Assignment 6: Trees and Forests

Load the libraries + functions

Load all the libraries or functions that you will use to for the rest of the assignment. It is helpful to define your libraries and functions at the top of a report, so that others can know what they need for the report to compile correctly.

The data for this project has already been loaded. You will be distinguishing between the categories of nerd and geek to determine the influence of respective variables on their category definition.

library(Rling)

data(nerd)

head(nerd)

##   Noun Num Century Register    Eval
## 1 nerd  pl      XX     ACAD Neutral
## 2 nerd  pl     XXI     ACAD Neutral
## 3 nerd  pl      XX     ACAD Neutral
## 4 nerd  pl      XX     ACAD Neutral
## 5 nerd  pl      XX     ACAD Neutral
## 6 nerd  pl     XXI     ACAD Neutral

#install.packages("party")
library(party)

## Warning: package 'party' was built under R version 3.5.3

## Loading required package: grid

## Loading required package: mvtnorm

## Warning: package 'mvtnorm' was built under R version 3.5.3

## Loading required package: modeltools

## Warning: package 'modeltools' was built under R version 3.5.2

## Loading required package: stats4

## Loading required package: strucchange

## Warning: package 'strucchange' was built under R version 3.5.3

## Loading required package: zoo

## Warning: package 'zoo' was built under R version 3.5.3

## 
## 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 3.5.3

table(nerd$Noun)

## 
## geek nerd 
##  670  646

Description of the data

Dependent variable:

Noun: which category is represented either nerd or geek.

Independent variables:

Num: a measure of social group, either pl (plural) or sg (single)
Century: time measurement, as XX (20th) or XXI (21st) century
Register: information about where the data was coded from ACAD (academic), MAG (magazine), NEWS (newspapers), and SPOK (spoken)
Eval: A measure of the semanticity of the word, Neg for negative, Neutral, and Positive

Conditional inference model

Add a random number generator to start the model.
Use ctree() to create a conditional inference model.

set.seed(12345)

tree.output = ctree(Noun ~ Num + Century + Register + Eval, data = nerd)

Make a plot

Plot the conditional inference model.

plot(tree.output)

Interpret the categories

Write out an interpretation of the results from the model. You can interpret the branches of the tree to determine what featurally defines each category.
With only two categories, you will see the proportion split as the output in the bar graph - look for the group with the larger proportion.

Conditional inference model predictiveness

Calculate the percent correct classification for the conditional inference model.

predResults = table(predict(tree.output), nerd$Noun)

predResults

##       
##        geek nerd
##   geek  227   61
##   nerd  443  585

sum(diag(predResults)) / sum(predResults) * 100

## [1] 61.70213

sum(predResults[1]) / sum(predResults[,1]) * 100

## [1] 33.8806

sum(predResults[4]) / sum(predResults[,2]) * 100

## [1] 90.55728

sum(predResults[,1]) / (sum(predResults[,1]) + sum(predResults[,2]))

## [1] 0.5091185

sum(predResults[1,]) / (sum(predResults[1,]) + sum(predResults[2,]))

## [1] 0.218845

Random forests

Create a random forest of the same model for geek versus nerd.

forestRand.output = cforest(Noun ~ Num + Century + Register + Eval,  data = nerd,   controls = cforest_unbiased(ntree = 1000,  mtry = 2))

Variable importance

Calculate the variable importance from the random forest model.
Include a dot plot of the importance values.
Which variables were the most important?

The most important variables as seen in the output are Eval and Century. Eval: A measure of the semanticity of the word Century: Time measurement - 20th or 21st century

forVariable.importance = varimp(forestRand.output,
                           conditional = T)
round(forVariable.importance, 3)

##      Num  Century Register     Eval 
##   -0.002    0.024   -0.003    0.056

dotchart(sort(forVariable.importance),
         main = "Variable Importance")

Forest model predictiveness

Include the percent correct for the random forest model.
Did it do better than the conditional inference tree?

Forest model is less bias in predicting “nerd”, Tree model shows a 22:78 split prediction. Actual split shows 51:49 whereas random forest has 37:63 split ratio.Prediction accuracy for nerd reduces to 70.8% whereas predicting greek goes upto 56.4%. So pro’s and cons for each method.

forestPredict.outcomes = table(predict(forestRand.output), nerd$Noun)

forestPredict.outcomes

##       
##        geek nerd
##   geek  337  149
##   nerd  333  497

sum(diag(forestPredict.outcomes)) / sum(forestPredict.outcomes) * 100

## [1] 63.37386

sum(forestPredict.outcomes[1]) / sum(forestPredict.outcomes[,1]) * 100

## [1] 50.29851

sum(forestPredict.outcomes[4]) / sum(forestPredict.outcomes[,2]) * 100

## [1] 76.93498

sum(forestPredict.outcomes[1,]) / (sum(forestPredict.outcomes[1,]) + sum(forestPredict.outcomes[2,]))

## [1] 0.3693009

Thought question

What other variables might be useful in understanding the category membership of geek versus nerd? Basically, what could we add to the model to improve it (there’s no one right answer here - it’s helpful to think about what other facets we have not measured)?

Geek is someone who is more knowledgeable with books while nerd is someone who specializes in a specific set on knwoledge.