Decision_Trees
Arnav Bhardwaj
25 February 2018
R Markdown
airline.df<-read.csv(paste("SixAirlinesDataV2.csv", sep=""))
summary(airline.df)## Airline Aircraft FlightDuration TravelMonth
## AirFrance: 74 AirBus:151 Min. : 1.250 Aug:127
## British :175 Boeing:307 1st Qu.: 4.260 Jul: 75
## Delta : 46 Median : 7.790 Oct:127
## Jet : 61 Mean : 7.578 Sep:129
## Singapore: 40 3rd Qu.:10.620
## Virgin : 62 Max. :14.660
## IsInternational SeatsEconomy SeatsPremium PitchEconomy
## Domestic : 40 Min. : 78.0 Min. : 8.00 Min. :30.00
## International:418 1st Qu.:133.0 1st Qu.:21.00 1st Qu.:31.00
## Median :185.0 Median :36.00 Median :31.00
## Mean :202.3 Mean :33.65 Mean :31.22
## 3rd Qu.:243.0 3rd Qu.:40.00 3rd Qu.:32.00
## Max. :389.0 Max. :66.00 Max. :33.00
## PitchPremium WidthEconomy WidthPremium PriceEconomy
## Min. :34.00 Min. :17.00 Min. :17.00 Min. : 65
## 1st Qu.:38.00 1st Qu.:18.00 1st Qu.:19.00 1st Qu.: 413
## Median :38.00 Median :18.00 Median :19.00 Median :1242
## Mean :37.91 Mean :17.84 Mean :19.47 Mean :1327
## 3rd Qu.:38.00 3rd Qu.:18.00 3rd Qu.:21.00 3rd Qu.:1909
## Max. :40.00 Max. :19.00 Max. :21.00 Max. :3593
## PricePremium PriceRelative SeatsTotal PitchDifference
## Min. : 86.0 Min. :0.0200 Min. : 98 Min. : 2.000
## 1st Qu.: 528.8 1st Qu.:0.1000 1st Qu.:166 1st Qu.: 6.000
## Median :1737.0 Median :0.3650 Median :227 Median : 7.000
## Mean :1845.3 Mean :0.4872 Mean :236 Mean : 6.688
## 3rd Qu.:2989.0 3rd Qu.:0.7400 3rd Qu.:279 3rd Qu.: 7.000
## Max. :7414.0 Max. :1.8900 Max. :441 Max. :10.000
## WidthDifference PercentPremiumSeats
## Min. :0.000 Min. : 4.71
## 1st Qu.:1.000 1st Qu.:12.28
## Median :1.000 Median :13.21
## Mean :1.633 Mean :14.65
## 3rd Qu.:3.000 3rd Qu.:15.36
## Max. :4.000 Max. :24.69Including Plots
You can also embed plots, for example:
## Warning: package 'caTools' was built under R version 3.4.3## Airline Aircraft FlightDuration TravelMonth IsInternational
## 2 British Boeing 12.25 Aug International
## 15 British Boeing 11.58 Sep International
## 16 British Boeing 11.58 Oct International
## 19 British Boeing 9.16 Oct International
## 26 British Boeing 8.75 Aug International
## 28 British Boeing 8.75 Oct International
## 37 British Boeing 13.50 Sep International
## 42 British Boeing 3.83 Oct International
## 50 British Boeing 12.75 Sep International
## 53 British Boeing 11.08 Aug International
## 54 British Boeing 11.08 Sep International
## 55 British Boeing 11.08 Oct International
## 56 British Boeing 6.08 Aug International
## 61 British Boeing 12.50 Oct International
## 64 Virgin AirBus 8.00 Sep International
## 73 Virgin AirBus 7.75 Aug International
## 78 Delta Boeing 2.33 Oct Domestic
## 83 British Boeing 6.83 Aug International
## 85 British Boeing 6.83 Oct International
## 87 British Boeing 7.58 Sep International
## 94 Jet Boeing 3.08 Aug International
## 101 British AirBus 11.16 Sep International
## 102 British AirBus 11.16 Oct International
