Bagging Model

Description

Bagging Model

Usage

BAG_Model(Data, xvar, yvar)

Arguments

Details

Decision trees suffer from high variance (If we split the training data-set randomly into two parts and set a decision tree to both parts, the results might be quite different). Bagging is an ensemble procedure which reduces the variance and increases the prediction accuracy of a statistical learning method by considering many training sets (\hat{f}^{1}(x),\hat{f}^{2}(x),\ldots,\hat{f}^{B}(x)) from the population. Since we can not have multiple training-sets, from a single training data-set, we can generate B different bootstrapped training data-sets (\hat{f}^{*1}(x), \hat{f}^{*2}(x), \ldots,\hat{f}^{*B}(x)) by each B trees and take a majority vote. Therefore, bagging for classification problem defined as

\hat{f}(x)=arg\max_{k}\hat{f}^{*b}(x)

Value

The output from BAG_Model.

Examples

yvar <- c("Loan.Type")
sample_data <- sample_data[c(1:750),]
xvar <- c("sex", "married", "age", "havejob", "educ", "political.afl",
"rural", "region", "fin.intermdiaries", "fin.knowldge", "income")
BchMk.BAG <- BAG_Model(sample_data, c(xvar, "networth"), yvar )
BchMk.BAG$Roc$auc

Combined Performance of the Data Splits

Description

Combined Performance of the Data Splits

Usage

Combined_Performance(Sub.Est.Mdls)

Arguments

Value

The output from Combined_Performance.

Examples

sample_data <- sample_data[c(1:750),]
yvar <- c("Loan.Type")
xvar <- c("sex", "married", "age", "havejob", "educ", "political.afl",
"rural", "region", "fin.intermdiaries", "fin.knowldge", "income")
CCP.RF <- Estimate_Models(sample_data, yvar, xvec = xvar, exog = "political.afl",
xadd = c("networth", "networth_homequity", "liquid.assets"),
type = "RF", dnames = c("0","1"))
Sub.CCP.RF <- list (Mdl.1 = CCP.RF$EstMdl$`D.1+networth`,
Mdl.0 = CCP.RF$EstMdl$`D.0+networth`)
CCP.NoCCP.RF <- Combined_Performance (Sub.CCP.RF)

Results of the Each Data and Data Splits

Description

Results of the Each Data and Data Splits

Usage

Estimate_Models(DataSet, yvar, exog = NULL, xvec, xadd, type, dnames)

Arguments

Value

The output from Estimate_Models.

Examples

sample_data <- sample_data[c(1:750),]
m2.xvar0 <- c("sex","married","age","havejob","educ","rural","region","income")
CCP.RF <- Estimate_Models(sample_data, yvar = c("Loan.Type"),
exog = "political.afl", xvec = m2.xvar0,
xadd = "networth", type = "RF", dnames = c("0","1"))

Gradient Boosting Model

Description

Gradient Boosting Model

Usage

GBM_Model(Data, xvar, yvar)

Arguments

Details

Unlike bagging trees, boosting does not use bootstrap sampling, rather each tree is fit using information from previous trees. An event probability of stochastic gradient boosting model is given by

\hat{\pi_i} = \frac{1}{1 + exp[-f(x)]^\prime}

where f(x) is in the range of [-\infty,\infty] and its initial estimate of the model is f^{(0)}_i=log(\frac{\pi_{i}}{1-\pi_{i}}), where \hat{\pi} is the estimated sample proportion of a single class from the training set.

Value

The output from GBM_Model.

Examples

yvar <- c("Loan.Type")
sample_data <- sample_data[c(1:120),]
xvar <- c("sex", "married", "age", "havejob", "educ", "political.afl",
"rural", "region", "fin.intermdiaries", "fin.knowldge", "income")
BchMk.GBM <- GBM_Model(sample_data, c(xvar, "networth"), yvar )
BchMk.GBM$finalModel
BchMk.GBM$Roc$auc

Generalized Linear Model

Description

Generalized Linear Model

Usage

GLM_Model(Data, xvar, yvar)

