A Comparative Analysis of Income Level Prediction

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ESAD KOPRU

Table of Contents

1. Data Exploration
2. Split Data into Training and Test
3. Classification:�
1. Logistic Regression
2. Classification: Tree Based Classification
3. Classification: Random Forest
4. Classification: Linear SVM
4. Discussion and Conclusion

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Data

• The dataset is from 1994; census income
• https://archive.ics.uci.edu/ml/datasets/Census+Income
• 14 attributes
• 32561 records.

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Data Exploration

NA Values

• First attempt was assigning average weights, however, later in the random forest analysis, the NA’s occurred again, so my second approach was to remove all NA values.
• inc_clean <- DMwR::knnImputation(inc, k=5, scale=T, meth="weighAve")
• summary(inc_clean)
• inc_clean <- inc[complete.cases(inc), ]

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Data Exploration

Income level vs. age, education num, marital status; married people earns higher than single or widowed.

, occupation

Income Level vs. Occupation, Marital Status

Data Exploration

Income Level vs. Race, Gender

Divide dataset into Training and Test

• set.seed(12345)
• # split training and test datasets, 80% and 20%
• train_sample <- sample(nrow(inc_clean), round(nrow(inc_clean)*0.8))
• inc_clean_train <- inc[train_sample, ]
• inc_clean_test <- inc[-train_sample, ]

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Logistic Regression Model

• log.base.model <- glm(incomelevel~., data=inc_clean_train, family="binomial")

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• vif(log.base.model) Error in vif.default(log.base.model) : there are aliased coefficients in the model

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• Education and educationnum are representing the same information, one with categorical and the latter is with numeric. So I removed the categorical education

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Logistic Regression Model 2

• inc_clean <- inc_clean[,-4]
• inc_clean_train <- inc_clean_train[,-4]
• inc_clean_test <- inc_clean_test[,-4]log.updated.model2 <- glm(incomelevel~age+workclass+fnlwgt+educationnum+ occupation+relationship+race+sex+capitalgain+capitalloss+ hoursperweek, data=inc_clean_train, family="binomial")

Final Logistic Regression model

Final logistic regression model VIF

Logistic Regression model Evaluation

Misclassification => 818+377/7788 = 0.153

Tree based Classification

• tree.incomelevel <- tree(incomelevel~., data=inc_clean_train)
• Error in tree(incomelevel ~ ., data = inc_clean_train) :
• factor predictors must have at most 32 levels

Pruning Tree

Tree Evaluation

Misclassification => 291+964/7788 = 0.1611

Random Forest Classification

The gini index shows that age, education, and the relationship are all important variables.

Random Forest Tuning

• ######### Tune Random Forest ###########
• > mtry <- tuneRF(inc_clean_train, inc_clean_train$incomelevel, ntreeTry=10,
• + stepFactor=1.5,improve=TRUE, trace=TRUE, plot=TRUE, doBest=TRUE)
• mtry = 3 OOB error = 0.16% Searching left ... mtry = 2 OOB error = 0.52% -2.190979
• TRUE Searching right ... mtry = 4 OOB error = 0.09% 0.4730805 TRUE

• rf2.incomelevel <- randomForest(incomelevel~., data=inc_clean_train, mtry=4,
• importance=TRUE) > varImpPlot(rf2.incomelevel)

Random forest Variable Importance Plot

Random Forest Evaluation

Misclassification => 439+692/7788 = 0.1452

SVM Classification, Linear

• svm.fit <- svm(incomelevel~.,data=inc_clean_train, cost=0.01, kernel='linear')
• summary(svm.fit)

SVM Evaluation, Linear

Misclassification => 818+377/7788 = 0.1534

Comparison

Misclassification => 818+377/7788 = 0.1534

Misclassification => 439+692/7788 = 0.1452

Misclassification => 291+964/7788 = 0.1611

Misclassification => 818+377/7788 = 0.153

Discussion and Conclusion

• Fine tuning of SVM could perform better (both for linear and polynomial).
• The tuned random forest model has the lowest classification rate (optimized mtry variable).
• Logistic regression model is strong in predicting the income level.

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