## 103 British AirBus 10.50 Jul International
## 108 British AirBus 13.08 Sep International
## 110 British AirBus 11.16 Sep International
## 114 British AirBus 3.58 Aug International
## 115 British AirBus 3.58 Sep International
## 119 British AirBus 3.58 Aug International
## 123 British AirBus 2.41 Aug International
## 124 British AirBus 3.25 Oct International
## 130 British AirBus 1.83 Aug International
## 144 British Boeing 1.25 Sep International
## 146 British AirBus 2.83 Oct International
## 151 British Boeing 1.33 Oct International
## 153 Delta Boeing 4.51 Aug Domestic
## 154 Delta Boeing 4.33 Jul Domestic
## 155 Delta Boeing 4.51 Jul Domestic
## 160 Virgin Boeing 12.08 Aug International
## 165 Virgin Boeing 9.91 Aug International
## 166 Virgin Boeing 9.91 Sep International
## 169 Virgin Boeing 10.83 Aug International
## 170 Virgin Boeing 10.83 Sep International
## 173 Virgin Boeing 12.58 Aug International
## 175 Virgin Boeing 10.75 Aug International
## 177 Virgin Boeing 10.75 Oct International
## 179 Virgin Boeing 11.33 Oct International
## 184 Virgin Boeing 12.58 Sep International
## 194 Virgin AirBus 6.91 Oct International
## 196 Virgin AirBus 6.58 Aug International
## 201 Virgin AirBus 10.41 Sep International
## 210 Virgin AirBus 7.75 Sep International
## 217 AirFrance AirBus 8.33 Sep International
## 218 AirFrance AirBus 8.33 Oct International
## 220 AirFrance AirBus 8.33 Aug International
## 221 AirFrance AirBus 8.33 Sep International
## 227 AirFrance AirBus 6.83 Oct International
## 231 AirFrance AirBus 8.08 Sep International
## 240 British Boeing 10.41 Aug International
## 246 British Boeing 9.91 Jul International
## 252 British Boeing 8.58 Oct International
## 261 British Boeing 8.66 Aug International
## 262 British Boeing 8.66 Sep International
## 265 British Boeing 7.25 Sep International
## 268 British Boeing 7.08 Aug International
## 270 British Boeing 7.08 Oct International
## 278 British Boeing 11.08 Sep International
## 283 Delta Boeing 4.63 Aug Domestic
## 284 Delta Boeing 4.65 Sep Domestic
## 285 Delta Boeing 4.66 Oct Domestic
## 286 Delta Boeing 4.70 Jul Domestic
## 289 Delta Boeing 4.36 Sep Domestic
## 296 Delta AirBus 1.95 Sep Domestic
## 297 Delta AirBus 2.26 Sep Domestic
## 298 Delta AirBus 2.55 Oct Domestic
## 313 Jet AirBus 9.50 Sep International
## 314 Jet AirBus 8.91 Aug International
## 320 Singapore Boeing 12.41 Sep International
## 321 Singapore Boeing 12.41 Oct International
## 325 Singapore Boeing 14.66 Aug International
## 331 Singapore Boeing 3.83 Jul International
## 333 Singapore Boeing 3.83 Sep International
## 336 Singapore Boeing 12.75 Sep International
## 342 AirFrance Boeing 7.50 Oct International
## 343 AirFrance Boeing 6.83 Aug International
## 353 AirFrance Boeing 9.50 Oct International
## 355 AirFrance Boeing 7.75 Aug International
## 358 AirFrance Boeing 9.41 Aug International
## 360 AirFrance Boeing 9.41 Oct International
