Identification of Key Drivers of Net Promoter Score Using a Statistical Classification Model - Efficient Decision Support Systems: Practice and Challenges from Current to Future - page 153

confusion matrix whose rows were constant, summing to the row total. In sum, we feel the
accuracy of the model is sufficient to learn something about what drives customers to give
high responses to Y, though perhaps not sufficient to learn as much about what drives
customers to give low responses to Y.
Figure 1 is a graphical display of the slopes for each of the customer satisfaction covariates.
The larger the coefficient value, the more detrimental the response level is to NPS. The y-
axis is therefore labeled as 'demerits.'

3.00

q82a
q82b
q82d
q82f

2.50

2.00

q79

1.50

1.00

0.50

0.00

0 1 2 3 4 5 6 7 8

Response Level

Fig. 1. MLEs of Slopes for 7-Point Likert Scale Customer Satisfaction Covariates
In view of the ordinal nature of the customer satisfaction covariates, the slopes, which
represent the effect of the Likert scale levels, should decrease monotonically. That is, the
penalty for a 'satisfied' covariate value should be less than or equal to that of a 'dissatisfied'
covariate value. As such, it would be logical to have the estimated values of the slopes
display the monotone decreasing trend as the response level of the covariates ascends.
Figure 1 shows that the unconstrained MLEs for the slopes associated with the customer
satisfaction covariates nearly satisfy the desired monotone property, but not exactly. The
aberrations are due to data deficiencies or minor model inadequacies and can be resolved by
using a constrained logistic regression model introduced in the next section.

3.3 Constrained logistic regression
Consider the situation where the i -th covariate is ordinal in nature, perhaps because it is
measured on a k -point Likert scale. The CSH data is a good illustration of this situation,
since all the customer satisfaction covariates are ordinal variables measured on 7-point
Likert scale. Let the corresponding group of k slopes for this covariate be denoted by

{ k
ijj

 . In order to reflect the information that the covariates are ordered, it is quite natural

 1