Logistic Regression with Interactions

Reading the data

library(data.table)
# reading data as data.table
CCdefault.dt <- fread("MCICreditCardDefault.csv")
# attach the data table
attach(CCdefault.dt)

Converting some data columns into factors

# convert 'Id' as a factor
CCdefault.dt[, Id := as.factor(Id)]
# convert 'Male' as a factor
CCdefault.dt[, Male := as.factor(Male)]
# convert 'Education' as a factor
CCdefault.dt[, Education := as.factor(Education)]
# convert 'MaritalStatus' as a factor
CCdefault.dt[, MaritalStatus := as.factor(MaritalStatus)]
# convert 'Default' as a factor
CCdefault.dt[, Default := as.factor(Default)]

Running Binomial Logistic Regression Model (Model1)

# model building
 Model1 <- glm(Default ~ CreditLimit
                 + Education,
                 data = CCdefault.dt,
                 family = binomial())
 
# summary of the model
summary(Model1)

## 
## Call:
## glm(formula = Default ~ CreditLimit + Education, family = binomial(), 
##     data = CCdefault.dt)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -0.8824  -0.7812  -0.6503  -0.4299   2.5123  
## 
## Coefficients:
##               Estimate Std. Error z value Pr(>|z|)    
## (Intercept) -8.089e-01  3.421e-02 -23.646  < 2e-16 ***
## CreditLimit -3.199e-06  1.307e-07 -24.482  < 2e-16 ***
## Education2   7.351e-02  3.284e-02   2.239 0.025164 *  
## Education3   9.840e-02  4.266e-02   2.307 0.021059 *  
## Education4  -1.342e+00  3.909e-01  -3.432 0.000599 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 31427  on 29600  degrees of freedom
## Residual deviance: 30629  on 29596  degrees of freedom
## AIC: 30639
## 
## Number of Fisher Scoring iterations: 5

Running Binomial Logistic Regression Model With Interaction (Model2)

# model building
 Model2 <- glm(Default ~ CreditLimit
                 + Education
                 + CreditLimit*Education,
                 data = CCdefault.dt,
                 family = binomial())
 
# summary of the model
summary(Model2)

## 
## Call:
## glm(formula = Default ~ CreditLimit + Education + CreditLimit * 
##     Education, family = binomial(), data = CCdefault.dt)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -0.8940  -0.7733  -0.6529  -0.4536   2.8191  
## 
## Coefficients:
##                          Estimate Std. Error z value Pr(>|z|)    
## (Intercept)            -9.262e-01  4.470e-02 -20.719  < 2e-16 ***
## CreditLimit            -2.555e-06  2.005e-07 -12.747  < 2e-16 ***
## Education2              2.493e-01  5.453e-02   4.572 4.83e-06 ***
## Education3              2.507e-01  6.689e-02   3.748 0.000178 ***
## Education4              1.318e-01  9.503e-01   0.139 0.889700    
## CreditLimit:Education2 -1.125e-06  2.824e-07  -3.983 6.80e-05 ***
## CreditLimit:Education3 -9.762e-07  4.067e-07  -2.400 0.016390 *  
## CreditLimit:Education4 -8.732e-06  5.802e-06  -1.505 0.132360    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 31427  on 29600  degrees of freedom
## Residual deviance: 30610  on 29593  degrees of freedom
## AIC: 30626
## 
## Number of Fisher Scoring iterations: 6

Full Model – Running Binomial Logistic Regression Model With Interactions (Model3)

# model building
 Model3 <- glm(Default ~ CreditLimit
                 + Male
                 + Education
                 + MaritalStatus
                 + Age
                 + BillOutstanding
                 + LastPayment
                 + CreditLimit*Male
                 + CreditLimit*Education
                 + CreditLimit*MaritalStatus
                 + CreditLimit*Age
                 + CreditLimit*BillOutstanding
                 + CreditLimit*LastPayment,
                 data = CCdefault.dt,
                 family = binomial())
 
