## Tuesday, November 24, 2015

### Statistical Models That Support Design Thinking: Driver Analysis vs. Partial Correlation Networks

We have been talking about design thinking in marketing since Tim Brown's Harvard Business Review article in 2008. It might be easy for the data scientist to dismiss the approach as merely a type of brainstorming for new products or services. Yet, design issues do arise in data visualization where we are concerned with communicating our findings. However, my interest is model selection: Should the analyst select one statistical model over another because the user might find it more helpful in planning interventions or designing new products and services?

For example, the marketing manager who wants to retain current customers seeks guidance from customer satisfaction questionnaires filled with performance ratings and intentions to recommend or purchase again. Motivated by the desire to keep it simple, common practice tends to focus attention on only the most important "causes" of customer retention. As I noted in my first post, Network Visualization of Key Driver Analysis, a more complete picture can be revealed by a correlation graph displaying all the interconnections among all the ratings. The edges or links are colored green or red so that we know if the relationship is positive or negative. The thickest of the path indicates the strength of the correlation. But correlations measure total effects, both those that are direct and those obtained through associations with other ratings.

The designer of intervention strategies aimed at preventing churn could acquire additional insights from the partial correlation graph depicting the effects between all pairs of ratings controlling for all the other ratings in the model. While the correlation map reveals total effects, the partial correlation map removes all but the direct effects. The graph below was created using the R code from my first post to simulate a data set that mimics what is often found when airline passengers complete satisfaction surveys. Once the data were generated, the procedures outlined in my post Undirected Graphs When the Causality is Mutual were followed. The R code is listed at the end of this discussion.

We can pick any node, such as the one labeled "Satisfaction" in the middle of the right-hand side of the figure. A simple way of interpreting this graph is to think of Satisfaction as the dependent variable and the lines radiating from Satisfaction as the weights obtained from the regression of this node on the other 14 ratings. Clearly, overall satisfaction serves as an inclusive summary measure with so many pathways from so many other nodes. Each of the four customer service ratings (below Satisfaction and in light pink) adds its own unique contribution with the greatest impact indicated by the thickest green edge from the Service node. Moreover, Easy Reservation and Ticket Price plus Clean Aircraft with room for people and baggage make incremental improvements in Satisfaction.

The same process can be repeated for any node. Instead of a driver analysis that narrows our thinking to a single dependent variable and its highest regression weights, the partial correlation map opens us to the possibilities. If the goal was customer retention, then the focus would be on the Fly Again node. Recommend seems to have the strongest link to Fly Again. Can the airline induce repeat purchase by encouraging recommendation? What if frequent flyer miles were offered when others entered your name as a recommender? Such a proposal may not be practical in its current form, but the graph supports this type of design thinking.

Because there are no direct paths from the four service nodes to Fly Again, a driver analysis would miss the indirect connection through Satisfaction. And what of this link between Courtesy and Easy Reservation? Do customers infer a "friendly" personality trait that links their perceptions of the way they are treated when they buy a ticket and when they board the plane? Design thinkers would entertain such a possibility and test the hypothesis. Such "cascaded inferences" fill the graph for those willing to look. Perhaps many small and less costly improvements might combine to have a greater impact than concentrating on a single aspect? Encouraging passengers to check their bags would create more overhead storage without reconfiguring the airplane. Let the design thinking begin!

The discussion ends with the identification of "the most important" in a driver analysis. The network, on the other hand, invites creative thought. Isn't this the point of data science? What can we learn from the data? The answer is a good deal more than can be revealed by the largest coefficient in a single regression equation.

```# Calculates Sparse Partial Correlation Matrix
sparse_matrix<-EBICglasso(cor(ratings), n=1000)
round(sparse_matrix,2)

# Plots results
gr<-list(1:4,5:8,9:12,13:15)
node_color<-c("lightgoldenrod","lightgreen","lightpink","cyan")
qgraph(sparse_matrix, fade = FALSE, layout="spring", groups=gr,
color=node_color,labels=names(ratings), label.scale=FALSE,
label.cex=1, node.width=.5, edge.width=.25, minimum=.05)```
Created by Pretty R at inside-R.org

#### 1 comment:

1. I think the analysis is quite interesting. We have used a similar analysis to predict customer churn in a social network where a set of customers form a community and churn of one customers lead to a churning influence of other customers. The case shown above is a great practical motivation of using such graph analysis in marketing world.