1. Models for individual demand
Hello again! This chapter deals with building response models for individual demand to explain customer purchase decisions.
2. Customer purchases
In the following example, we investigate beer purchases for two brands recorded for several hundred households. The dataset named choice-dot-data is again already loaded for you in R.
We start with compactly displaying the structure of the data by using the structure function. The data contains information on 2798 purchases for the two beer brands HOPPINESS and BUD, and 15 variables providing information on marketing activities run for the two brands. The two numeric variables provide the corresponding price information.
In addition, we have information on the observation week the purchase was recorded, the household ID of the purchase record and The last purchase that was recorded for the each household.
3. To purchase or not to purchase?
Before purchasing a product, customers usually go through a decision process. In the first instance of this process, customers choose to buy or not to buy. If they decide to buy, they choose a certain product category, and within that category, a certain brand. As a result, we observe two outcomes: Purchase or No-Purchase.
The key issue now is the specification of the form of the relationship between the purchases and the marketing tools. Again, the simplest form to assume is linear. As the purchase decisions can be interpreted as the probability to purchase - we start with fitting a linear probability model.
4. Competition
Our response variable HOPPINESS takes on the value one, if a customer purchases the brand, or zero when a customer purchases the competing brand BUD.
Therefore, the real question is whether the probability that a customer purchases HOPPINESS - or purchases the competing brand BUD - depends on the changes in the PRICE for HOPPINESS relative to the PRICE for BUD. In this case, it is more convenient to work with the ratio between the prices for HOPPINESS and BUD.
For this reason, we define a new variable price-dot-ratio by taking the log() of the ratio of between HOPPINESS and BUD. Here negative values indicate that the price for HOPPINESS was lower than the PRICE for BUD and the lower the price for HOPPINESS compared to BUD the more negative becomes the price ratio. If both prices are equal the price ratio is 0.
5. A linear probability model for beer demand
We describe the effects of changes in the price-ratio on the purchase probabilities for HOPPINESS - by using the linear model function. The result is assigned to an object called probability-dot-model.
Next, we display the relation between the purchase probabilities and the price ratio by the function plot(). The predicted purchase probabilities are added to the graph by using the function abline().
The model predictions can be interpreted as the predicted probability to purchase HOPPINESS for a given price ratio. The graph indicates: when the price for HOPPINESS is lower compared to BUD the corresponding purchase probability is higher.
6. Let's practice!
Now it's your turn!