# summary of the model
summary(Model3)

## 
## Call:
## glm(formula = Default ~ CreditLimit + Male + Education + MaritalStatus + 
##     Age + BillOutstanding + LastPayment + CreditLimit * Male + 
##     CreditLimit * Education + CreditLimit * MaritalStatus + CreditLimit * 
##     Age + CreditLimit * BillOutstanding + CreditLimit * LastPayment, 
##     family = binomial(), data = CCdefault.dt)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -1.8760  -0.7729  -0.6405  -0.3706   3.9782  
## 
## Coefficients:
##                               Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                 -4.497e-01  1.157e-01  -3.887 0.000102 ***
## CreditLimit                 -6.111e-06  6.773e-07  -9.023  < 2e-16 ***
## Male1                        1.640e-01  4.533e-02   3.619 0.000296 ***
## Education2                   1.535e-01  5.523e-02   2.780 0.005442 ** 
## Education3                   1.489e-01  6.952e-02   2.142 0.032222 *  
## Education4                   5.819e-02  9.464e-01   0.061 0.950977    
## MaritalStatus2              -2.545e-01  5.204e-02  -4.891 1.00e-06 ***
## MaritalStatus3              -4.309e-02  1.879e-01  -0.229 0.818591    
## Age                         -6.267e-03  2.605e-03  -2.406 0.016146 *  
## BillOutstanding              2.053e-07  4.769e-07   0.431 0.666816    
## LastPayment                 -3.292e-05  4.886e-06  -6.738 1.61e-11 ***
## CreditLimit:Male1           -7.796e-08  2.528e-07  -0.308 0.757817    
## CreditLimit:Education2      -9.232e-07  2.851e-07  -3.238 0.001204 ** 
## CreditLimit:Education3      -1.028e-06  4.104e-07  -2.504 0.012296 *  
## CreditLimit:Education4      -8.349e-06  5.773e-06  -1.446 0.148108    
## CreditLimit:MaritalStatus2   3.766e-07  2.864e-07   1.315 0.188434    
## CreditLimit:MaritalStatus3  -8.342e-07  1.686e-06  -0.495 0.620816    
## CreditLimit:Age              7.844e-08  1.526e-08   5.139 2.76e-07 ***
## CreditLimit:BillOutstanding  5.185e-12  1.432e-12   3.622 0.000292 ***
## CreditLimit:LastPayment      2.387e-11  1.803e-11   1.324 0.185499    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 31427  on 29600  degrees of freedom
## Residual deviance: 30250  on 29581  degrees of freedom
## AIC: 30290
## 
## Number of Fisher Scoring iterations: 6

StepAIC Model – Running Binomial Logistic Regression Model With Interactions (Model4)

library(MASS)
# step AIC model
Model4 <- stepAIC(Model3)

