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| The TREE Procedure |
Example 91.1 Mammals’ Teeth
The following statements produce a data set containing the numbers of different kinds of teeth for a variety of mammals:
data teeth;
title 'Mammals'' Teeth';
input mammal $ 1-16 @21 (v1-v8) (1.);
label V1='Right Top Incisors'
V2='Right Bottom Incisors'
V3='Right Top Canines'
V4='Right Bottom Canines'
V5='Right Top Premolars'
V6='Right Bottom Premolars'
V7='Right Top Molars'
V8='Right Bottom Molars';
datalines;
Brown Bat 23113333
Mole 32103333
Silver Hair Bat 23112333
Pigmy Bat 23112233
House Bat 23111233
Red Bat 13112233
Pika 21002233
Rabbit 21003233
Beaver 11002133
Groundhog 11002133
Gray Squirrel 11001133
House Mouse 11000033
Porcupine 11001133
Wolf 33114423
Bear 33114423
Raccoon 33114432
Marten 33114412
Weasel 33113312
Wolverine 33114412
Badger 33113312
River Otter 33114312
Sea Otter 32113312
Jaguar 33113211
Cougar 33113211
Fur Seal 32114411
Sea Lion 32114411
Grey Seal 32113322
Elephant Seal 21114411
Reindeer 04103333
Elk 04103333
Deer 04003333
Moose 04003333
;
run;
The following statements use the CLUSTER procedure to cluster the mammals by average linkage and the TREE procedure to produce a horizontal tree diagram that uses the average-linkage distance as its height axis:
proc cluster method=average std pseudo noeigen outtree=tree;
id mammal;
var v1-v8;
run;
proc tree horizontal; run;
Output 91.1.1 displays the information about how the clusters are joined. For example, the cluster history shows that the observations Wolf and Bear form cluster 29, which is merged with Raccoon to form cluster 11.
| Root-Mean-Square Total-Sample Standard Deviation | 1 |
|---|
| Cluster History | |||||||
|---|---|---|---|---|---|---|---|
| NCL | Clusters Joined | FREQ | PSF | PST2 | Norm RMS Dist |
T i e |
|
| 31 | Beaver | Groundhog | 2 | . | . | 0 | T |
| 30 | Gray Squirrel | Porcupine | 2 | . | . | 0 | T |
| 29 | Wolf | Bear | 2 | . | . | 0 | T |
| 28 | Marten | Wolverine | 2 | . | . | 0 | T |
| 27 | Weasel | Badger | 2 | . | . | 0 | T |
| 26 | Jaguar | Cougar | 2 | . | . | 0 | T |
| 25 | Fur Seal | Sea Lion | 2 | . | . | 0 | T |
| 24 | Reindeer | Elk | 2 | . | . | 0 | T |
| 23 | Deer | Moose | 2 | . | . | 0 | |
| 22 | Pigmy Bat | Red Bat | 2 | 281 | . | 0.2289 | |
| 21 | CL28 | River Otter | 3 | 139 | . | 0.2292 | |
| 20 | CL31 | CL30 | 4 | 83.2 | . | 0.2357 | T |
| 19 | Brown Bat | Silver Hair Bat | 2 | 76.7 | . | 0.2357 | T |
| 18 | Pika | Rabbit | 2 | 73.2 | . | 0.2357 | |
| 17 | CL27 | Sea Otter | 3 | 67.4 | . | 0.2462 | |
| 16 | CL22 | House Bat | 3 | 62.9 | 1.7 | 0.2859 | |
| 15 | CL21 | CL17 | 6 | 47.4 | 6.8 | 0.3328 | |
| 14 | CL25 | Elephant Seal | 3 | 45.0 | . | 0.3362 | |
| 13 | CL19 | CL16 | 5 | 40.8 | 3.5 | 0.3672 | |
| 12 | CL15 | Grey Seal | 7 | 38.9 | 2.8 | 0.4078 | |
| 11 | CL29 | Raccoon | 3 | 38.0 | . | 0.423 | |
| 10 | CL18 | CL20 | 6 | 34.5 | 10.3 | 0.4339 | |
| 9 | CL12 | CL26 | 9 | 30.0 | 7.3 | 0.5071 | |
| 8 | CL24 | CL23 | 4 | 28.7 | . | 0.5473 | |
| 7 | CL9 | CL14 | 12 | 25.7 | 7.0 | 0.5668 | |
| 6 | CL10 | House Mouse | 7 | 28.3 | 4.1 | 0.5792 | |
| 5 | CL11 | CL7 | 15 | 26.8 | 6.9 | 0.6621 | |
| 4 | CL13 | Mole | 6 | 31.9 | 7.2 | 0.7156 | |
| 3 | CL4 | CL8 | 10 | 31.0 | 12.7 | 0.8799 | |
| 2 | CL3 | CL6 | 17 | 27.8 | 16.1 | 1.0316 | |
| 1 | CL2 | CL5 | 32 | . | 27.8 | 1.1938 | |
Output 91.1.2 shows the corresponding tree diagram.
