431, 1.2976921375398363, 1.396995761268865, 
1.6929706118595762, 1.9372544801264491, 1.5743918472558274, 1.7290003346789455, 
1.4503454917151744, 1.2619211328766329, 1.6514817181957517, 1.1920190321774888, 
1.1849116367367556, 1.4740065959904969, 1.6178121448277849, 1.9276121952947523, 
1.6233203508926528, 1.8327493936340957, 1.7411185838368783, 1.3104285058093768, 
1.6168445765157122, 1.4438092734512702, 1.6440570004696733, 1.4931641803723936, 
1.4603329652076242, 1.6295693854945206, 1.6626034905325522, 1.3045103333015082, 
1.396995761268865, 1.6929625033782352, 1.9372544801264491, 1.5743918472558274, 
1.7260520731878721, 1.4503454917151744, 1.2637257547253735, 1.6513443555583887, 
1.1883733624634991, 1.1863997319748505, 1.4764286827980524, 1.6186181192133293, 
1.9280009028411622, 1.6273160246900988, 1.834451757711534, 1.7470392021149754, 
1.3186632230372306, 1.6204466242936837, 1.445388162688414, 1.6440869291267266, 
1.4931641803723936, 1.4603329652076242, 1.6295693854945206, 1.6624546810087431, 
1.3061920384979004, 1.396995761268865, 1.6785669277120703, 1.9372544801264491, 
1.5743918472558274, 1.7250666697024684, 1.4503454917151744, 1.2655303765741142
), .Dim = c(25L, 100L), .Dimnames = list(c("1", "2", "3", "4", 
"5", "6", "7", "8", "9", "10", "11", "12", "13", "14", "15", 
"16", "17", "18", "19", "20", "21", "22", "23", "24", "25"), 
    c("10", "20", "30", "40", "50", "60", "70", "80", "90", "100", 
    "110", "120", "130", "140", "150", "160", "170", "180", "190", 
    "200", "210", "220", "230", "240", "250", "260", "270", "280", 
    "290", "300", "310", "320", "330", "340", "350", "360", "370", 
    "380", "390", "400", "410", "420", "430", "440", "450", "460", 
    "470", "480", "490", "500", "510", "520", "530", "540", "550", 
    "560", "570", "580", "590", "600", "610", "620", "630", "640", 
    "650", "660", "670", "680", "690", "700", "710", "720", "730", 
    "740", "750", "760", "770", "780", "790", "800", "810", "820", 
    "830", "840", "850", "860", "870", "880", "890", "900", "910", 
    "920", "930", "940", "950", "960", "970", "980", "990", "1000"
    )), risk = "Quantile Regression", call = "mboost(formula = fm, data = bodyfat, family = QuantReg(tau = 0.5))", mstop = c(10, 
20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 
160, 170, 180, 190, 200, 210, 220, 230, 240, 250, 260, 270, 280, 
290, 300, 310, 320, 330, 340, 350, 360, 370, 380, 390, 400, 410, 
420, 430, 440, 450, 460, 470, 480, 490, 500, 510, 520, 530, 540, 
550, 560, 570, 580, 590, 600, 610, 620, 630, 640, 650, 660, 670, 
680, 690, 700, 710, 720, 730, 740, 750, 760, 770, 780, 790, 800, 
810, 820, 830, 840, 850, 860, 870, 880, 890, 900, 910, 920, 930, 
940, 950, 960, 970, 980, 990, 1000), type = "25-fold bootstrap", class = "cvrisk")


###################################################
### code chunk number 2: setup
###################################################
### make sure package mboost is available
if (!require("mboost"))
    install.packages("mboost", dependencies = TRUE)
library("mboost")
### package partykit is necessary for fitting trees
if (!require("partykit"))
    install.packages("partykit", dependencies = TRUE)
library("partykit")
### speed up things a little bit: if the model is already