## 364 AirFrance Boeing 11.91 Aug International
## 367 British Boeing 13.83 Aug International
## 370 British Boeing 13.33 Aug International
## 372 British Boeing 13.33 Oct International
## 377 British Boeing 9.58 Oct International
## 383 Jet Boeing 3.25 Oct International
## 389 Jet Boeing 2.50 Oct International
## 390 Jet Boeing 2.66 Jul International
## 396 Jet Boeing 4.16 Oct International
## 399 Jet Boeing 2.66 Aug International
## 405 Jet Boeing 3.25 Jul International
## 407 AirFrance Boeing 6.91 Oct International
## 410 Singapore AirBus 13.33 Jul International
## 418 Singapore AirBus 12.66 Jul International
## 423 Singapore AirBus 6.50 Aug International
## 424 Singapore AirBus 6.50 Sep International
## 426 AirFrance AirBus 13.00 Sep International
## 432 AirFrance Boeing 10.66 Oct International
## 435 AirFrance AirBus 8.50 Sep International
## 436 AirFrance Boeing 8.50 Oct International
## 441 Jet Boeing 3.16 Jul International
## 443 Jet Boeing 5.66 Jul International
## 444 Jet Boeing 5.66 Aug International
## 447 Jet Boeing 5.66 Jul International
## 450 Jet Boeing 2.58 Sep International
## 453 Jet Boeing 2.58 Jul International
## SeatsEconomy SeatsPremium PitchEconomy PitchPremium WidthEconomy
## 2 122 40 31 38 18
## 15 122 40 31 38 18
## 16 122 40 31 38 18
## 19 122 40 31 38 18
## 26 122 40 31 38 18
## 28 122 40 31 38 18
## 37 122 40 31 38 18
## 42 122 40 31 38 18
## 50 122 40 31 38 18
## 53 127 39 31 38 18
## 54 127 39 31 38 18
## 55 127 39 31 38 18
## 56 127 39 31 38 18
## 61 127 39 31 38 18
## 64 185 48 31 38 18
## 73 185 48 31 38 18
## 78 78 20 31 34 18
## 83 243 56 31 38 18
## 85 243 56 31 38 18
## 87 243 56 31 38 18
## 94 138 28 30 40 17
## 101 303 55 31 38 18
## 102 303 55 31 38 18
## 103 303 55 31 38 18
## 108 303 55 31 38 18
## 110 303 55 31 38 18
## 114 303 55 31 38 18
## 115 303 55 31 38 18
## 119 303 55 31 38 18
## 123 303 55 31 38 18
## 124 303 55 31 38 18
## 130 303 55 31 38 18
## 144 303 55 31 38 18
## 146 303 55 31 38 18
## 151 303 55 31 38 18
## 153 171 29 32 35 18
## 154 171 29 32 35 18
## 155 171 29 32 35 18
## 160 198 35 31 38 18
## 165 375 66 31 38 18
## 166 375 66 31 38 18
## 169 198 35 31 38 18
## 170 198 35 31 38 18
## 173 198 35 31 38 18
## 175 375 66 31 38 18
## 177 375 66 31 38 18
## 179 198 35 31 38 18
## 184 198 35 31 38 18
## 194 233 38 31 38 18
## 196 233 38 31 38 18
## 201 233 38 31 38 18
## 210 233 38 31 38 18
## 217 147 21 32 38 18
## 218 147 21 32 38 18
## 220 147 21 32 38 18
## 221 147 21 32 38 18
## 227 147 21 32 38 18
## 231 147 21 32 38 18
## 240 243 36 31 38 18
## 246 243 36 31 38 18
## 252 243 36 31 38 18
## 261 243 36 31 38 18
## 262 243 36 31 38 18
## 265 243 36 31 38 18
## 268 243 36 31 38 18
## 270 243 36 31 38 18
## 278 243 36 31 38 18
## 283 126 18 32 34 17
## 284 126 18 32 34 17
## 285 126 18 32 34 17
## 286 139 21 31 34 17
## 289 126 18 32 34 17
## 296 120 18 32 34 17
## 297 120 18 32 34 17
## 298 136 20 33 35 17
