r – recursively split a dataframe with partykit::lmtree as a stump tree

I am trying to recursively split my data using a stump tree based on the lmtree function from the partykitlibrary. The idea is the following:

  • [1] for each variable of interest run and lmtree with a depth of 2, store the regression model’s results and splitting rules.
  • [2] for each subset of data created from the rule-splits run [1]
  • [3] …keep on going until there is nothing to split
  • [4] return all the rules generated and all the regression models at every iteration.

I have created the following data set as an example

dataCheck<-structure(list(Y = c(8.25182880801735, 4.38905581711409, 4.3723003426479, 
8.95352964997245, 3.11700618762515, 3.1034226537366, 7.89646389368191, 
6.85501406564123, 9.14109165528899, 1.76168520924609, -0.0186423064878894, 
4.05085948895797, 9.3290668201337, -0.688712840604117, 4.15315642195899, 
-0.00971512402195501, 5.42811470891677, 2.46276739480922, 8.19194673663205, 
1.73449749373474, 5.11176729680431, 6.99704403247248, 8.19840241595093, 
3.11060513769226, 7.90068926820612, 2.76471024799475, -1.94707392888114, 
8.70720034430486, 1.87038416922914, 6.20663570735997, 4.09386155410738, 
3.22531843927543, 0.830783579350356, -1.89145826468231, 4.83659003642515, 
8.42672861512832, 3.64564224371417, -1.15773582661539, 9.0284462831185, 
8.83097868528031, 6.45672650028379, 5.27430330162195, 1.67266323394736, 
9.77833830342575, 5.52833125887379, 6.02558241863665, 9.32123924173233, 
9.59814558462498, 4.99387919879268, 6.49466500856929, 7.2896720828623, 
1.45305800877985, 7.9206838214584, 3.10094680249827, 6.47011468231269, 
4.50777097352803, 2.80590591034666, 8.48494126341584, 5.28136515607325, 
7.26296418616002, 7.58618091344727, 0.657159517213753, 4.63042456168453, 
6.95119391263247, 5.81217832756039, 6.98278274815032, 1.87540163589012, 
6.71792941091317, -1.29432787337523, 7.78940895663812, 7.37649159209526, 
0.675702298998388, -0.00368332855764775, 6.73187085031259, 4.90496061288267, 
5.9489529474397, 6.38188340303357, 1.49060261962588, 8.02748275174409, 
2.68375327263568, 0.536734269942505, 10.9804396086597, 5.77181428022011, 
8.02014063211585, -0.154299594612417, 11.5771087779023, 3.15668239446356, 
10.9688804025395, 3.02557450708542, 2.13768854535059, 4.9987900600247, 
5.77251800446134, 5.69338793536718, 7.48847879852273, 4.61918663507178, 
5.31242784333302, 3.31453219290204, 5.43559388358608, 2.72114624838099, 
0.283680211264713, 7.32084446410466, 9.36726403837086, 6.28712663547282, 
9.68442109468396, 2.1771978188826, 2.91207121946027, 8.62268371794479, 
5.41172945001701, 5.38373182957917, 7.95353655623665, 10.4130862095915, 
6.25081183779213, 8.54684927325094, 8.17251249575749, 5.72201913971001, 
0.981509806109492, -1.23648317875867, 3.86213151478364, -0.0584268109220522, 
4.88005249800849, 5.42670918687429, 6.4038980260246, 7.14503570378985, 
8.88305747736355, 1.70163134436323, 0.62926133984831, 6.332538349964, 
5.85926583090084, 7.60153681164436, 1.18354110441859, 6.21376082513293, 
6.72176938214484, 0.327537651877887, 7.43424865766649, 9.5345481861972, 
3.36521469337704, 5.15683513556837, 6.05183146409861, 1.47921224995724, 
8.14770415530154, 5.5357695364988, 6.37292822354104, 10.4408451690402, 
10.6286558881235, 3.11671629644448, 4.33997804421313, 4.27598096655774, 
8.81901613584242, 8.48445947041034, 10.4418692374179, 7.52723751645487, 
4.9570006189033, 4.23525434076004, 4.61233757658881, 5.97883596964654, 
8.92350768169135, 3.36744748717257, 7.5935668820036, 10.1530021272265, 
4.44781564448189, -0.249607613297988, 7.71200039180305, 6.06313433331344, 
3.51906505864441, 1.03215089097043, 6.90937324325054, 9.12875026148115, 
9.21902600933707, 0.0144208736886396, 3.62417570727636, 7.02168510403701, 
6.85147195840605, 3.47082453284862, -0.0848457381909239, 8.11569632204266, 
7.82069734436052, 6.09482844636063, 0.951714826858227, 6.68025842180694, 
0.83503748042638, 7.73552283142719, 0.166199593532002, 5.55737073827801, 
9.60315749786249, 2.34268963194322, 5.06130544981114, 8.41498517401806, 
6.47923805898893, 3.60160770616943, 1.93479805024185, 5.15513930951948, 
6.52441526450235, 8.12845225663792, 4.79311355060987, 0.979200604605808, 
1.8268590440232, 9.48019794908497, 1.08410154255385, 9.27908007601209, 
8.68019897887756), Treat = c(1L, 1L, 1L, 1L, 0L, 1L, 1L, 0L, 
1L, 1L, 0L, 1L, 1L, 0L, 1L, 0L, 1L, 0L, 1L, 0L, 0L, 1L, 1L, 1L, 
1L, 1L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 1L, 
1L, 1L, 0L, 1L, 1L, 0L, 1L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 1L, 
0L, 1L, 0L, 1L, 1L, 0L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 
0L, 1L, 1L, 1L, 1L, 0L, 1L, 0L, 0L, 1L, 1L, 1L, 0L, 1L, 0L, 1L, 
1L, 0L, 0L, 1L, 1L, 1L, 0L, 1L, 1L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 
0L, 0L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 
0L, 1L, 1L, 1L, 1L, 0L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 1L, 1L, 1L, 
0L, 0L, 0L, 1L, 0L, 0L, 1L, 1L, 1L, 0L, 0L, 1L, 1L, 1L, 0L, 1L, 
0L, 0L, 0L, 1L, 0L, 1L, 1L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 1L, 