###################################################
### code chunk number 3: mboost-bodyfat-setup
###################################################
### set-up model formula
### names of features
data("bodyfat", package = "TH.data")
features <- names(bodyfat)[-2]
### set up model structure:
fml <- paste("bols(", features, ")", collapse = " + ") ### linear functions
fms <- paste("bbs(", features, ", center = TRUE, df = 1)",
             collapse = " + ")  ### smooth deviations from linearity
fmt <- "btree(hipcirc, waistcirc, tree_controls = ctree_control(maxdepth = 2, mincriterion = 0))" ### tree-based interaction
fm <- as.formula(paste("DEXfat", paste(fml, fms, fmt, sep = "+"), sep = "~"))


###################################################
### code chunk number 4: mboost-fm
###################################################
library("mboost")               ### attach package `mboost'
print(fm)                       ### model structure


###################################################
### code chunk number 5: mboost-bodyfat
###################################################
### fit model for conditional median of DEXfat
model <- mboost(fm,                           ### model structure
                data = bodyfat,               ### 71 observations
                family = QuantReg(tau = 0.5)) ### median regression


###################################################
### code chunk number 6: mboost-mstop
###################################################
model[1000]                     ### 900 more iterations


###################################################
### code chunk number 7: mboost-cvrisk (eval = FALSE)
###################################################
## ### bootstrap for assessing the `optimal' number of boosting iterations
## cvm <- cvrisk(model, grid = 1:100 * 10)
## model[mstop(cvm)]               ### restrict model to optimal mstop(cvm) iterations


###################################################
### code chunk number 8: mboost-cvrisk-stored
###################################################
model[mstop(cvm)]


###################################################
### code chunk number 9: bodyfat-plot (eval = FALSE)
###################################################
## plot(cvm); plot(model)          ### depict out-of bag risk & selected components


###################################################
### code chunk number 10: mboost-bodyfat-plot-1
###################################################
### plot age and kneebreadth
cex <- 1.3
layout(matrix(c(1, 2, 1, 3), nr = 2))
par(mai = par("mai") * c(0.8, 1.1, 0.8, 0.8))
plot(cvm, cex.lab = cex)
mtext(text = "(A)", side = 3, 1, adj = 1)
plot(model, which = "bols(anthro3b", cex.lab = cex)
mtext(text = "(B)", side = 3, 1, adj = 1)
plot(model, which = "bbs(anthro3b",
     ylim = range(predict(model, which = "bols(anthro3b")),
     cex.lab = cex)
mtext(text = "(C)", side = 3, 1, adj = 1)