## 313 147 21 32 38 18
## 314 147 21 32 38 18
## 320 184 28 32 38 19
## 321 184 28 32 38 19
## 325 184 28 32 38 19
## 331 184 28 32 38 19
## 333 184 28 32 38 19
## 336 184 28 32 38 19
## 342 200 28 32 38 17
## 343 200 28 32 38 17
## 353 200 28 32 38 17
## 355 174 24 32 38 17
## 358 200 28 32 38 17
## 360 200 28 32 38 17
## 364 200 28 32 38 17
## 367 203 24 31 38 18
## 370 203 24 31 38 18
## 372 203 24 31 38 18
## 377 203 24 31 38 18
## 383 124 16 30 40 17
## 389 124 16 30 40 17
## 390 124 16 30 40 17
## 396 124 16 30 40 17
## 399 124 16 30 40 17
## 405 124 16 30 40 17
## 407 216 24 32 38 17
## 410 333 36 32 38 19
## 418 333 36 32 38 19
## 423 333 36 32 38 19
## 424 333 36 32 38 19
## 426 389 38 32 38 18
## 432 389 38 32 38 18
## 435 389 38 32 38 18
## 436 389 38 32 38 18
## 441 162 8 30 40 17
## 443 162 8 30 40 17
## 444 162 8 30 40 17
## 447 162 8 30 40 17
## 450 162 8 30 40 17
## 453 162 8 30 40 17
## WidthPremium PriceEconomy PricePremium PriceRelative SeatsTotal
## 2 19 2707 3725 0.38 162
## 15 19 1750 2656 0.52 162
## 16 19 1750 2656 0.52 162
## 19 19 1813 2504 0.38 162
## 26 19 1542 2084 0.35 162
## 28 19 1566 2084 0.33 162
## 37 19 940 1548 0.65 162
## 42 19 1224 1512 0.24 162
## 50 19 509 773 0.52 162
## 53 19 2156 2933 0.36 166
## 54 19 2156 2933 0.36 166
## 55 19 2156 2933 0.36 166
## 56 19 1634 2195 0.34 166
## 61 19 509 818 0.61 166
## 64 21 1813 3128 0.73 233
## 73 21 540 594 0.10 233
## 78 18 216 231 0.07 98
## 83 19 1444 2982 1.07 299
## 85 19 1444 2982 1.07 299
## 87 19 1824 2549 0.40 299
## 94 21 464 616 0.33 166
## 101 19 2384 3563 0.49 358
## 102 19 2384 3563 0.49 358
## 103 19 1848 3536 0.91 358
## 108 19 1758 2592 0.47 358
## 110 19 719 1634 1.27 358
## 114 19 402 442 0.10 358
## 115 19 402 442 0.10 358
## 119 19 322 348 0.08 358
## 123 19 276 306 0.11 358
## 124 19 249 285 0.14 358
## 130 19 201 237 0.18 358
## 144 19 109 141 0.30 358
## 146 19 97 125 0.29 358
## 151 19 65 86 0.33 358
## 153 18 423 467 0.10 200
## 154 18 483 527 0.09 200
## 155 18 713 757 0.06 200
## 160 21 1086 2964 1.73 233
## 165 21 1781 3509 0.97 441
## 166 21 1781 3509 0.97 441
## 169 21 1580 3019 0.91 233
## 170 21 1580 3019 0.91 233
## 173 21 1096 1710 0.56 233
## 175 21 2445 3694 0.51 441
## 177 21 2445 3694 0.51 441
## 179 21 2369 3540 0.49 233
## 184 21 1356 1710 0.26 233
## 194 21 1434 2982 1.08 271
## 196 21 1476 2997 1.03 271
## 201 21 1903 3509 0.84 271
## 210 21 540 594 0.10 271
## 217 19 2659 2859 0.08 168
## 218 19 2659 2859 0.08 168
## 220 19 2659 2859 0.08 168
## 221 19 2659 2859 0.08 168
## 227 19 2860 3063 0.07 168
## 231 19 2813 2922 0.04 168
## 240 19 1651 3509 1.13 279
## 246 19 2356 3200 0.36 279
## 252 19 1562 3099 0.98 279
## 261 19 1609 2292 0.42 279
## 262 19 1609 2292 0.42 279
## 265 19 1632 2278 0.40 279
## 268 19 1736 1866 0.07 279
## 270 19 1736 1866 0.07 279
## 278 19 1023 1199 0.17 279
## 283 17 363 407 0.12 144
## 284 17 363 407 0.12 144
## 285 17 