Predicting shares with hierarchical models

1. Predicting shares with hierarchical models

The last thing to cover is how to predict shares with a hierarchical model. It is very similar to predicting shares with a non-hierarchical model, but requires one additional step.

2. Hierarchical model with correlations

We'll start by fitting one last model to the sportscar data. For this model, we're including the extra input correlation = TRUE, which indicates that we want to find a model where decision makers' parameters are potentially correlated. Our previous hierarchical models assumed preferences for different features are independent, which may not be true. Once we have this model, we can look at the estimated correlations between parameters using the command cor-dot-mlogit(m10). This prints out the matrix of correlations which tell us how preferences for the various features are related across decision makers. For example, the largest correlation is the one between transmanual and convertyes, which is -0-point-72. This tells us that people who prefer manual transmissions tend to dislike convertibles. This can be a useful insight when you are designing a set of sports cars to offer to the market. You probably shouldn't make a sports car with a convertible top and a manual. And this will be accounted for when we look at share predictions with model m10.

3. Products we want to predict shares for

So, how do we predict shares using m10? Let's predict share for the same pair of products we used in the previous chapter. Both are 2-seaters without convertible tops. One has a manual transmission at $35K and the other has an automatic at $30K. Since we've switched to effects coding, we've effects-coded those products and saved them in prod-dot-coded.

4. Share prediction for hierarchical model

Now that we've got a model and a set of products, we're ready to predict shares. Let's walk through the code for doing that. First, we extract the mean and covariance of the individual parameters from the model object and store them as mean and Sigma. These are the parameters of m10. Then we follow the model structure we talked about before. The code loops over 1000 hypothetical decision makers. For each decision maker, we first draw their personal coefficients from a multivariate normal distribution with a mean of mean and a variance of Sigma. Then, once we have the individual's coefficients, we compute the utility for the two products by multiplying the coded product matrix by the individual coefficient vector coef. Then we compute the share for that person following the logit formula that we've seen a few times before. If you aren't familiar with matrix and vector operations in R, you may need to run the different pieces of this code and inspect the results to figure out exactly how it works. Finally, if we average the shares for each person across all 1,000 people using colMeans(), we get our share prediction. You can see that the share for the first car is about 13%, which is very close to the 13-point-3% we got from the non-hierarchical model. Because this is a simulation, the number will move around a little each time you run it. In general, when we account for differences in preferences across consumers, niche products like this manual transmission sports car tend to pick up share and mainstream products tend to lose a little. In this particular data the two predictions land in almost the same place.

5. Let's practice!

Now it's your turn to predict shares for the chocolate data. And this will be your last exercise for this course!

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Choice Modeling for Marketing in R

AdvancedSkill Level

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Our goal for this chapter is to get you through the entire choice modeling process as quickly as possible, so that you get a broad understanding of what we can do with choice models and how the choice modeling process works. The main idea here is that we can use a choice model to understand how customers' product choices depend on the features of those products. Do sportscar buyers prefer manual transmissions to automatic? By how much? In order to give you an overview, we will skip over many of the details. In later chapters, we will go back and cover important issues in preparing data, specifying and interpreting models and reporting your findings, so that you are fully prepared to use these methods with your own choice data.

Exercise 1: Why choice?Exercise 2: Choice data Exercise 3: Inspecting choice data Exercise 4: Finding the levels of a factor Exercise 5: Inspecting a choice observation Exercise 6: What did people choose?Exercise 7: Fitting and interpreting a choice model Exercise 8: Fitting a choice model Exercise 9: Interpreting parameters Exercise 10: Using choice models to make decisions Exercise 11: Predicting choice shares Exercise 12: Plotting choice shares