As you view the diagram in Output 91.1.2 from left to right, objects and clusters are progressively joined until a single, all-encompassing cluster is formed at the right (or root) of the tree. Clusters exist at each level of the diagram, and every vertical line connects leaves and branches into progressively larger clusters. For example, the five bats form a cluster at the 0.6 level, while the next cluster consists only of the mole. The observations Reindeer, Elk, Deer, and Moose form the next cluster at the 0.6 level, the mammals Pika through House Mouse are in the fourth cluster, The observations Wolf, Bear, and Raccoon form the fifth cluster, while the last cluster contains the observations Marten through Elephant Seal.
The following statements create the same tree with line printer graphics in a vertical orientation:
proc tree lineprinter; run;
The tree is displayed in Output 91.1.3.
Name of Observation or Cluster
S
i
l G E
v r l
e a H R e
r y o i p
B P H G P u W v S G h
r H i o R r S o s o e e r F S a
o a g R u e o q r e R l r a e u e n
w i m e s i R B u u c a M v W B y J C r a t
n r y d e n M a e n i u M c a e O e a O a o
M d D o P b a d r p o W B c r r t a d t S g u S L S
B B B B B o e E e o i b v h r i u o e o t i t s g t e u g e i e
a a a a a l e l e s k i e o e n s l a o e n e e e e a a a a o a
t t t t t e r k r e a t r g l e e f r n n e r l r r l r r l n l
A 1.5 +
v |
e |
r |
a |XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
g |XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXX
e 1 +XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXX
|XXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXX
D |XXXXXXXXXXX XXXXXXX XXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXX
i |XXXXXXXXXXX XXXXXXX XXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXX
s |XXXXXXXXX . XXXXXXX XXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXX
t |XXXXXXXXX . XXXXXXX XXXXXXXXXXXXX XXXXX XXXXXXXXXXXXXXXXXXXXXXX
a 0.5 +XXXXXXXXX . XXX XXX XXXXXXXXXXX . XXXXX XXXXXXXXXXXXXXXXX XXXXX
n |XXXXXXXXX . XXX XXX XXXXXXXXXXX . XXXXX XXXXXXXXXXXXX XXX XXXXX
c |XXXXXXXXX . XXX XXX XXX XXXXXXX . XXX . XXXXXXXXXXX . XXX XXXXX
e |XXX XXXXX . XXX XXX XXX XXXXXXX . XXX . XXXXX XXXXX . XXX XXX .
|. . . . . . XXX XXX . . XXX XXX . XXX . XXX . XXX . . XXX XXX .
B |. . . . . . XXX XXX . . XXX XXX . XXX . XXX . XXX . . XXX XXX .
e 0 +. . . . . . XXX XXX . . XXX XXX . XXX . XXX . XXX . . XXX XXX .
t
w
|
As you look up from the bottom of the diagram, objects and clusters are progressively joined until a single, all-encompassing cluster is formed at the top (or root) of the root. Clusters exist at each level of the diagram. For example, the unbroken line of Xs at the leftmost side of the 0.6 level indicates that the five bats have formed a cluster. The next cluster is represented by a period because it contains only one mammal, Mole. Reindeer, Elk, Deer, and Moose form the next cluster, indicated by Xs again. The mammals Pika through House Mouse are in the fourth cluster. The observations Wolf, Bear, and Raccoon form the fifth cluster, while the last cluster contains the observations Marten through Elephant Seal.
The next statements sort the clusters at each branch in order of formation and use the number of clusters as the height axis:
proc tree sort height=n horizontal; run;
The resulting tree is displayed in Output 91.1.4.
Because the CLUSTER procedure always produces binary trees, the number of internal (root and branch) nodes in the tree is one less than the number of leaves. Therefore 31 clusters are formed from the 32 mammals in the input data set. These are represented by the 31 vertical line segments in the tree diagram, each at a different value along the horizontal axis.
As you examine the tree from left to right, the first vertical line segment is where Beaver and Groundhog are clustered and the number of clusters is 31. The next cluster is formed from Gray Squirrel and Porcupine. The third contains Wolf and Bear. Note how the tree graphically displays the clustering order information that was presented in tabular form by the CLUSTER procedure in Output 91.1.1.
The same clusters as in Output 91.1.2 and Output 91.1.3 can be seen at the six-cluster level of the tree diagram in Output 91.1.4, although the SORT and HEIGHT= options make them appear in a different order.