363 407 0.12 144
## 286 17 413 457 0.11 160
## 289 17 413 457 0.11 144
## 296 17 166 181 0.09 138
## 297 17 329 354 0.08 138
## 298 17 243 262 0.08 156
## 313 19 661 928 0.40 168
## 314 19 676 931 0.38 168
## 320 20 1215 1947 0.60 212
## 321 20 1215 1947 0.60 212
## 325 20 1406 1584 0.13 212
## 331 20 563 619 0.10 212
## 333 20 563 619 0.10 212
## 336 20 1431 1564 0.09 212
## 342 19 2581 2781 0.08 228
## 343 19 2860 3063 0.07 228
## 353 19 3414 3524 0.03 228
## 355 19 3215 3325 0.03 198
## 358 19 3480 3589 0.03 228
## 360 19 3480 3589 0.03 228
## 364 19 3159 3243 0.03 228
## 367 19 3102 7414 1.39 227
## 370 19 2166 2470 0.14 227
## 372 19 2166 2470 0.14 227
## 377 19 524 797 0.52 227
## 383 21 149 398 1.67 140
## 389 21 118 267 1.26 140
## 390 21 108 228 1.11 140
## 396 21 156 318 1.04 140
## 399 21 127 228 0.79 140
## 405 21 594 696 0.17 140
## 407 19 648 1710 1.64 240
## 410 20 505 1004 0.99 369
## 418 20 690 1110 0.61 369
## 423 20 690 1110 0.61 369
## 424 20 690 1110 0.61 369
## 426 19 1522 3289 1.16 427
## 432 19 2996 3196 0.07 427
## 435 19 2979 3088 0.04 427
## 436 19 2979 3088 0.04 427
## 441 21 148 397 1.68 170
## 443 21 187 430 1.30 170
## 444 21 187 430 1.30 170
## 447 21 245 545 1.22 170
## 450 21 172 304 0.77 170
## 453 21 281 451 0.60 170
## PitchDifference WidthDifference PercentPremiumSeats
## 2 7 1 24.69
## 15 7 1 24.69
## 16 7 1 24.69
## 19 7 1 24.69
## 26 7 1 24.69
## 28 7 1 24.69
## 37 7 1 24.69
## 42 7 1 24.69
## 50 7 1 24.69
## 53 7 1 23.49
## 54 7 1 23.49
## 55 7 1 23.49
## 56 7 1 23.49
## 61 7 1 23.49
## 64 7 3 20.60
## 73 7 3 20.60
## 78 3 0 20.41
## 83 7 1 18.73
## 85 7 1 18.73
## 87 7 1 18.73
## 94 10 4 16.87
## 101 7 1 15.36
## 102 7 1 15.36
## 103 7 1 15.36
## 108 7 1 15.36
## 110 7 1 15.36
## 114 7 1 15.36
## 115 7 1 15.36
## 119 7 1 15.36
## 123 7 1 15.36
## 124 7 1 15.36
## 130 7 1 15.36
## 144 7 1 15.36
## 146 7 1 15.36
## 151 7 1 15.36
## 153 3 0 14.50
## 154 3 0 14.50
## 155 3 0 14.50
## 160 7 3 15.02
## 165 7 3 14.97
## 166 7 3 14.97
## 169 7 3 15.02
## 170 7 3 15.02
## 173 7 3 15.02
## 175 7 3 14.97
## 177 7 3 14.97
## 179 7 3 15.02
## 184 7 3 15.02
## 194 7 3 14.02
## 196 7 3 14.02
## 201 7 3 14.02
## 210 7 3 14.02
## 217 6 1 12.50
## 218 6 1 12.50
## 220 6 1 12.50
## 221 6 1 12.50
## 227 6 1 12.50
## 231 6 1 12.50
## 240 7 1 12.90
## 246 7 1 12.90
## 252 7 1 12.90
## 261 7 1 12.90
## 262 7 1 12.90
## 265 7 1 12.90
## 268 7 1 12.90
## 270 7 1 12.90
## 278 7 1 12.90
## 283 2 0 12.50
## 284 2 0 12.50
## 285 2 0 12.50
## 286 3 0 13.13
## 289 2 0 12.50
## 296 2 0 13.04
## 297 2 0 13.04
## 298 2 0 12.82
## 313 6 1 12.50
## 314 6 1 12.50
## 320 6 1 13.21
## 321 6 1 13.21
## 325 6 1 13.21
## 331 6 1 13.21
## 333 6 1 13.21
## 336 6 1 13.21
## 342 6 2 12.28
## 343 6 2 12.28
## 353 6 2 12.28
## 355 6 2 12.12
## 358 6 2 12.28
## 360 6 2 12.28
## 364 6 2 12.28
## 367 7 1 10.57
## 370 7 1 10.57
## 372 7 1 10.57
## 377 7 1 10.57
## 383 10 4 11.43
## 