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# JEDM_RR_JF_Final

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### JEDM_RR_JF_Final

1. 1. STAT 897D – Applied Data Mining and Statistical Learning Final Team Project on Analyzing Charitable Donation Data Using Classification and Prediction Models Rebecca Ray Jonathan Fivelsdal Joana E. Matos May 1st, 2016
2. 2. 1 INTRODUCTION Colleges, religions, non-profits and other humanitarian organizations receive charitable donations on a regular basis. Every one of these organizations could benefit from identifying cost-effective methods to achieve higher volumes of net profit. In this case study, we consider different data mining models in order to improve the cost-effectiveness of direct marketing campaigns to previous donors carried out by a particular charitable organization. The task of this study is two-fold. The first objective is to build a classification model from the most recent direct marketing campaign in order to identify likely donors such that the expected net profit is maximized. The second objective consists of developing a model that will predict donation amounts based on donor characteristics. For this, we fit a multitude of models to a training subset of the data in order to identify the most appropriate classification and prediction models. ANALYSIS The organization’s entire dataset included 8009 observations. In order to analyze and fit the data to several models, the entire dataset had been previously split into three groups: a training dataset comprising of 3984 observations, a validation dataset with 2018 observations, and test dataset comprising of 2007 observations. The training and validation data used a weighted model, over- representing the responders so that the training and validation samples have approximately equal numbers of donors and non-donors. The test dataset has the traditional 10% response rate making it necessary to adjust the mailing rate to calculate profit correctly. The outcome variables of interest are DONR (donor and non-donor) and donation amounts (DAMT). Twenty predictors were considered in our models: REG1-4, HOME, CHLD, HINC, GENF, WRAT, AVHV, INCM, INCA, PLOW, NPRO, TGIF, LGIF, RGIF, TDON, TLAG and AGIF (to see the details of each variable please refer to Appendix 1). An exploratory data analysis checked for missing values in the data set. Finding none, we next visualized the continuous variables. Histograms and a table of Box-Cox lambda values can be found in the Appendix (Figure 1. in Appendix 2). Skewed variables AVHV, INCM, INCA, TGIF, LGIF, RGIF, TLAG and AGIF were log -transformed. A cube root transformation was found to be more suitable to the PLOW variable. When called for, we also standardized the values in the training data such that each predictor variable has a mean of 0 and a standard deviation of 1. Classification To classify donors into two classes – donor and not-donor, we have made use of multiple resources learned throughout the course: General additive models (GAM), Logistic Regression (LR), Linear Discriminant Analysis (LDA), Quadratic Discriminant Analysis (QDA), K-nearest neighbors (KNN),
3. 3. 2 Decision trees, Bagged trees, Random forests, Boosting, and Support Vector Machines (SVM). All these approaches can be used for classification purposes. Models were compared by classification error rates, and more importantly based on profit. Prediction An array of models were used to find the best prediction model, namely, Linear Regression, Best subset selection, Ridge regression, Lasso, Gradient Boosting Machine and Random Forest. Cross validation was employed with several methods to improve model fit. To choose the best prediction models, we have considered the mean prediction error obtained when fitting the model to the training dataset and the validation dataset. The model that produced the lowest mean prediction error was chosen. Once the best classification and prediction models were identified, these models were applied to the test dataset. The DONR and DAMT variables in this dataset were set to “NA”. The application of the classification model to the test dataset classified individuals into the DONR variable as donor or nondonor. Similarly, the prediction model when applied to the test data produced a new variable DAMT as the predicted Donation Amounts in dollars. Please refer to the file “JEDM-RR-JF.csv” for these results. R was used to conduct all the analysis in this report. Some figures are included in the report as an example. The entire code and additional details can be found in the Appendix. RESULTS Classification Models developed for the DONR variable The first objective of this study was to generate a model that classifies donors in two classes: class 0 and class 1. In order to choose the model that best performs this task, we used two criteria: lowest classification error rate and highest projected profit. Ideally, projected mailings would also be the lowest. Logistic Regression Logistic regression models will investigate the probability that a certain response will belong to one of two categories, in this case being a donor or not. The logistic regression model that performed the best was one that included HINC 2 and excluded PLOW, REG4, and AVHV achieved through backward elimination. There were others that gave lower AIC scores but when applied to the validation data produced larger error rates and less profit. With the above-mentioned logistic regression model, the classification error rate was 34.1%, projected maximum profit was \$10,943.50 and projected mailings were 1,655.
4. 4. 3 Linear Discriminant Analysis (LDA) Linear Discriminant Analysis models the distribution of the different predictors separately for each of the response classes and then estimates the probability of a response Y to be in a certain class, given the predictor X. Here, we found that the best linear discriminant analysis included all variables including HINC 2. Removal of REG4 which has been the least helpful variable in other models did not improve the model. Fitting an LDA model to the data resulted in a model with a classification error rate of 19.9%, a projected profit of \$11,620.50 and 1,389 projected mailings (Table 1.). This was quite an improvement over the logistic regression model above. Quadratic Discriminant Analysis (QDA) QDA is very similar to LDA, except that it assumes that each class (donors and not donors in this case) will have its own covariance matrix. The best QDA also included all variables including the HINC 2. As in the LDA, removal of REG4 was detrimental to the model, so it was added back in. With the QDA model, the classification error rate was 23.5%, the projected profit was \$11,243.50 and there were 1,418 projected mailings. QDA performed slightly poorer than LDA. K-Nearest Neighbor (KNN) KNN is the most non-parametric model of the models created so far. It tries to estimate the distribution of all predictor variables to come closest to a Bayes classifier. The k values tested were between k=3 and k=14. The model that performed the best was the mode that used k=13 which is less flexible than the k=3 model. Generalized Additive Model (GAM) A smoothing spline was applied to the continuous variables. The best fitting model used a df = 10 and excluded the variables REG3, REG4, GENF, RGIF, AGIF, and LGIF. Eliminations were made using backward elimination. This model achieved both the best AIC score and profit amounts of the GAM candidate models (Figure 1). Decision Trees: Random Forests, Bagging and Gradient Boosting Model Random forests have a higher degree of flexibility than more traditional methods such as logistic regression and linear discriminant analysis and can provide a higher quality of classification than building a single decision tree. All random forest models in this report build 3500 trees with an interaction depth of 4. In order to identify a tree with low error, 10-fold cross-validation (CV) was performed. We concluded that random forests with 10 and 20 predictors displayed the lowest CV error (0.12 and 0.11, respectively). Even though CV error was slightly higher for the random forest with 10 predictors, the profit and validation error rates were much better. The maximum profit achieved by the random forest model using 10 predictors was \$11,774.50 with 1,254 mailings. Most actual donors and actual non-donors were correctly classified by the model when applied to the validation data set. The classification error rate for the model is 13.73%.
5. 5. 4 Figure 1. Expected net profit vs. number of mailings for the Gradient Boosting Machine model: maximum profit = \$11,941.50, number of mailings: 1,214. When using bagging, the model with 10 predictors also out-performed the model with 20 predictors. The classification error rate for this model was 16.5%, and the maximum profit was \$11,695.50 with 1,308 mailings (Table 1). For the GBM models, we experimented with different values for shrinkage (0.001 to 0.01) and number of trees (2,500 to 3,500). The GBM that we found performed the best used 3500 trees, a depth of 4 and a shrinkage of 0.005. For this model, we found that the maximum profit \$11,941.50 with 1,214 mailings, and the classification error rate was 11.4% (Table 1). This model out-performed all the remaining models, in terms of both classification error rate and maximum profit. We summarize the relevant results for all the classification models in the next table (Table 1). We observe that the models consisting of decision trees performed much better than the other classification models, both in terms of classification error rates, but also on the projected maximum profit. Among the decision trees models, we have found that the gradient boosting model with 3500 trees, a depth of 4 and a shrinkage of 0.005 was the best and it would therefore be our selection.