Arguments

Details

Let y be a vector of response variable of accessing credit for each applicant n, such that y_{i}=1 if the applicant-i has access to credit, and zero otherwise. Furthermore, let let \bold{x} = x_{ij}, where i=1,\ldots,n and j=1,\ldots,p characteristics of the applicants. The log-odds can be define as:

log(\frac{\pi_{i}}{1-\pi_{i}}) = \beta_{0}+\bold{x}_{\bold{i}}\beta = \beta_{0}+\sum_{i=1}^{p}\beta_{i}\bold{x}_{i}

\beta_{0} is the intercept, \beta = (\beta_{1},\ldots, \beta_{p}) is a p x 1 vector of coefficients and \bold{x_{i}} is the i_{th} row of x.

Value

The output from GLM_Model.

Examples

yvar <- c("multi.level")
sample_data <- sample_data[c(1:750),]
xvar <- c("sex", "married", "age", "havejob", "educ", "political.afl",
"rural", "region", "fin.intermdiaries", "fin.knowldge", "income")
BchMk.GLM <- GLM_Model(sample_data, c(xvar, "networth"), yvar )
BchMk.GLM$finalModel
BchMk.GLM$Roc$auc

Multinominal Logistic Model

Description

Multinominal Logistic Model

Usage

MLM_Model(Data, xvar, yvar)

Arguments

Details

Multi-nominal model is the generalized form of generalized logistic model and can be define as

\pi_{i}^{h} = P(y_{i}^{h} = 1 | \bold{x}_{\bold{i}}^{h})

where h presents the class labels ("1-of-h") on the basis of an input vector x_j, in our case x_j is loan types ("Formal Loan", "Informal Loan", "Both Loan", and "No Loan"). Furthermore,

y_{i}^h = 1if the weight w of x_j corresponds to belong a class and y_{i}^h=0 otherwise. For i \in 1,\ldots,h and the weight vectors w^i corresponds to class i.

We set {\bold{{w}}^{h}} = 0 and the parameters to be learned are the weight vectors w^i for i \in 1,\ldots,h-1 . And the class probabilities must satisfy

\sum_{i=1}^{h} P(y_{i}^{h} = 1 | \bold{x}_{\bold{i}}^{h}, \bold{w}) = 1.

Value

The output from MLM_Model.

Examples

yvar <- c("Loan.Type")
sample_data <- sample_data[c(1:750),]
xvar <- c("sex", "married", "age", "havejob", "educ", "political.afl",
"rural", "region", "fin.intermdiaries", "fin.knowldge", "income")
BchMk.MLM <- MLM_Model(sample_data, c(xvar, "networth"), yvar )
BchMk.MLM$finalModel
BchMk.MLM$Roc$auc

Random Forest

Description

Random Forest

Usage

RF_Model(Data, xvar, yvar)

Arguments

Details

Rather than considering the random sample of m predictors from the total of p predictors in each split, random forest does not consider a majority of the p predictors, and considers in each split a fresh sample of m_{try} which we usually set to m_{try} \approx \sqrt{p} Random forests which de-correlate the trees by considering m_{try} \approx \sqrt{p} show an improvement over bagged trees m = p.

Value

The output from RF_Model.

Examples

sample_data <- sample_data[c(1:750),]
yvar <- c("Loan.Type")
xvar <- c("sex", "married", "age", "havejob", "educ", "political.afl",
"rural", "region", "fin.intermdiaries", "fin.knowldge", "income")
BchMk.RF <- RF_Model(sample_data, c(xvar, "networth"), yvar )
BchMk.RF
 

Sample data for analysis. A dataset containing information of access to credit.

Description

Sample data for analysis.

A dataset containing information of access to credit.

Usage

sample_data

Format

A data_frame with 53940 rows and 10 variables:

x1

hhid, household id number

x2

swgt, survey weight

x3

region, 3 factor level, west, east, and center

x4

No.Loan, if the household has no loan

x5

Formal, if the household has formal loan

x6

Both, if the household has both loan

x7

Informal, if the household has informal loan

x8

sex, if the household has male

y1

Loan.Type, 4 factor level type of the loan

y2

multi.level, 2 factor level if the household has access to loan or not

...