Analysis of Sales Promotion Effects on Household Purchase Behavior

The reaction mechanisms that can occur during the promotional period are brand switching,
purchase timing (buying sooner or later), and purchase quantity (buying more or less). This
second angle provides detailed insights in households’ reaction to a promotion during the
promotional shopping trip itself, but does not take the intertemporal dynamics into
consideration.
The two-step approach presented in this section is used throughout the remainder
<strong>of</strong> this dissertation. In the next section, we will develop two research models, one for each
step.
5.4 Research Models
5.4.1 <strong>Promotion</strong> Response Model
We want to predict whether a household will make use <strong>of</strong> a specific promotion or not.
There is a variety <strong>of</strong> multivariate statistical techniques that can be used to predict a
dependent variable from a set <strong>of</strong> independent variables. For example, multiple regression
analysis and discriminant analysis are two techniques that quickly come to mind. However,
linear regression analysis poses difficulties when the dependent variable can have only two
values. For such a binary variable, the assumptions for hypothesis testing in regression
analysis are violated. For example, the distribution <strong>of</strong> errors can never be normal. Another
difficulty with multiple regression analysis is that predicted values cannot be interpreted as
probabilities. They are not constrained to fall in the interval between 0 and 1. Linear
discriminant analysis does allow direct prediction <strong>of</strong> group membership, but the assumption
<strong>of</strong> multivariate normality <strong>of</strong> the independent variables is not appropriate here.
The logistic regression model requires far less assumptions. In logistic regression,
one directly estimates the probability <strong>of</strong> an event occurring. For more than one independent
variable the model can be written as
z
e
Pr(event) =
1+
e
or equivalently
z
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