6. 6. 5 Table 1. Summary of results for the eight chosen classification models. Shown are the classification error rates, projected mailings and projected profit. Validation DataValidation DataValidation DataValidation Data Classification Model for DONRClassification Model for DONRClassification Model for DONRClassification Model for DONR Classification error rate Projected Mailings Projected Profit Logistic RegressionLogistic RegressionLogistic RegressionLogistic Regression 34.1% 1,655 \$10,943.50 LDALDALDALDA 19.9% 1,389 \$11,620.50 QDAQDAQDAQDA 23.5% 1,418 \$11,243.50 KNNKNNKNNKNN 18.4% 1,267 \$11,197.50 GAM with df=10GAM with df=10GAM with df=10GAM with df=10 27.8% 1,528 \$11,197.50 Decision Trees:Decision Trees:Decision Trees:Decision Trees: BaggingBaggingBaggingBagging 16.5% 1,308 \$11,695.50 Random ForestRandom ForestRandom ForestRandom Forest –––– 10 predictors10 predictors10 predictors10 predictors 13.7% 1,254 \$11,774.50 Gradient BoostingGradient BoostingGradient BoostingGradient Boosting 11.4% 1,214 \$11,941.50 Prediction Models developed for the DAMT variable The second goal of this project was to develop a model to predict donation amounts based on the characteristics of the donors. For this, we chose among our models using the criteria of the lowest mean prediction error. Least Squares, Best Subset and Backward Stepwise Regressions Some benefits of linear regression models are that they have low bias which makes them less prone to overfitting versus more flexible methods and they are also highly interpretable. We have performed Least Squares Regression, Best Subset Selection and Backward Stepwise selection. In order to evaluate these models, we have analyzed the BIC values. Figure 2. Shows the BIC values for models with different numbers of predictors obtained from fitting a Backwards Stepwise Regression to the training dataset. All three regressions had similar results and we found that the model with the lowest BIC contained 8 predictors: REG3, REG4, CHLD, HINC, TGIF, LGIF, RGIF, AGIF. Least Squares regression had the lowest Mean Prediction error – 1.62. However, the mean prediction error obtained when fitting a best subsets regression was only slightly bigger (1.63). Please refer to Table 2. For a summary of these results-
7. 7. 6 Figure 2. BIC values for Backwards Stepwise Regression models with different numbers of predictors. Support Vector Machine Support vector machines are called Support Vector regressions (SVR) when used in the prediction setting. It contains tuning parameters such as cost, gamma and epsilon. In order to fit a SVR model to the data, we used a fixed gamma value of 0.5 and we performed 10-fold CV to find useful values for the cost and epsilon parameters. The potential epsilon values we considered in the CV process were 0.1, 0.2 and 0.3 along with potential cost values of 0.01, 1 and 5. After performing 10-fold cross- validation, it appeared that 0.2 and 1 were promising values for epsilon and cost respectively. Using a cost value of 1, epsilon value of 0.2 and a gamma value of 0.5, we obtained a support vector regression model with 1,347 support vectors. When this was applied to the validation set, it resulted in a mean prediction error of 1.553 and a standard error of 0.174. Ridge Regression Ridge regression is similar to least squares, though the coefficients are estimated differently. This model creates shrinkage of the predictors by using a tuning parameter λ to obtain a set of coefficient estimates. For this problem, the best λ was 0.1141. The mean prediction error that resulted was 1.63 with a standard error of 0.16. Lasso Regression Lasso is another extension of linear regression, which used an alternative procedure of fitting in order to estimate the coefficients. Given that this procedure is somewhat restrictive, it shrinks some of the coefficients to exactly zero, unlike what it happens with Ridge. Despite being less flexible than linear regression, it is more interpretable. We fitted our dataset with a lasso regression model and concluded
8. 8. 7 that the mean prediction error was similar to the ones obtained with the other models (1.62), and the standard error was 0.16 (Table 2.) Principal Components Regression The PCR uses clustering to decrease the dimensionality of the problem space. Looking at the cluster graph below (Figure 3.), 14 components reduces the mean squared error to the lowest point. This suggests that there is very little redundancy in the variance accounted for in the prediction variables. This has been confirmed in earlier regression models. Like the other regression models, the PCR produced the same mean prediction error (1.63) and standard error (0.16). Figure 3. Mean Standard Error of Prediction for models with increasing number of components. Gradient Boosting Machine Apart from being used in classification problems, GBM models can also be used for prediction. GBM models that were composed of 3,500 trees appeared to perform well in the classification setting and so we considered a GBM model with 3,500 trees and a shrinkage value of 0.001 for prediction. When examining GBM models for classifying donors in the first part, we found that adjusting the shrinkage value created a higher performing model. After applying different shrinkage values, a GBM model with 3,500 trees and a shrinkage value of 0.01, produced a mean prediction error of 1.414 and a standard error of 0.162. This GBM model had the lowest mean prediction error considered thus far.
9. 9. 8 Random Forests Just as gradient boosting machines can be used for both classification and prediction, random forests can also be used for classification and prediction. After applying the random forest model using 10 predictors to the validation set, we obtained a mean prediction error of 1.679 and a standard error of 0.175. The mean prediction error of this random forest model was higher than every other prediction model considered thus far except for the GBM model with 3,500 trees and a shrinkage value of 0.001. The SVR model has a mean prediction error lower than most of the prediction models considered in this report, however, the mean prediction error of the SVR model is still higher than the GBM model using 3,500 trees and a shrinkage value of 0.01 (this GBM model has a mean prediction error of 1.414). PredictionPredictionPredictionPrediction Model for DModel for DModel for DModel for DAMTAMTAMTAMT Mean Prediction Error Standard Error Least Squares RegressionLeast Squares RegressionLeast Squares RegressionLeast Squares Regression 1.62 0.16 Best Subsets RegressionBest Subsets RegressionBest Subsets RegressionBest Subsets Regression 1.63 0.16 Backward Stepwise SelectionBackward Stepwise SelectionBackward Stepwise SelectionBackward Stepwise Selection 1.66 0.16 Support Vector MachineSupport Vector MachineSupport Vector MachineSupport