## Start:  AIC=30290.43
## Default ~ CreditLimit + Male + Education + MaritalStatus + Age + 
##     BillOutstanding + LastPayment + CreditLimit * Male + CreditLimit * 
##     Education + CreditLimit * MaritalStatus + CreditLimit * Age + 
##     CreditLimit * BillOutstanding + CreditLimit * LastPayment
## 
##                               Df Deviance   AIC
## - CreditLimit:MaritalStatus    2    30253 30289
## - CreditLimit:Male             1    30251 30289
## - CreditLimit:LastPayment      1    30252 30290
## <none>                              30250 30290
## - CreditLimit:Education        3    30265 30299
## - CreditLimit:BillOutstanding  1    30264 30302
## - CreditLimit:Age              1    30276 30314
## 
## Step:  AIC=30288.49
## Default ~ CreditLimit + Male + Education + MaritalStatus + Age + 
##     BillOutstanding + LastPayment + CreditLimit:Male + CreditLimit:Education + 
##     CreditLimit:Age + CreditLimit:BillOutstanding + CreditLimit:LastPayment
## 
##                               Df Deviance   AIC
## - CreditLimit:Male             1    30253 30287
## - CreditLimit:LastPayment      1    30254 30288
## <none>                              30253 30289
## - CreditLimit:Education        3    30269 30299
## - CreditLimit:BillOutstanding  1    30266 30300
## - CreditLimit:Age              1    30278 30312
## - MaritalStatus                2    30290 30322
## 
## Step:  AIC=30286.55
## Default ~ CreditLimit + Male + Education + MaritalStatus + Age + 
##     BillOutstanding + LastPayment + CreditLimit:Education + CreditLimit:Age + 
##     CreditLimit:BillOutstanding + CreditLimit:LastPayment
## 
##                               Df Deviance   AIC
## - CreditLimit:LastPayment      1    30254 30286
## <none>                              30253 30287
## - CreditLimit:Education        3    30269 30297
## - CreditLimit:BillOutstanding  1    30266 30298
## - CreditLimit:Age              1    30278 30310
## - Male                         1    30279 30311
## - MaritalStatus                2    30290 30320
## 
## Step:  AIC=30286.22
## Default ~ CreditLimit + Male + Education + MaritalStatus + Age + 
##     BillOutstanding + LastPayment + CreditLimit:Education + CreditLimit:Age + 
##     CreditLimit:BillOutstanding
## 
##                               Df Deviance   AIC
## <none>                              30254 30286
## - CreditLimit:Education        3    30271 30297
## - CreditLimit:BillOutstanding  1    30275 30305
## - CreditLimit:Age              1    30280 30310
## - Male                         1    30281 30311
## - MaritalStatus                2    30292 30320
## - LastPayment                  1    30434 30464

summary(Model4)

## 
## Call:
## glm(formula = Default ~ CreditLimit + Male + Education + MaritalStatus + 
##     Age + BillOutstanding + LastPayment + CreditLimit:Education + 
##     CreditLimit:Age + CreditLimit:BillOutstanding, family = binomial(), 
##     data = CCdefault.dt)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -1.7631  -0.7746  -0.6425  -0.3637   4.3991  
## 
## Coefficients:
##                               Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                 -5.332e-01  1.007e-01  -5.296 1.18e-07 ***
## CreditLimit                 -5.537e-06  5.391e-07 -10.271  < 2e-16 ***
## Male1                        1.509e-01  2.921e-02   5.164 2.42e-07 ***
## Education2                   1.655e-01  5.483e-02   3.018 0.002546 ** 
## Education3                   1.601e-01  6.927e-02   2.311 0.020827 *  
## Education4                   6.554e-02  9.466e-01   0.069 0.944803    
## MaritalStatus2              -2.010e-01  3.298e-02  -6.095 1.10e-09 ***
## MaritalStatus3              -1.026e-01  1.311e-01  -0.783 0.433761    
## Age                         -5.040e-03  2.426e-03  -2.077 0.037778 *  
## BillOutstanding              4.235e-08  4.562e-07   0.093 0.926033    
## LastPayment                 -2.771e-05  2.683e-06 -10.327  < 2e-16 ***
## CreditLimit:Education2      -9.933e-07  2.818e-07  -3.525 0.000424 ***
## CreditLimit:Education3      -1.087e-06  4.097e-07  -2.653 0.007988 ** 
## CreditLimit:Education4      -8.406e-06  5.774e-06  -1.456 0.145449    
## CreditLimit:Age              6.942e-08  1.352e-08   5.136 2.81e-07 ***
## CreditLimit:BillOutstanding  5.939e-12  1.307e-12   4.544 5.51e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 31427  on 29600  degrees of freedom
## Residual deviance: 30254  on 29585  degrees of freedom
## AIC: 30286
## 
## Number of Fisher Scoring iterations: 6

Logistic Regression with Interactions

Sameer Mathur

Reading the data

Converting some data columns into factors

Running Binomial Logistic Regression Model (Model1)

Running Binomial Logistic Regression Model With Interaction (Model2)

Full Model – Running Binomial Logistic Regression Model With Interactions (Model3)

StepAIC Model – Running Binomial Logistic Regression Model With Interactions (Model4)