###################################################
### code chunk number 11: mboost-bodyfat-plot-2
###################################################
### plot interaction of hip and waist circumference
### first setup grid of hip and waist values
nd <- with(bodyfat,
           expand.grid(hipcirc = h <- seq(from = min(hipcirc),
                                          to = max(hipcirc),
                                          length = 100),
                  waistcirc = w <- seq(from = min(waistcirc),
                                       to = max(waistcirc),
                                       length = 100)))
### define colors for plot
col <-
c("#023FA5", "#1141A4", "#1A44A4", "#2146A4", "#2749A4", "#2C4BA4",
"#304DA4", "#3550A5", "#3852A5", "#3C54A6", "#4056A6", "#4359A7",
"#465BA7", "#495DA8", "#4C5FA9", "#4F61AA", "#5264AA", "#5566AB",
"#5868AC", "#5B6AAD", "#5D6CAE", "#606EAE", "#6270AF", "#6572B0",
"#6775B1", "#6A77B2", "#6C79B3", "#6F7BB4", "#717DB5", "#747FB6",
"#7681B6", "#7883B7", "#7B85B8", "#7D87B9", "#7F89BA", "#828BBB",
"#848DBC", "#868FBD", "#8891BE", "#8A93BE", "#8D94BF", "#8F96C0",
"#9198C1", "#939AC2", "#959CC3", "#979EC4", "#99A0C4", "#9BA1C5",
"#9DA3C6", "#9FA5C7", "#A1A7C8", "#A3A8C9", "#A5AAC9", "#A7ACCA",
"#A9AECB", "#ABAFCC", "#ACB1CC", "#AEB3CD", "#B0B4CE", "#B2B6CF",
"#B4B8CF", "#B5B9D0", "#B7BBD1", "#B9BCD2", "#BABED2", "#BCBFD3",
"#BEC1D4", "#BFC2D4", "#C1C4D5", "#C3C5D6", "#C4C7D6", "#C6C8D7",
"#C7C9D7", "#C9CBD8", "#CACCD9", "#CBCDD9", "#CDCFDA", "#CED0DA",
"#CFD1DB", "#D1D2DB", "#D2D3DC", "#D3D4DC", "#D4D6DD", "#D6D7DD",
"#D7D8DE", "#D8D9DE", "#D9DADF", "#DADBDF", "#DBDCDF", "#DCDCE0",
"#DDDDE0", "#DEDEE0", "#DEDFE1", "#DFDFE1", "#E0E0E1", "#E1E1E2",
"#E1E1E2", "#E2E2E2", "#E2E2E2", "#E2E2E2", "#E2E2E2", "#E2E2E2",
"#E2E2E2", "#E2E1E1", "#E2E0E1", "#E2E0E0", "#E1DFDF", "#E1DEDF",
"#E1DDDE", "#E1DCDD", "#E0DBDC", "#E0DADB", "#E0D9DA", "#DFD8D9",
"#DFD7D8", "#DFD6D7", "#DED5D6", "#DED3D5", "#DDD2D4", "#DDD1D3",
"#DDCFD2", "#DCCED0", "#DCCDCF", "#DBCBCE", "#DBCACD", "#DAC8CB",
"#DAC7CA", "#D9C5C8", "#D9C4C7", "#D8C2C6", "#D8C0C4", "#D7BFC3",
"#D7BDC1", "#D6BBC0", "#D5B9BE", "#D5B8BD", "#D4B6BB", "#D3B4B9",
"#D3B2B8", "#D2B0B6", "#D1AEB4", "#D1ADB3", "#D0ABB1", "#CFA9AF",
"#CEA7AE", "#CEA5AC", "#CDA3AA", "#CCA1A8", "#CB9FA7", "#CB9CA5",
"#CA9AA3", "#C998A1", "#C8969F", "#C7949D", "#C6929C", "#C5909A",
"#C48D98", "#C38B96", "#C38994", "#C28792", "#C18490", "#C0828E",
"#BF808C", "#BE7D8A", "#BD7B88", "#BB7986", "#BA7684", "#B97482",
"#B87180", "#B76F7E", "#B66C7C", "#B56A7A", "#B46777", "#B26575",
"#B16273", "#B05F71", "#AF5D6F", "#AE5A6D", "#AC576B", "#AB5569",
"#AA5266", "#A84F64", "#A74C62", "#A64960", "#A4475E", "#A3445B",
"#A24159", "#A03D57", "#9F3A55", "#9D3752", "#9C3450", "#9A304E",
"#992C4C", "#982949", "#962447", "#942045", "#931B42", "#911640",
"#900F3E", "#8E063B")
### use plot method to draw fitted values of the tree component only
print(plot(model, which = "btree", newdata = nd, col.regions = col,
     at = seq(from = -16, to = 16, length = 100)))


###################################################
### code chunk number 12: mboost-predict
###################################################
### new data on a grid on range(anthro3b)
nd <- with(bodyfat, data.frame(anthro3b = seq(min(anthro3b), max(anthro3b),
                                              length = 100)))
### predictions for all base-learners of `anthro3b'
pr <- predict(model, which = "anthro3b", newdata = nd)
pr <- rowSums(pr)    ### aggregate linear and smooth effect


###################################################
### code chunk number 13: mboost-anthro3b
###################################################
plot(nd$anthro3b, pr, type = "l", xlab = "anthro3b",
     ylab = "f(anthro3b)")
lines(nd$anthro3b, predict(model, which = "bols(anthro3b", newdata = nd),
      type = "l", lty = "dashed")