Vector Machine (cost =1, ε = 0.2 and γ = 0.5) 1.55 0.17 Ridge RegressionRidge RegressionRidge RegressionRidge Regression 1.63 0.16 Lasso RegressionLasso RegressionLasso RegressionLasso Regression 1.62 0.16 Principal Components RegressionPrincipal Components RegressionPrincipal Components RegressionPrincipal Components Regression 1.63 0.16 Random ForestRandom ForestRandom ForestRandom Forest (10 predictors)(10 predictors)(10 predictors)(10 predictors) 1.68 0.17 Gradient Boosting MachineGradient Boosting MachineGradient Boosting MachineGradient Boosting Machine (3,500 trees and shrinkage = 0.01) 1.41 0.16 Table 2. Summary of results for the seven prediction models. Shown are the mean prediction and standard errors. DISCUSSION Every single kind of business requires some sort of investment and some kind of return, and its main objective is to maximize profit. Organizations that receive charitable donations are no different. This particular charitable organization is looking at a way of maximizing their net profit by capturing likely donors instead of targeting everyone with their current marketing strategy. The initial exploratory data analysis revealed that some variables would benefit from being transformed. In fact, it is common for amounts of money to be lognormally distributed and thus benefit from a logarithmic transformation. Versions of such variables will be normally distributed or approximately normally distributed (Mount and Zumel, 1973). Upon analysis, we log-transformed all the variables in the training set corresponding to an amount of money (AVHV, INCM, INCA, TGIF, LGIF,
10. 10. 9 RGIF and AGIF). We also considered useful to log-transform TLAG and to apply a cube root transformation to the PLOW variable. Several models were then fit to the dataset in order to identify the classification model that would achieve the highest maximum expected net profit value, as well as the predictive model with the lowest mean prediction error. From the battery of models we were taught throughout the course, we chose to investigate how Logistic Regression, LDA, QDA, KNN, GAM with df=10, Decision Trees, Bagging, Random Forest with 10 predictors and Gradient Boosting would perform to tackle the classification of the DONR response variable. The Gradient Boosting Machine model (GBM) with 3,500 trees and a shrinkage value of 0.05 produced the highest maximum net expected profit (\$11,941), together with the lowest classification error rate (11.4%). Interestingly it is also the model with the lowest number of projected mailings – 1,214. This type of boosting models grows trees sequentially, using information from previously grown trees. It uses shrinkage in order to shrink or reduce the impact of each additional fitted base-learners, and it reduces the size of incremental steps. Shrinkage is a classic method of controlling model complexity through introducing regularization and is used in model techniques such as lasso, ridge regression and GBMs (Gunn, 1998). It is therefore a method that will tend to keep only the most relevant variables, and it is a very flexible method in the sense that three different parameters can be tuned. It has been shown that increasing the value of the shrinkage parameter in a GBM model results in a more generalizable model (Natekin and Knoll, 2013). Whilst we considered initially a default value of 0.001, we have concluded later that a shrinkage value of 0.005 yields better results. Another tuning parameter is the number of trees that the model produces. We have started with a GBM that used 2,500 trees but concluded that increasing this number to 3,500 improved the performance of the model. This model was therefore the model that we would recommend the charitable organization to use in order to classify the donors. In order to develop a prediction model for the DAMT variable, we used the set of tools made available to us throughout this course that allows to fit a model to a quantitative response: Least Squares Regression, Best Subsets Regression, Support Vector Machine, Ridge Regression, Lasso Regression, Principal Components Regression and Gradient Boosting Machine. GBMs are interesting given that they allow to fit models regardless of whether the response variable is qualitative or quantitative. Also here, we found that the GBM model with a shrinkage value of 0.01 and 3,400 trees yielded the best results with the lowest mean prediction error of 1.41 and standard error. Thus, the GBM model with 3,500 trees and shrinkage of 0.01 was used to classify DONR responses in and predict donation amounts (DAMT responses) in the test dataset (please refer to the file “TeamJ_class_preds.csv” for these results). It is interesting to note that this flexibility of GBMs has been previously documented and reported by Natekin and Knoll (2013) who stated that their “…high flexibility makes the GBMs highly customizable to any particular data driven task” and that “GBMs have shown considerable success in not only practical applications, but also in various machine-learning and data-mining challenges.”
11. 11. 10 REFERENCES Gunn SR (1998). Support Vector Machines for Classification and Regression. University of Southampton. James G, Witten D, Hastie T, Tibshirani R. (2015). An Introduction to Statistical Learning with Applications in R. Springer New York Heidelberg Dordrecht London. Mount J and Zumel N (2014). Practical Data Science With R. Manning Publication Co. Natekin A and Knoll A (2013). Gradient boosting machines, a tutorial. Frontier in Neurorobotics, Volume 7, Article 21. (Retrieved from: http://doi.org/10.3389/fnbot.2013.00021). R Core Team. (2015). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. (Retrieved from: http://www.R-project.org/) Course notes for STAT 897D – Applied Data Mining and Statistical Learning. [Online]. [Accessed January - April 2016]. Available from: < https://onlinecourses.science.psu.edu/stat857/>
12. 12. 11 APPENDIX
13. 13. 12 APPENDIX 1 - VARIABLES Vars. Description Vars. Description ID Identification number PLOW % categorized as “low income” in potential donor’s neighborhood REG 5 regions indicator variables respectively called REG1, REG2, REG3 and REG4 NPRO Lifetime number of promotions received to date HOME (1 = homeowner, 0 = not a homeowner TGIF Dollar amount of lifetime gifts to date CHLD Number of children LGIF Dollar amount of largest gift to date HINC Household income (7 categories) RGIF Dollar amount of most recent gift GENF Gender (0 = Male, 1 = Female) TDON Number of months since last donation WRAT Wealth Rating (Wealth rating uses median family income and population statistics from each area to index relative within each state. The segments are denoted 0-9, with 9 being the highest wealth group and 0 being the lowest TLAG Number of months between first and second gift AVHV Average Home Value in potential donor’s neighborhood in \$ thousands AGIF Average dollar amount of gifts to date INCM Median Family Income in potential donor’s neighborhood in \$ thousands DONR Classification Response Variable (1=Donor, 0 = Non-donor) INCA Average Family Income in potential donor’s neighborhood in \$ thousands DAMT Prediction Response Variable (Donation amount in \$)