0L, 0L, 1L, 0L, 1L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 
1L, 0L, 1L, 1L, 1L, 0L, 1L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 1L, 1L
), V1 = c(-0.512224184361134, 0.236874945466597, -1.87889995137573, 
0.417180920995462, -0.671381865721995, 0.287167828494884, 0.489380353826899, 
-0.0882793575066059, 0.317742648720351, 1.22953756109929, -0.411584735880727, 
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-0.0292939926335329, -1.19627566198503, 0.129016676567211, 1.01388479182626, 
-1.77853019823201, 1.70834544836442, 0.0454885896688708, 0.0522602787427178, 
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0.588982048814097, -2.51335929144276, -0.33718609396271, 1.23629555181408, 
2.21920877408719, 2.00276718551955, -0.266133894204283, 0.0463897977044271, 
-1.28942121425525, 1.84913424106894, -1.17352670639698, -0.00604822691863582, 
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1.5613690865751, -0.298506285466049, -0.495281299842039, 1.00812101114208, 
1.11685818214117, -0.505794287012676, -1.40273953487652, 2.06123765465717, 
0.368184101316567, 0.420456807959395, 0.00599354238077596, -1.1398273773676, 
0.783863027697299, 1.12470121951805, -0.708307856061111, -0.0906433568083879, 
-1.25738689932716, 1.26095202154429, 0.301138661248989, 0.045843974918831, 
1.03024799700031, 0.949019551531677, -1.39380451586336, -0.528730424300515, 
0.0369965771020032, -1.18171381017, 1.49979891866957, 0.15676325449813, 
0.402736509896824, -1.03099304732686, -0.48056251405081, 1.11384829811643, 
-0.218085210734798, -1.25125131426365, 0.0768043975792328, -0.0859557017662965, 
-0.634842234143288, 0.605421881599738, 0.50271688606003, 0.0544965175079416, 
0.254883531339007, 0.724258364968426, -0.870650774526025, 0.253029590313987, 
-2.0986762438242, -0.0240824333410968, 0.174296097882529, 1.33359836459227, 
-0.346308257138143, -0.563106795944062, -0.260627921956495, -0.268980353567251, 
0.185828017673224, 2.01233897740523, 0.16357851917081, -0.776176022489553, 
1.89540402776715, -0.6615289177093, 0.131681717006018, -1.21145287910156, 
0.932690336174062, 0.585783815391921, -0.571349415819544, -1.42497017096838, 
1.10888317549818, 0.283311326326235, -0.414969695561733, -0.939616281339742, 
0.110492068893627, -0.746014266098047, -1.07991576386102, -0.432025117819907, 
0.830391245203387, 0.164428464782244, -1.51572185585929, -0.421075043960813, 
0.23777931298336, -1.17495654928808, -0.100265604687606, 0.435095241672069, 
1.04859111394976, 1.21578829328542, 0.444072958180845, -0.694238471712357, 
-0.739705032889642, 0.389192710410273, 0.0937806873880687, 0.462085160399263, 
0.156974707854046, 0.266963975753482, -0.29707267641139, 0.354079230828466, 
-0.0971026416271703, 0.673191241548993, -0.530180479720613, -0.66580050863429, 
-0.26721804945571, -1.92264958452522, -0.185099340678194, 0.485163365007242, 
0.638813737506359, -1.23177250938818, 0.439975847642966, 0.716863270101894, 
1.02688539285126, -1.72807904491845, -0.786367064946864, -1.68678578842494, 
1.22942039351412, -1.70618655825219, -1.22990651413465, -0.324950136558707, 
0.624858269195195, -0.828068321649018, 0.947486788826015, -0.108630973427409, 
-2.40250570840112, 1.44771355228476, -1.24199088371159, 2.0917304355165, 
-1.77311409695832, 0.0954605832796433, -0.740994505927424, 1.61778488533527, 
-1.40573129075368, -1.00370633649212, 1.38162617605784, 0.884164534682012, 
0.267169875178434, 1.9057917321543, 0.206145940614585, -1.18383159869387, 
0.481036958396535, 1.31027045373907, 0.358433947320302, -0.29237023947135, 
0.282768651359503, 0.781651423368563, -0.138721715418646, -0.381835428164467, 
1.70428320688559, 0.106774777090092, -0.843309921038093, -0.143242083596126, 
0.698361373594494), V2 = c(0.380304375791841, -1.02059433700002, 
0.250167152859078, 1.19197310535082, -0.665212884381305, 1.55101992940286, 
0.0677143288757891, 0.475101191357759, -1.03947212891308, 1.33093806534135, 
-1.53024562146233, 0.264721134679345, -0.850689035040517, -0.957133686252826, 
1.87696618529297, -2.15775600281697, -0.338372884575403, -0.65534425003225, 
0.000341190135952188, -0.325103882313815, 1.35236410406428, 0.71204447686019, 
-0.832202393832718, -0.104160072249246, 0.548770775839287, -1.02555695096039, 
-0.545265782667373, -0.0716200430572802, -0.416112028859363, 
0.227288103381536, 0.267105299509607, 0.797786411399094, 0.588039577794279, 
-1.35531243965783, -0.191960436342607, 0.802287953041775, 0.688984565302114, 
-1.38282061870725, -0.145188087012673, -0.164918559770532, 0.151817539241955, 
0.579936723341327, -1.82374499984194, -0.770579614791879, 0.169550022479414, 
2.19606347734814, 0.680134653059498, -0.185915544520268, -2.21291386243485, 
-0.902294133219532, -0.387497535879364, -1.67055198613076, 1.96212040244854, 
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-0.966018134129389, -0.304971980458869, -0.444854699256305), 
    V3 = c(-0.783029123458224, -2.86136360818513, 1.698849090337, 
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    -0.326746686522603)), row.names = c(NA, -200L))

