In the 1975 edition of “Applied multiple regression/correlation analysis for the behavioral sciences” by Jacob Cohen, an interesting approach of handling missing values in numeric variables was proposed with the purpose to improve the traditional single-value imputation, as described below:

– First of all, impute missing values by the value of mean or median

– And then create a dummy variable to flag out imputed values

In the setting of a regression model, both imputed and dummy variables would be included and therefore the number of independent variables are doubled.

Although the aforementioned approach has long been criticized and eventually abandoned by Cohen himself in the recent edition of the book, I was told that this obsolete technique is still being actively used.

Out of my own curiosity, I applied this dummy imputation approach to the data used in https://statcompute.wordpress.com/2019/05/04/why-use-weight-of-evidence and then compared it with the WoE imputation in the context of Logistic Regression.

Below are my observations:

– Since the dummy approach converts each numeric variable with missing values, the final model tends to have more independent variables, which is not desirable in terms of the model parsimony. For instance, there are 7 independent variables in the model with dummy imputation and only 5 in the model with WoE approach.

– The model performance doesn’t seem to justify the use of more independent variables in the regression with the dummy imputation. As shown in the output below, ROC statistic from the model with WoE approach is significantly better than the one with the dummy imputation based on the DeLong’s test, which is also consistent with the result of Vuong test.

df <- readRDS("df.rds") | |

source("mob.R") | |

bin_out <- batch_bin(df, 3) | |

bin_out$BinSum[order(–bin_out$BinSum$iv), ] | |

# var nbin unique miss min median max ks iv | |

# bureau_score 34 315 315 443 692.5 848 35.2651 0.8357 | |

# tot_rev_line 20 3617 477 0 10573.0 205395 26.8943 0.4442 | |

# age_oldest_tr 25 460 216 1 137.0 588 20.3646 0.2714 | |

# tot_derog 7 29 213 0 0.0 32 20.0442 0.2599 | |

# ltv 17 145 1 0 100.0 176 16.8807 0.1911 | |

# rev_util 12 101 0 0 30.0 100 16.9615 0.1635 | |

# tot_tr 15 67 213 0 16.0 77 17.3002 0.1425 | |

# tot_rev_debt 8 3880 477 0 3009.5 96260 8.8722 0.0847 | |

# tot_rev_tr 4 21 636 0 3.0 24 9.0779 0.0789 | |

# tot_income 17 1639 5 0 3400.0 8147167 10.3386 0.0775 | |

# tot_open_tr 7 26 1416 0 5.0 26 6.8695 0.0282 | |

# ONLY SELECT VARIABLES WITH IV > 0.1 | |

dummies <- data.frame( | |

bad = df$bad, | |

tot_derog = ifelse(is.na(df$tot_derog), mean(df$tot_derog, na.rm = T), df$tot_derog), | |

dummy.tot_derog = ifelse(is.na(df$tot_derog), 1, 0), | |

tot_tr = ifelse(is.na(df$tot_tr), mean(df$tot_tr, na.rm = T), df$tot_tr), | |

dummy.tot_tr = ifelse(is.na(df$tot_tr), 1, 0), | |

age_oldest_tr = ifelse(is.na(df$age_oldest_tr), mean(df$age_oldest_tr, na.rm = T), df$age_oldest_tr), | |

dummy.age_oldest_tr = ifelse(is.na(df$age_oldest_tr), 1, 0), | |

tot_rev_line = ifelse(is.na(df$tot_rev_line), mean(df$tot_rev_line, na.rm = T), df$tot_rev_line), | |

dummy.tot_rev_line = ifelse(is.na(df$tot_rev_line), 1, 0), | |

rev_util = ifelse(is.na(df$rev_util), mean(df$rev_util, na.rm = T), df$rev_util), | |

dummy.rev_util = ifelse(is.na(df$rev_util), 1, 0), | |

bureau_score = ifelse(is.na(df$bureau_score), mean(df$bureau_score, na.rm = T), df$bureau_score), | |

dummy.bureau_score = ifelse(is.na(df$bureau_score), 1, 0), | |

ltv = ifelse(is.na(df$ltv), mean(df$ltv, na.rm = T), df$ltv), | |

dummy.ltv = ifelse(is.na(df$ltv), 1, 0)) | |

dm1 <- summary(glm(bad ~ ., data = dummies, family = "binomial")) | |

dx1 <- paste(row.names(dm1$coefficients)[dm1$coefficients[, 4] < 0.05][–1]) | |

dl1 <- as.formula(paste("bad", paste(dx1, collapse = " + "), sep = " ~ ")) | |

dm2 <- glm(dl1, data = dummies, family = "binomial") | |

# Estimate Std. Error z value Pr(>|z|) | |

#(Intercept) 5.827e+00 5.651e-01 10.311 < 2e-16 *** | |

#age_oldest_tr -1.595e-03 4.526e-04 -3.523 0.000426 *** | |

#tot_rev_line -1.684e-05 2.910e-06 -5.785 7.25e-09 *** | |

#dummy.tot_rev_line 5.314e-01 1.434e-01 3.707 0.000210 *** | |

#rev_util 3.183e-03 1.171e-03 2.718 0.006574 ** | |

#bureau_score -1.390e-02 8.075e-04 -17.209 < 2e-16 *** | |

#dummy.bureau_score 7.339e-01 1.518e-01 4.835 1.33e-06 *** | |

#ltv 2.451e-02 2.249e-03 10.895 < 2e-16 *** | |

roc1 <- pROC::roc(response = df$bad, predictor = fitted(mdl2)) | |

roc2 <- pROC::roc(response = df$bad, predictor = fitted(dm2)) | |

pROC::roc.test(roc1, roc2, method = "delong", paired = T) | |

# DeLong's test for two correlated ROC curves | |

# data: roc1 and roc2 | |

# Z = 4.2369, p-value = 2.266e-05 | |

# alternative hypothesis: true difference in AUC is not equal to 0 | |

# sample estimates: | |

# AUC of roc1 AUC of roc2 | |

# 0.7751298 0.7679757 | |

pscl::vuong(mdl2, dm2) | |

# Vuong Non-Nested Hypothesis Test-Statistic: | |

# Vuong z-statistic H_A p-value | |

# Raw 4.275484 model1 > model2 9.5361e-06 | |

# AIC-corrected 4.565833 model1 > model2 2.4876e-06 | |

# BIC-corrected 5.534434 model1 > model2 1.5612e-08 |