14. 14. 13 APPENDIX 2 – EXPLORATORY DATA ANALYSIS Figure 1. Histograms for all predictor variables
15. 15. 14 APPENDIX 3 – CODES
16. 16. library(ggplot2) library(tree) #Use tree package to create classification tree library(randomForest) library(nnet) library(gbm) library(caret) library(ggplot2) library(pbkrtest) library(glmnet) library(lme4) library(Matrix) library(gam) library(MASS) library(leaps) library(glmnet) #charity <- read.csv("~/Penn_State/STAT897D/Projects/Final_Project/charity.csv") #charity <- read.csv("charity.csv") charity <- read.csv("~/Penn_State/STAT897D/Projects/Final_Project/charity.csv") #charity <- read.csv("~/Documents/teaching/psu/charity.csv") #charity <- read.csv("charity.csv") #A subset of the data without the donr and damt variables charitySub <- subset(charity,select = -c(donr,damt)) #Check for missing values in the data excluding the donr and damt variables sum(is.na(charitySub)) #There are no missing data among the other variables # predictor transformations charity.t <- charity #A log transformed version of "avhv" is approximately normally distributed # versus the untransformed version of "avhv" charity.t\$avhv <- log(charity.t\$avhv) charity.t\$incm <- log(charity.t\$incm) charity.t\$inca <- log(charity.t\$inca) charity.t\$plow <- charity.t\$plow^(1/3) charity.t\$tgif <- log(charity.t\$tgif) charity.t\$lgif <- log(charity.t\$lgif) charity.t\$rgif <- log(charity.t\$rgif) charity.t\$tlag <- log(charity.t\$tlag) charity.t\$agif <- log(charity.t\$agif) # add further transformations if desired # for example, some statistical methods can struggle when predictors are highly skewed # set up data for analysis #Training Set Section data.train <- charity.t[charity\$part=="train",] x.train <- data.train[,2:21] c.train <- data.train[,22] # donr n.train.c <- length(c.train) # 3984 y.train <- data.train[c.train==1,23] # damt for observations with donr=1 n.train.y <- length(y.train) # 1995 #Validation Set Section data.valid <- charity.t[charity\$part=="valid",] x.valid <- data.valid[,2:21] c.valid <- data.valid[,22] # donr n.valid.c <- length(c.valid) # 2018 y.valid <- data.valid[c.valid==1,23] # damt for observations with donr=1 n.valid.y <- length(y.valid) # 999 #Test Set Section data.test <- charity.t[charity\$part=="test",] n.test <- dim(data.test)[1] # 2007 x.test <- data.test[,2:21] #Training Set Mean and Standard Deviation x.train.mean <- apply(x.train, 2, mean) x.train.sd <- apply(x.train, 2, sd) #Standardizing the Variables in the Training Set x.train.std <- t((t(x.train)-x.train.mean)/x.train.sd) # standardize to have zero mean and unit sd
17. 17. apply(x.train.std, 2, mean) # check zero mean apply(x.train.std, 2, sd) # check unit sd #Data Frame for the "donr" variable in the Training Set data.train.std.c <- data.frame(x.train.std, donr=c.train) # to classify donr data.train.std.y <- data.frame(x.train.std[c.train==1,], damt=y.train) # to predict damt when donr=1 #Standardizing the Variables in the Validation Set x.valid.std <- t((t(x.valid)-x.train.mean)/x.train.sd) # standardize using training mean and sd data.valid.std.c <- data.frame(x.valid.std, donr=c.valid) # to classify donr #Data Frame for the "donr" variable in the Validation Set data.valid.std.y <- data.frame(x.valid.std[c.valid==1,], damt=y.valid) # to predict damt when donr=1 #Standardizing the Variables in the Test Set x.test.std <- t((t(x.test)-x.train.mean)/x.train.sd) # standardize using training mean and sd data.test.std <- data.frame(x.test.std) # logistic Regression Model 3 is best library(MASS) boxplot(data.train) model.logistic <- glm(donr ~ reg1 + +reg2 + reg3 + reg4 + home + chld + hinc + I(hinc^2)+genf + wrat + avhv + incm + inca + plow + npro + tgif + lgif + rgif + tdon + tlag + agif, data.train, family=binomial("logit")) summary(model.logistic) model.logistic1 <- glm(donr ~ reg1 + +reg2 + reg3 + reg4 + home + chld + hinc + I(hinc^2)+genf + wrat + avhv + incm + inca + npro + tgif + lgif + rgif + tdon + tlag + agif, data.train, family=binomial("logit")) summary(model.logistic1) model.logistic2 <- glm(donr ~ reg1 + +reg2 + reg3 + home + chld + hinc + I(hinc^2)+genf + wrat + avhv + incm + inca + npro + tgif + lgif + rgif + tdon + tlag + agif, data.train, family=binomial("logit")) summary(model.logistic2) model.logistic3 <- glm(donr ~ reg1 + +reg2 + reg3 + home + chld + hinc + I(hinc^2)+genf + wrat + rgif + incm + inca + npro + tgif + lgif + tdon + tlag + agif, data.train, family=binomial("logit")) summary(model.logistic3) model.logistic4 <- glm(donr ~ reg1 + +reg2 + home + chld + hinc + I(hinc^2)+genf + wrat + rgif + incm + inca + npro + tgif + lgif + tdon + tlag + agif, data.train, family=binomial("logit")) summary(model.logistic4) model.logistic5 <- glm(donr ~ reg1 + +reg2 + home + chld + hinc + I(hinc^2)+genf + wrat + rgif + incm + inca + npro + tgif + tdon + tlag + agif, data.train, family=binomial("logit")) summary(model.logistic5) model.logistic6 <- glm(donr ~ reg1 + +reg2 + home + chld + hinc + I(hinc^2)+genf + wrat + rgif + incm + inca + tgif + tdon + tlag + agif, data.train, family=binomial("logit")) summary(model.logistic6) model.logistic7 <- glm(donr ~ reg1 + +reg2 + home + chld + hinc + I(hinc^2)+genf + wrat + rgif + incm + inca + tgif + tdon + tlag, data.train, family=binomial("logit")) summary(model.logistic7) post.valid.logistic <- predict(model.logistic,data.valid.std.c,type="response") # n.valid.c post probs post.valid.logistic1 <- predict(model.logistic1,data.valid.std.c,type="response") # n.valid.c post probs post.valid.logistic2 <- predict(model.logistic2,data.valid.std.c,type="response") # n.valid.c post probs post.valid.logistic3 <- predict(model.logistic3,data.valid.std.c,type="response") # n.valid.c post probs post.valid.logistic4 <- predict(model.logistic4,data.valid.std.c,type="response") # n.valid.c post probs post.valid.logistic5 <- predict(model.logistic5,data.valid.std.c,type="response") # n.valid.c post probs post.valid.logistic6 <- predict(model.logistic6,data.valid.std.c,type="response") # n.valid.c post probs post.valid.logistic7 <- predict(model.logistic7,data.valid.std.c,type="response") # n.valid.c post probs # calculate ordered profit function using average donation = \$14.50 and mailing cost = \$2 profit.logistic <- cumsum(14.5*c.valid[order(post.valid.logistic, decreasing=T)]-2) plot(profit.logistic) # see how profits change as more mailings are made n.mail.valid <- which.max(profit.logistic) # number of mailings that maximizes profits c(n.mail.valid, max(profit.logistic)) # report