I can easily run the first loop in on the variables and extract all the information I need after the first iteration, but I do not understand how to make the function recursive.

library(data.table)
library(partykit)
library(jtools)

setDT(dataCheck)

first<-lapply(setdiff(names(dataCheck),c("Y","Treat")), function(x){
  
  tr<-lmtree(as.formula(paste("Y ~ Treat | ",x )), data = dataCheck,maxdepth = 2 )
  
  if (length(tr)>2){# if it is less than 2 there are no splits on the variable x
  rules<-partykit:::.list.rules.party(tr) # get the rules
  subChunks<-lapply(rules,function(x){ # parse the text of the rule and extract the subset of data
  DataChunk=dataCheck[eval(parse(text = rules)),]
  })
  
#extract SE from ech regression
    allse<-nodeapply(tr, nodeids(tr,terminal = T), function(x){
      seIn<-summ(info_node(x)$object)
      seIn$coeftable[2,2]})
      #wextract terminal node sample size
      allw<-nodeapply(tr, nodeids(tr,terminal = T), function(x) info_node(x)$nobs)
      #extract coef of the regression
      coefz<-coef(tr)

  lapply(unlist(subChunks), function(dt){
  lapply(setdiff(names(dt),c("Y","Treat")), function(x){
  tr<-lmtree(as.formula(paste("Y ~ Treat | ",x )), data = dt,maxdepth = 2 )
  })
  })
  
  }else {
    NULL
  }
  
})

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