The following statements create these six clusters and save the result in the output data set part:
proc tree noprint out=part nclusters=6;
id mammal;
copy v1-v8;
proc sort;
by cluster;
The PROC TREE statement produces no output but creates an output data set indicating the cluster to which each observation belongs at the six-cluster level in the tree. The following statements print part, with the results shown in Output 91.1.5:
proc print label uniform;
id mammal;
var v1-v8;
format v1-v8 1.;
by cluster;
run;
| mammal | Right Top Incisors |
Right Bottom Incisors |
Right Top Canines |
Right Bottom Canines |
Right Top Premolars |
Right Bottom Premolars |
Right Top Molars |
Right Bottom Molars |
|---|---|---|---|---|---|---|---|---|
| Beaver | 1 | 1 | 0 | 0 | 2 | 1 | 3 | 3 |
| Groundhog | 1 | 1 | 0 | 0 | 2 | 1 | 3 | 3 |
| Gray Squirrel | 1 | 1 | 0 | 0 | 1 | 1 | 3 | 3 |
| Porcupine | 1 | 1 | 0 | 0 | 1 | 1 | 3 | 3 |
| Pika | 2 | 1 | 0 | 0 | 2 | 2 | 3 | 3 |
| Rabbit | 2 | 1 | 0 | 0 | 3 | 2 | 3 | 3 |
| House Mouse | 1 | 1 | 0 | 0 | 0 | 0 | 3 | 3 |
| mammal | Right Top Incisors |
Right Bottom Incisors |
Right Top Canines |
Right Bottom Canines |
Right Top Premolars |
Right Bottom Premolars |
Right Top Molars |
Right Bottom Molars |
|---|---|---|---|---|---|---|---|---|
| Wolf | 3 | 3 | 1 | 1 | 4 | 4 | 2 | 3 |
| Bear | 3 | 3 | 1 | 1 | 4 | 4 | 2 | 3 |
| Raccoon | 3 | 3 | 1 | 1 | 4 | 4 | 3 | 2 |
| mammal | Right Top Incisors |
Right Bottom Incisors |
Right Top Canines |
Right Bottom Canines |
Right Top Premolars |
Right Bottom Premolars |
Right Top Molars |
Right Bottom Molars |
|---|---|---|---|---|---|---|---|---|
| Marten | 3 | 3 | 1 | 1 | 4 | 4 | 1 | 2 |
| Wolverine | 3 | 3 | 1 | 1 | 4 | 4 | 1 | 2 |
| Weasel | 3 | 3 | 1 | 1 | 3 | 3 | 1 | 2 |
| Badger | 3 | 3 | 1 | 1 | 3 | 3 | 1 | 2 |
| Jaguar | 3 | 3 | 1 | 1 | 3 | 2 | 1 | 1 |
| Cougar | 3 | 3 | 1 | 1 | 3 | 2 | 1 | 1 |
| Fur Seal | 3 | 2 | 1 | 1 | 4 | 4 | 1 | 1 |
| Sea Lion | 3 | 2 | 1 | 1 | 4 | 4 | 1 | 1 |
| River Otter | 3 | 3 | 1 | 1 | 4 | 3 | 1 | 2 |
| Sea Otter | 3 | 2 | 1 | 1 | 3 | 3 | 1 | 2 |
| Elephant Seal | 2 | 1 | 1 | 1 | 4 | 4 | 1 | 1 |
| Grey Seal | 3 | 2 | 1 | 1 | 3 | 3 | 2 | 2 |
| mammal | Right Top Incisors |
Right Bottom Incisors |
Right Top Canines |
Right Bottom Canines |
Right Top Premolars |
Right Bottom Premolars |
Right Top Molars |
Right Bottom Molars |
|---|---|---|---|---|---|---|---|---|
| Reindeer | 0 | 4 | 1 | 0 | 3 | 3 | 3 | 3 |
| Elk | 0 | 4 | 1 | 0 | 3 | 3 | 3 | 3 |
| Deer | 0 | 4 | 0 | 0 | 3 | 3 | 3 | 3 |
| Moose | 0 | 4 | 0 | 0 | 3 | 3 | 3 | 3 |
| mammal | Right Top Incisors |
Right Bottom Incisors |
Right Top Canines |
Right Bottom Canines |
Right Top Premolars |
Right Bottom Premolars |
Right Top Molars |
Right Bottom Molars |
|---|---|---|---|---|---|---|---|---|
| Pigmy Bat | 2 | 3 | 1 | 1 | 2 | 2 | 3 | 3 |
| Red Bat | 1 | 3 | 1 | 1 | 2 | 2 | 3 | 3 |
| Brown Bat | 2 | 3 | 1 | 1 | 3 | 3 | 3 | 3 |
| Silver Hair Bat | 2 | 3 | 1 | 1 | 2 | 3 | 3 | 3 |
| House Bat | 2 | 3 | 1 | 1 | 1 | 2 | 3 | 3 |
| mammal | Right Top Incisors |
Right Bottom Incisors |
Right Top Canines |
Right Bottom Canines |
Right Top Premolars |
Right Bottom Premolars |
Right Top Molars |
Right Bottom Molars |
|---|---|---|---|---|---|---|---|---|
| Mole | 3 | 2 | 1 | 0 | 3 | 3 | 3 | 3 |
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Copyright © 2009 by SAS Institute Inc., Cary, NC, USA. All rights reserved.