number of mailings and maximum profit cutoff.logistic <- sort(post.valid.logistic, decreasing=T)[n.mail.valid+1] # set cutoff based on n.mail.valid chat.valid.logistic <- ifelse(post.valid.logistic>cutoff.logistic, 1, 0) # mail to everyone above the cutoff table(chat.valid.logistic, c.valid) # classification table 1-mean(chat.valid.logistic==c.valid) # True Neg 345 True Pos 983 Miss 34.19% Profit 10937.5 profit.logistic1 <- cumsum(14.5*c.valid[order(post.valid.logistic1, decreasing=T)]-2) plot(profit.logistic1) # see how profits change as more mailings are made n.mail.valid <- which.max(profit.logistic1) # number of mailings that maximizes profits c(n.mail.valid, max(profit.logistic1)) # report number of mailings and maximum profit cutoff.logistic1 <- sort(post.valid.logistic1, decreasing=T)[n.mail.valid+1] # set cutoff based on n.mail.valid chat.valid.logistic1 <- ifelse(post.valid.logistic1>cutoff.logistic1, 1, 0) # mail to everyone above the cutoff table(chat.valid.logistic1, c.valid) # classification table 1-mean(chat.valid.logistic1==c.valid)
18. 18. # True Neg 345 True Pos 983 Miss 34.19% Profit 10939.5 profit.logistic2 <- cumsum(14.5*c.valid[order(post.valid.logistic2, decreasing=T)]-2) plot(profit.logistic2) # see how profits change as more mailings are made n.mail.valid <- which.max(profit.logistic2) # number of mailings that maximizes profits c(n.mail.valid, max(profit.logistic2)) # report number of mailings and maximum profit cutoff.logistic2 <- sort(post.valid.logistic2, decreasing=T)[n.mail.valid+1] # set cutoff based on n.mail.valid chat.valid.logistic2 <- ifelse(post.valid.logistic2>cutoff.logistic2, 1, 0) # mail to everyone above the cutoff table(chat.valid.logistic2, c.valid) # classification table 1-mean(chat.valid.logistic2==c.valid) # True Neg 345 True Pos 983 Miss 34.19% Profit 10939.5 profit.logistic3 <- cumsum(14.5*c.valid[order(post.valid.logistic3, decreasing=T)]-2) plot(profit.logistic3) # see how profits change as more mailings are made n.mail.valid <- which.max(profit.logistic3) # number of mailings that maximizes profits c(n.mail.valid, max(profit.logistic3)) # report number of mailings and maximum profit cutoff.logistic3 <- sort(post.valid.logistic3, decreasing=T)[n.mail.valid+1] # set cutoff based on n.mail.valid chat.valid.logistic3 <- ifelse(post.valid.logistic3>cutoff.logistic3, 1, 0) # mail to everyone above the cutoff table(chat.valid.logistic3, c.valid) # classification table 1-mean(chat.valid.logistic3==c.valid) # True Neg 347 True Pos 983 Miss 34.09% Profit 10943.5 profit.logistic4 <- cumsum(14.5*c.valid[order(post.valid.logistic4, decreasing=T)]-2) plot(profit.logistic4) # see how profits change as more mailings are made n.mail.valid <- which.max(profit.logistic4) # number of mailings that maximizes profits c(n.mail.valid, max(profit.logistic4)) # report number of mailings and maximum profit cutoff.logistic4 <- sort(post.valid.logistic4, decreasing=T)[n.mail.valid+1] # set cutoff based on n.mail.valid chat.valid.logistic4 <- ifelse(post.valid.logistic4>cutoff.logistic4, 1, 0) # mail to everyone above the cutoff table(chat.valid.logistic4, c.valid) # classification table 1-mean(chat.valid.logistic4==c.valid) # True Neg 346 True Pos 983 Miss 34.14% Profit 10941.5 profit.logistic5 <- cumsum(14.5*c.valid[order(post.valid.logistic5, decreasing=T)]-2) plot(profit.logistic5) # see how profits change as more mailings are made n.mail.valid <- which.max(profit.logistic5) # number of mailings that maximizes profits c(n.mail.valid, max(profit.logistic5)) # report number of mailings and maximum profit cutoff.logistic5 <- sort(post.valid.logistic5, decreasing=T)[n.mail.valid+1] # set cutoff based on n.mail.valid chat.valid.logistic5 <- ifelse(post.valid.logistic5>cutoff.logistic5, 1, 0) # mail to everyone above the cutoff table(chat.valid.logistic5, c.valid) # classification table 1-mean(chat.valid.logistic5==c.valid) # True Neg 345 True Pos 982 Miss 34.24% Profit 10927 profit.logistic6 <- cumsum(14.5*c.valid[order(post.valid.logistic6, decreasing=T)]-2) plot(profit.logistic6) # see how profits change as more mailings are made n.mail.valid <- which.max(profit.logistic6) # number of mailings that maximizes profits c(n.mail.valid, max(profit.logistic6)) # report number of mailings and maximum profit cutoff.logistic6 <- sort(post.valid.logistic6, decreasing=T)[n.mail.valid+1] # set cutoff based on n.mail.valid chat.valid.logistic6 <- ifelse(post.valid.logistic6>cutoff.logistic6, 1, 0) # mail to everyone above the cutoff table(chat.valid.logistic6, c.valid) # classification table 1-mean(chat.valid.logistic6==c.valid) # True Neg 323 True Pos 986 35.13% profit.logistic7 <- cumsum(14.5*c.valid[order(post.valid.logistic7, decreasing=T)]-2) plot(profit.logistic7) # see how profits change as more mailings are made n.mail.valid <- which.max(profit.logistic7) # number of mailings that maximizes profits c(n.mail.valid, max(profit.logistic7)) # report number of mailings and maximum profit cutoff.logistic7 <- sort(post.valid.logistic7, decreasing=T)[n.mail.valid+1] # set cutoff based on n.mail.valid chat.valid.logistic7 <- ifelse(post.valid.logistic7>cutoff.logistic7, 1, 0) # mail to everyone above the cutoff table(chat.valid.logistic7, c.valid) # classification table 1-mean(chat.valid.logistic7==c.valid) # True Neg 324, True Pos 986 35.08% miss # linear discriminant analysis library(MASS) model.lda1 <- lda(donr ~ reg1 +reg2 + reg3 + reg4 + home + chld + hinc + I(hinc^2) + genf + wrat + avhv + incm + inca + plow + npro + tgif + lgif + rgif + tdon + tlag + agif, data.train.std.c) # include additional terms on the fly using I()
19. 19. # Note: strictly speaking, LDA should not be used with qualitative predictors, # but in practice it often is if the goal is simply to find a good predictive model post.valid.lda1 <- predict(model.lda1, data.valid.std.c)\$posterior[,2] # n.valid.c post probs # calculate ordered profit function using average donation = \$14.50 and mailing cost = \$2 profit.lda1 <- cumsum(14.5*c.valid[order(post.valid.lda1, decreasing=T)]-2) plot(profit.lda1) # see how profits change as more mailings are made n.mail.valid <- which.max(profit.lda1) # number of mailings that maximizes profits c(n.mail.valid, max(profit.lda1)) # report number of mailings and maximum profit # 1389.0 11620.5 cutoff.lda1 <- sort(post.valid.lda1, decreasing=T)[n.mail.valid+1] # set cutoff based on n.mail.valid chat.valid.lda1 <- ifelse(post.valid.lda1>cutoff.lda1, 1, 0) # mail to everyone above the cutoff table(chat.valid.lda1, c.valid) # classification table # c.valid #chat.valid.lda1 0 1 # 0 623 6 # 1 396 993 1-mean(chat.valid.lda1==c.valid) #Error rate # Quadratic Discriminant Analysis model.qda <- qda(donr ~ reg1 +reg2 + reg3 + reg4 + home + chld + hinc + I(hinc^2) + genf + wrat + avhv + incm + inca + plow + npro + tgif + lgif + rgif + tdon + tlag + agif, data.train.std.c) # include additional terms on the fly using I() post.valid.qda <- predict(model.qda, data.valid.std.c)\$posterior[,2] # n.valid.c post probs # calculate ordered profit function using average donation = \$14.50 and mailing cost = \$2 profit.qda <- cumsum(14.5*c.valid[order(post.valid.qda, decreasing=T)]-2) plot(profit.qda) # see how profits change as more mailings are made n.mail.valid <- which.max(profit.qda) # number of mailings that maximizes profits c(n.mail.valid, max(profit.qda)) # report number of mailings and maximum profit # 1418.0 11243.5 cutoff.qda <- sort(post.valid.qda, decreasing=T)[n.mail.valid+1] # set cutoff based on n.mail.valid chat.valid.qda <- ifelse(post.valid.qda>cutoff.qda, 1, 0) # mail to everyone above the cutoff table(chat.valid.qda, c.valid) # classification table # c.valid #chat.valid.qda 0 1 # 0 572 28 # 1 447 971 1-mean(chat.valid.qda==c.valid) #Error rate #K Nearest Neighbors library(class) set.seed(1) post.valid.knn=knn(x.train.std,x.valid.std,c.train,k=13) # calculate ordered profit function using average donation = \$14.50 and mailing cost = \$2 profit.knn <- cumsum(14.5*c.valid[order(post.valid.knn, decreasing=T)]-2) plot(profit.knn) # see how profits change as more mailings are made n.mail.valid <- which.max(profit.knn) # number of mailings that maximizes profits c(n.mail.valid, max(profit.knn)) # report number of mailings and maximum profit # 1267.0 11197.5 table(post.valid.knn, c.valid) # classification table # c.valid #chat.valid.knn 0 1 # 0 699 52 # 1 320 947 # check n.mail.valid = 320+947 = 1267 # check profit = 14.5*947-2*1267 = 11197.5 1-mean(post.valid.knn==c.valid) #Error rate #Mailings and Profit values for different values of k # k=3 1231 10617
20. 20. # k=8 1248 11018 # k=10 1261.0 11151.5 # k=13 1267.0 11197.5 # k=14 1268.0 11137.5 #GAM library(gam) model.gam <- gam(donr ~ reg1 + reg2 + reg3 + reg4 + home + s(chld,df=5)+ s(hinc,df=5) +s(I(hinc^2), df=5) + genf + s(wrat,df=5) + s(avhv,df=5) + s(inca,df=5)+ s(plow,df=5) + s(npro,df=5) + s(tgif,df=5) + s(lgif,df=5) + s(rgif,df=5) + s(tdon,df=5) + s(tlag,df=5) + s(agif,df=5), data.train, family=binomial) summary(model.gam) model.gam <- gam(donr ~ reg1 + reg2 + reg3 + home + s(chld,df=5)+ s(hinc,df=5) +s(I(hinc^2), df=5) + genf + s(wrat,df=5) + s(avhv,df=5) + s(inca,df=5)+ s(plow,df=5) + s(npro,df=5) + s(tgif,df=5) + s(lgif,df=5) + s(rgif,df=5) + s(tdon,df=5) + s(tlag,df=5) + s(agif,df=5), data.train, family=binomial) summary(model.gam) model.gam <- gam(donr ~ reg1 + reg2 + reg3 + home + s(chld,df=5)+ s(hinc,df=5) +s(I(hinc^2), df=5) + s(wrat,df=5) + s(avhv,df=5) + s(inca,df=5)+ s(plow,df=5) + s(npro,df=5) + s(tgif,df=5) + s(lgif,df=5) + s(rgif,df=5) + s(tdon,df=5) + s(tlag,df=5) + s(agif,df=5), data.train, family=binomial) summary(model.gam) model.gam <- gam(donr ~ reg1 + reg2 + home + s(chld,df=5)+ s(hinc,df=5) +s(I(hinc^2), df=5) + s(wrat,df=5) + s(avhv,df=5) + s(inca,df=5)+ s(plow,df=5) + s(npro,df=5) + s(tgif,df=5) + s(lgif,df=5) + s(rgif,df=5) + s(tdon,df=5) + s(tlag,df=5) + s(agif,df=5), data.train, family=binomial) summary(model.gam) model.gam <- gam(donr ~ reg1 + reg2 + home + s(chld,df=5)+ s(hinc,df=5) +s(I(hinc^2), df=5) + s(wrat,df=5) + s(avhv,df=5) + s(inca,df=5)+ s(plow,df=5) + s(npro,df=5) + s(tgif,df=5) + s(lgif,df=5) + s(tdon,df=5) + s(tlag,df=5) + s(agif,df=5), data.train, family=binomial) summary(model.gam) model.gam <- gam(donr ~ reg1 + reg2 + home + s(chld,df=5)+ s(hinc,df=5) +s(I(hinc^2), df=5) + s(wrat,df=5) + s(avhv,df=5) + s(inca,df=5)+ s(plow,df=5) + s(npro,df=5) + s(tgif,df=5) + s(lgif,df=5) + s(tdon,df=5) + s(tlag,df=5), data.train, family=binomial) summary(model.gam) model.gam <- gam(donr ~ reg1 + reg2 + home + s(chld,df=5)+ s(hinc,df=5) +s(I(hinc^2), df=5) + s(wrat,df=5) + s(avhv,df=5) + s(inca,df=5)+ s(plow,df=5) + s(npro,df=5) + s(tgif,df=5) + s(tdon,df=5) + s(tlag,df=5), data.train, family=binomial) summary(model.gam) post.valid.gam <- predict(model.gam,data.valid.std.c,type="response") # n.valid.c post probs profit.gam <- cumsum(14.5*c.valid[order(post.valid.gam, decreasing=T)]-2) plot(profit.gam) # see how profits change as more mailings are made n.mail.valid <- which.max(profit.gam) # number of mailings that maximizes profits c(n.mail.valid, max(profit.gam)) # report number of mailings and maximum profit cutoff.gam <- sort(post.valid.gam, decreasing=T)[n.mail.valid+1] # set cutoff based on n.mail.valid chat.valid.gam <- ifelse(post.valid.gam>cutoff.gam, 1, 0) # mail to everyone above the cutoff table(chat.valid.gam, c.valid) # classification table 1-mean(chat.valid.gam==c.valid) # error rate 21.6% Profit 10461.5 mailings 2012 #GAM df=10 library(gam) model.gam2 <- gam(donr ~ reg1 + reg2 + home + s(chld,df=10) + s(hinc,df=10) +s(I(hinc^2), df=10) + s(wrat,df=10) + s(avhv,df=10) + s(inca,df=10)+ s(plow,df=10) + s(npro,df=10) + s(tgif,df=10) + s(tdon,df=10) + s(tlag,df=10), data.train, family=binomial) summary(model.gam2) post.valid.gam2 <- predict(model.gam2,data.valid.std.c,type="response") # n.valid.c post probs profit.gam2 <- cumsum(14.5*c.valid[order(post.valid.gam2, decreasing=T)]-2) plot(profit.gam2) # see how profits change as more mailings are made n.mail.valid <- which.max(profit.gam2) # number of mailings that maximizes profits c(n.mail.valid, max(profit.gam2)) # report number of mailings and maximum profit cutoff.gam2 <- sort(post.valid.gam2, decreasing=T)[n.mail.valid+1] # set cutoff based on n.mail.valid chat.valid.gam2 <- ifelse(post.valid.gam2>cutoff.gam2, 1, 0) # mail to everyone above the cutoff table(chat.valid.gam2, c.valid) # classification table 1-mean(chat.valid.gam2==c.valid) # 27.8% Profit 11197.5 Mailing 1528 #GAM df=15 library(gam)
21. 21. model.gam <- gam(donr ~ reg1 + reg2 + home + s(chld,df=15)+ s(hinc,df=15)+s(I(hinc^2),df=10) + s(wrat,df=15) + s(avhv,df=15) + s(inca,df=15)+ s(plow,df=15) + s(npro,df=15) + s(tgif,df=15) + s(tdon,df=15) + s(tlag,df=15), data.train, family=binomial) summary(model.gam) post.valid.gam <- predict(model.gam,data.valid.std.c,type="response") # n.valid.c post probs profit.gam <- cumsum(14.5*c.valid[order(post.valid.gam, decreasing=T)]-2) plot(profit.gam) # see how profits change as more mailings are made n.mail.valid <- which.max(profit.gam) # number of mailings that maximizes profits c(n.mail.valid, max(profit.gam)) # report number of mailings and maximum profit cutoff.gam <- sort(post.valid.gam, decreasing=T)[n.mail.valid+1] # set cutoff based on n.mail.valid chat.valid.gam <- ifelse(post.valid.gam>cutoff.gam, 1, 0) # mail to everyone above the cutoff table(chat.valid.gam, c.valid) # classification table 1-mean(chat.valid.gam==c.valid) # errror rate 41.1 Profit 10764.5 Mailings 1817 #GAM df=15 library(gam) model.gam <- gam(donr ~ reg1 + reg2 + reg3 + reg4 + home + s(chld,df=20)+ s(hinc,df=20) + genf + s(wrat,df=20) + s(avhv,df=20) + s(inca,df=20)+ s(plow,df=20) + s(npro,df=20) + s(tgif,df=20) + s(lgif,df=20) + s(rgif,df=20) + s(tdon,df=20) + s(tlag,df=20) + s(agif,df=20), data.train, family=binomial) summary(model.gam) post.valid.gam <- predict(model.gam,data.valid.std.c,type="response") # n.valid.c post probs profit.gam <- cumsum(14.5*c.valid[order(post.valid.gam, decreasing=T)]-2) plot(profit.gam) # see how profits change as more mailings are made n.mail.valid <- which.max(profit.gam) # number of mailings that maximizes profits c(n.mail.valid, max(profit.gam)) # report number of mailings and maximum profit cutoff.gam <- sort(post.valid.gam, decreasing=T)[n.mail.valid+1] # set cutoff based on n.mail.valid chat.valid.gam <- ifelse(post.valid.gam>cutoff.gam, 1, 0) # mail to everyone above the cutoff table(chat.valid.gam, c.valid) # classification table 1-mean(chat.valid.gam==c.valid) #error rate 48.6% Profit 10517 Mailing 1977 ############################# #Random Forests for Classification ############################# library(randomForest) #Possible Predictors for the random forest data.train.std.c.predictors <- data.train.std.c[,names(data.train.std.c)!="donr"] #This code evaluates the performance of random forests using different numbers #of predictors by means of 10 fold cross-validation rf.cv.results <- rfcv(data.train.std.c.predictors, as.factor(data.train.std.c\$donr), cv.fold=10) with(rf.cv.results,plot(n.var,error.cv,main = "Random Forest CV Error Vs. Number of Predictors", xlab = "Number of Predictors", ylab = "CV Error", type="b",lwd=5,col="red")) #Table of number of the number of predictors versus errors in random forest random.forest.error <- rbind(rf.cv.results\$n.var,rf.cv.results\$error.cv) rownames(random.forest.error) <- c("Number of Predictors","Random Forest Error") random.forest.error #The minimum cross-validated error for a random forest is the random forest #with 20 predictors. The CV error for a random forest using 20 predictors is 0.11 # and the CV error for a random forest using 10 predictors is 0.12. Since the
22. 22. # CV error is not that much higher for the random forest with 10 predictors # than the random forest using 20 predictors, we will first use a random forest # using 10 predictors. ################################ #Random Forest Using 10 Predictors ################################ require(randomForest) set.seed(1) #Seed for the random forest that uses 10 predictors rf.charity.10 <- randomForest(x = data.train.std.c.predictors ,y=as.factor(data.train.std.c\$donr), mtry=10) rf.charity.10.posterior.valid <- predict(rf.charity.10, data.valid.std.c, type="prob")[,2] # n.valid post probs profit.charity.RF.10 <- cumsum(14.5*c.valid[order(rf.charity.10.posterior.valid, decreasing=T)]-2) n.mail.valid <- which.max(profit.charity.RF.10 ) # number of mailings that maximizes profits c(n.mail.valid, max(profit.charity.RF.10)) # report number of mailings and maximum profit cutoff.charity.10 <- sort(rf.charity.10.posterior.valid, decreasing=T)[n.mail.valid+1] # set cutoff based on n.mail.valid chat.valid.charity.10 <- ifelse(rf.charity.10.posterior.valid>cutoff.charity.10, 1, 0) # mail to everyone above the cutoff table(chat.valid.charity.10, c.valid) # classification table #Classification Matrix #0 1 #0 760 18 #1 259 981 ################################ #Bag - (Random Forest using all 20 possible predictors) ################################ require(randomForest) set.seed(1) bag.charity <- randomForest(x = data.train.std.c.predictors ,y=as.factor(data.train.std.c\$donr), mtry=20) bag.charity.posterior.valid <- predict(bag.charity, data.valid.std.c, type="prob")[,2] # n.valid post probs profit.charity.bag <- cumsum(14.5*c.valid[order(bag.charity.posterior.valid, decreasing=T)]-2) n.mail.valid <- which.max(profit.charity.bag ) # number of mailings that maximizes profits c(n.mail.valid, max(profit.charity.bag)) # report number of mailings and maximum profit #1308 mailings and Maximum Profit \$11,695.50 cutoff.bag <- sort(bag.charity.posterior.valid, decreasing=T)[n.mail.valid+1] # set cutoff based on n.mail.valid chat.valid.bag <- ifelse(bag.charity.posterior.valid >cutoff.bag, 1, 0) # mail to everyone above the cutoff table(chat.valid.bag, c.valid) # classification table # Classification Matrix #0 1 #0 699 13 #1 320 986 #Comparision of the random forest that uses all 20 predictors (the bag) #Versus the random forest that uses 10 predictors. # The maximum profit produced by the random forest using 10 predictors # is \$11,744.50 while the maximum profit produced by the random forest # using all 20 predictors is \$11,695.50. The number of mailings required # for the maximum profit produced by the random forest using 10 predictors # is 1,240 mailings while the number of mailings required for the maximum profit # produced by the bag model (random forest using all 20 predictors) # is 1,308 mailings. #Gradient Boosting Machine (GBM) - Section
23. 23. library(gbm) set.seed(1) #GBM with 2,500 trees boost.charity <- gbm(donr~., data= data.train.std.c, distribution = "bernoulli",n.trees=2500,interaction.depth=5) yhat.boost.charity <- predict(boost.charity,newdata=data.valid.std.c, n.trees=2500) mean((yhat.boost.charity - data.valid.std.y)^2) #Validation Set MSE = 12.64 boost.charity.posterior.valid <- predict(boost.charity,n.trees=2500, data.valid.std.c, type="response") # n.valid post probs profit.charity.GBM <- cumsum(14.5*c.valid[order(boost.charity.posterior.valid, decreasing=T)]-2) plot(profit.charity.GBM ) # see how profits change as more mailings are made n.mail.valid <- which.max(profit.charity.GBM ) # number of mailings that maximizes profits c(n.mail.valid, max(profit.charity.GBM )) # report number of mailings and maximum profit #Send out 1280 mailing and maximum profit: \$11,737 cutoff.gbm <- sort(boost.charity.posterior.valid , decreasing=T)[n.mail.valid+1] # set cutoff based on n.mail.valid chat.valid.gbm <- ifelse(boost.charity.posterior.valid >cutoff.gbm, 1, 0) # mail to everyone above the cutoff table(chat.valid.gbm, c.valid) # classification table #Confusion Matrix for GBM with 2,500 trees # 0 1 #0 725 13 #1 294 986 #GBM with 3,500 trees set.seed(1) boost.charity.3500 <- gbm(donr~., data= data.train.std.c, distribution = "bernoulli",n.trees=3500,interaction.depth=5) yhat.boost.charity.3500 <- predict(boost.charity.3500,newdata=data.valid.std.c, n.trees=3500) mean((yhat.boost.charity.3500 - data.valid.std.y)^2) #Validation Set MSE = 13.37 boost.charity.posterior.valid.3500 <- predict(boost.charity.3500,n.trees=3500, data.valid.std.c, type="response") # n.valid post probs profit.charity.GBM.3500 <- cumsum(14.5*c.valid[order(boost.charity.posterior.valid.3500, decreasing=T)]-2) plot(profit.charity.GBM.3500 ) # see how profits change as more mailings are made n.mail.valid <- which.max(profit.charity.GBM.3500 ) # number of mailings that maximizes profits c(n.mail.valid, max(profit.charity.GBM.3500 )) # report number of mailings and maximum profit #Send out 1300 mailing and maximum profit: \$11,784.00 cutoff.gbm.3500 <- sort(boost.charity.posterior.valid.3500 , decreasing=T)[n.mail.valid+1] # set cutoff based on n.mail.valid chat.valid.gbm.3500 <- ifelse(boost.charity.posterior.valid.3500 >cutoff.gbm.3500, 1, 0) # mail to everyone above the cutoff table(chat.valid.gbm.3500, c.valid) # classification table #Confusion Matrix for GBM with 3500 trees with shrinkage = 0.001 # 0 1 #0 711 7 #1 308 992 require(gbm) set.seed(1) boost.charity.3500.hundreth.Class <- gbm(donr~.,
