In-sample model fit and thresholding

Machine Learning for Marketing Analytics in R

Verena Pflieger

Data Scientist at INWT Statistics

Pseudo $R^2$ statistics I

$$ \text{McFadden:~} \quad R^2 =1-\frac{lnL_{\text{full}}}{lnL_{\text{null}}} $$

$$ \text{Cox \& Snell:~} R^2 = 1-\left(\frac{L_{\text{null}}}{L_{\text{full}}}\right)^{\frac{2}{n}} $$

$$ \text{Nagelkerke:~} R^2 = \frac{1-\left(\frac{L_{\text{null}}}{L_{\text{full}}}\right)^{\frac{2}{n}}}{1-(L_{\text{null}})^{\frac{2}{n}}} $$

Interpretation:

Reasonable if > 0.2
Good if > 0.4
Very Good if > 0.5

Pseudo $R^2$ statistics II

library(descr)

LogRegR2(logitModelNew)

Chi2                     1321.717
Df                       19
Sig.                     0
Cox and Snell Index      0.02879553
Nagelkerke Index         0.0469131
McFadden's R2            0.03071032

Predict probabilities

churnData$predNew <- predict(logitModelNew, 
                             type = "response", 
                              na.action = na.exclude)
data %>% select(returnCustomer, predNew) %>% tail()

      returnCustomer   predNew
45231              0 0.2843944
45232              0 0.1552756
45233              1 0.2522597
45234              1 0.1454276
45235              0 0.2698819
45236              0 0.2886988

Confusion matrix

library(SDMTools)
# Note that `SDMTools` cannot be downloaded from CRAN anymore. 
# Install it instead via `remotes::install_version("SDMTools", "1.1-221.2")`
confMatrixNew <- confusion.matrix(churnData$returnCustomer, 
                    churnData$predNew, threshold = 0.5)
confMatrixNew

     obs
pred 0     1
   0 36921 8242
   1 43    30

Prediction \ Truth	negative	positive
negative	true-negative	false-negative
positive	false-positive	true-positive

Accuracy

accuracyNew <- sum(diag(confMatrixNew)) / sum(confMatrixNew)
accuracyNew

0.8168494

Finding the optimal threshold

Prediction \ Truth	returnCustomer = 0	returnCustomer = 1
returnCustomer = 0	5	-15
returnCustomer = 1	0	0

payoff = 5 * true negative - 15 * false negative

Threshold	Accuracy	Payoff
0.5	0.817	60975
0.4	0.815	62180
[0.3]	[0.794]	[65740]
0.2	0.668	65670
0.1	0.241	10550

Overfitting

Let's try it out!

Machine Learning for Marketing Analytics in R