389 10 4 11.43
## 390 10 4 11.43
## 396 10 4 11.43
## 399 10 4 11.43
## 405 10 4 11.43
## 407 6 2 10.00
## 410 6 1 9.76
## 418 6 1 9.76
## 423 6 1 9.76
## 424 6 1 9.76
## 426 6 1 8.90
## 432 6 1 8.90
## 435 6 1 8.90
## 436 6 1 8.90
## 441 10 4 4.71
## 443 10 4 4.71
## 444 10 4 4.71
## 447 10 4 4.71
## 450 10 4 4.71
## 453 10 4 4.71The reason that you may not see all the variables in the output of the tree is because they don’t have a significant influence on the dependend variable. Unlike linear or logistic regression, that will show all the variables and give you the P-value in order to determine if they are significant or not, the decision tree does not return the unsiginifcant variables, i.e, it doesn’t split by them.
library(party)## Warning: package 'party' was built under R version 3.4.3## Loading required package: grid## Loading required package: mvtnorm## Loading required package: modeltools## Loading required package: stats4## Loading required package: strucchange## Warning: package 'strucchange' was built under R version 3.4.3## Loading required package: zoo## Warning: package 'zoo' was built under R version 3.4.3##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric## Loading required package: sandwich## Warning: package 'sandwich' was built under R version 3.4.3output.tree<-ctree(PriceEconomy~PercentPremiumSeats+PitchDifference+WidthDifference, data=airline.df)
plot(output.tree)
output.tree<-ctree(PricePremium~PercentPremiumSeats+PitchDifference+WidthDifference, data=airline.df)
plot(output.tree)
output.tree<-ctree(PricePremium~PercentPremiumSeats+SeatsTotal+SeatsPremium, data=airline.df)
plot(output.tree)
No significant correlation, hence, no split.
output.tree<-ctree(PriceEconomy~WidthDifference, data=airline.df)
plot(output.tree) RELAX CRITERION So, the case weight is simply a vector indicating if an observation is in a node or in a particular final cell (final cell can be read as ‘terminal node’) of the partition space. The sum of case weights in a terminal node is the same as how many observations are in that final cell. Note that the length of the case weight vector is equal to the number of records. 1)mincriterion the value of the test statistic (for testtype == “Teststatistic”), or 1 - p-value (for other values of testtype) that must be exceeded in order to implement a split. 2)minsplit the minimum sum of weights in a node in order to be considered for splitting. 3)minbucket the minimum sum of weights in a terminal node.
output.tree<-ctree(PriceEconomy~WidthDifference, data=airline.df, controls=ctree_control(mincriterion = 0.01, minsplit=5, minbucket=1))
plot(output.tree)
output.tree<-ctree(PriceEconomy~PercentPremiumSeats, data=airline.df, controls=ctree_control(mincriterion = 0.7, minsplit=5, minbucket=1))
plot(output.tree)
Note that the echo = FALSE parameter was added to the code chunk to prevent printing of the R code that generated the plot.