24. 24. data= data.train.std.c, distribution = "bernoulli",n.trees=3500,interaction.depth=4, shrinkage = 0.005) yhat.boost.charity.3500.hundreth.Class <- predict(boost.charity.3500.hundreth.Class,newdata=data.valid.std.c, n.trees=3500) mean((yhat.boost.charity.3500.hundreth.Class - data.valid.std.y)^2) #Validation Set MSE = 23.02 boost.charity.posterior.valid.3500.hundreth.Class <- predict(boost.charity.3500.hundreth.Class,n.trees=3500, data.valid.std.c, type="response") # n.valid post probs profit.charity.GBM.3500.hundreth.Class <- cumsum(14.5*c.valid[order(boost.charity.posterior.valid.3500.hundreth.Class, decreasing=T)]-2) plot(profit.charity.GBM.3500.hundreth.Class) # see how profits change as more mailings are made n.mail.valid <- which.max(profit.charity.GBM.3500.hundreth.Class) # number of mailings that maximizes profits c(n.mail.valid, max(profit.charity.GBM.3500.hundreth.Class)) # report number of mailings and maximum profit #Send out 1214 mailing and maximum profit: \$11,941.50 cutoff.gbm.3500.hundreth.Class <- sort(boost.charity.posterior.valid.3500.hundreth.Class , decreasing=T) [n.mail.valid+1] # set cutoff based on n.mail.valid chat.valid.gbm.3500.hundreth.Class <- ifelse(boost.charity.posterior.valid.3500.hundreth.Class >cutoff.gbm.3500.hundreth.Class, 1, 0) # mail to everyone above the cutoff table(chat.valid.gbm.3500.hundreth.Class, c.valid) # classification table #Confusion Matrix for GBM with 3500 trees with shrinkage = 0.01 # 0 1 #0 796 8 #1 223 991 ## Prediction Modeling ## # Multiple regression model.ls1 <- lm(damt ~ reg1 + reg2 + reg3 + reg4 + home + chld + hinc + genf + wrat + avhv + incm + inca + plow + npro + tgif + lgif + rgif + tdon + tlag + agif, data.train.std.y) pred.valid.ls1 <- predict(model.ls1, newdata = data.valid.std.y) # validation predictions mean((y.valid - pred.valid.ls1)^2) # mean prediction error # 1.621358 sd((y.valid - pred.valid.ls1)^2)/sqrt(n.valid.y) # std error # 0.1609862 # drop wrat, npro, inca model.ls2 <- lm(damt ~ reg1 + reg2 + reg3 + reg4 + home + chld + hinc + genf + avhv + incm + plow + tgif + lgif + rgif + tdon + tlag + agif, data.train.std.y) pred.valid.ls2 <- predict(model.ls2, newdata = data.valid.std.y) # validation predictions mean((y.valid - pred.valid.ls2)^2) # mean prediction error # 1.621898 sd((y.valid - pred.valid.ls2)^2)/sqrt(n.valid.y) # std error # 0.1608288 # Best Subset, Backwards Stepwise Regression library(leaps) charity.sub.reg.back_step <- regsubsets(damt ~.,data.train.std.y,method = "backward", nvmax= 20) plot(charity.sub.reg.back_step,scale="bic") #reg3,reg4,home,chld,hinc,incm,tgif, lgif, rgif and agif #Checked forwards stepwise, same variables returned for minimum bic #Prediction Model #1 #Least Squares Regression Model - Using predcitors from backward stepwise regression model.pred.model.1 <- lm(damt ~ reg3 + reg4 + home + chld + hinc + incm + tgif + lgif + rgif + agif, data = data.train.std.y) pred.valid.model1 <- predict(model.pred.model.1, newdata = data.valid.std.y) # validation predictions
25. 25. mean((y.valid - pred.valid.model1)^2) # mean prediction error # 1.628554 sd((y.valid - pred.valid.model1)^2)/sqrt(n.valid.y) # std error # 0.1603296 charity.sub.reg.best <- regsubsets(damt ~.,data.train.std.y,nvmax= 20) plot(charity.sub.reg.best,scale="bic") #reg3,reg4,home,chld,hinc,incm,tgif, lgif, rgif and agif #Same variables as backwards stepwise #Principal Components Regression library(pls) set.seed(1) pcr.fit=pcr(damt~.,data=data.train.std.y,scale=TRUE,validation="CV") validationplot(pcr.fit,val.type="MSEP") pred.valid.pcr=predict(pcr.fit,data.valid.std.y,ncomp=15) mean((pred.valid.pcr-y.valid)^2) # 1.630981 sd((y.valid - pred.valid.pcr)^2)/sqrt(n.valid.y) # std error #0.1609462 #Support Vector Machine (SVM) library(e1071) set.seed(1) svm.charity <- svm(damt ~.,kernel = "radial",data = data.train.std.y) pred.valid.SVM.model1 <- predict(svm.charity,newdata=data.valid.std.y) mean((y.valid - pred.valid.SVM.model1)^2) # mean prediction error # 1.566 sd((y.valid - pred.valid.SVM.model1)^2)/sqrt(n.valid.y) # std error # 0.175 set.seed(1) #10-fold cross validation for SVM using the default gamma of 0.5 # and using varying values of epsilon and cost charity.svm.tune <- tune(svm,damt~.,kernel = "radial",data=data.train.std.y, ranges = list(epsilon = c(0.1,0.2,0.3), cost = c(0.01,1,5))) summary(charity.svm.tune) #The SVM model has an epsilon of 0.2, a cost of 1 and a gamma of 0.5 svm.charity1 <- charity.svm.tune\$best.model #For the SVM chosen; cost = 1, gamma =0.05 and epsilon=0.2 #There are 1,345 support vectors summary(charity.svm.tune\$best.model) pred.valid.SVM.model <- predict(svm.charity1,newdata=data.valid.std.y) mean((y.valid - pred.valid.SVM.model)^2) # mean prediction error # 1.552217 sd((y.valid - pred.valid.SVM.model)^2)/sqrt(n.valid.y) # std error # 0.1736719 library(glmnet) x=model.matrix(damt~.,data.train.std.y) y=y.train grid=10^seq(10,-2,length=100) ridge.mod=glmnet(x,y,alpha=0,lambda=grid) dim(coef(ridge.mod)) set.seed(1) cv.out=cv.glmnet(x,y,alpha=0)
27. 27. cutoff.test <- sort(post.test, decreasing=T)[n.mail.test+1] # set cutoff based on n.mail.test chat.test <- ifelse(post.test>cutoff.test, 1, 0) # mail to everyone above the cutoff table(chat.test) # 0 1 # 1719 288 # based on this model we'll mail to the 288 highest posterior probabilities # See below for saving chat.test into a file for submission # select GBM with 3,500 trees and shrinkage = 0.01 (with Gaussian Distribution) #since it has minimum mean prediction error in the validation sample yhat.test <- predict(boost.charity.3500.hundreth.Pred,n.trees = 3500, newdata = data.test.std) # test predictions # Save final results for both classification and regression length(chat.test) # check length = 2007 length(yhat.test) # check length = 2007 chat.test[1:10] # check this consists of 0s and 1s yhat.test[1:10] # check this consists of plausible predictions of damt ip <- data.frame(chat=chat.test, yhat=yhat.test) # data frame with two variables: chat and yhat write.csv(ip, file="JEDM-RR-JF.csv", row.names=FALSE) # use group member initials for file name # submit the csv file in Angel for evaluation based on actual test donr and damt values

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