Analysis of Sales Promotion Effects on Household Purchase Behavior

Summarizing, binary logistic regression models are used to estimate the influence
<strong>of</strong> household characteristics, characteristics <strong>of</strong> the purchasing process, and types <strong>of</strong> sales
promotion on promotion response. One possible limitation <strong>of</strong> the empirical approach
chosen is that we assume that all households in the dataset come from one distribution.
Mixture models have found widespread application in marketing (Andrews et al. 2002). It
is based on the assumption that the data arise from a mixture <strong>of</strong> distributions, and it
estimates the probability that objects belong to each class. The purpose <strong>of</strong> mixture models
is to “unmix” the sample, that is to identify groups or segments, and to estimate the
parameters <strong>of</strong> the density function underlying the observed data within each group (Wedel
and Kamakura 2000). The underlying assumption <strong>of</strong> mixture models is that because <strong>of</strong> one
or more an additional variables, not incorporated in the model, consumers may come from
different segments.
The purpose <strong>of</strong> the current analysis is to get insights in drivers <strong>of</strong> sales promotions
response, where sales promotion response, the dependent variable, is measured as a single
binary variable. A large number <strong>of</strong> independent variables are incorporated in the model.
According to Wedel and Kamakura (2000), a large number <strong>of</strong> independent variables
decreases parameter recovery <strong>of</strong> mixture regression models. Furthermore, mixture
modeling has an additional problem, related to the independent variables. As there are
fewer observations for estimation the regression model in each segment, collinearity among
the independent variables could lead to severe identification problems (Wedel and
Kamakure 2000). Based on the large number <strong>of</strong> independent variables, the limited number
<strong>of</strong> households, and the possible presence <strong>of</strong> collinearity, it was chosen to identify the
drivers <strong>of</strong> sales promotion response by incorporating the dependent and independent into a
traditional, non-mixture model. Still, the outcomes <strong>of</strong> this non-mixture binary logistic
regression model can a posteriori be used to identify segments based on different levels <strong>of</strong>
relevant, significant independent variables. We will come back to the topic <strong>of</strong> mixture
models in Section 9.4 when dealing with limitations and interesting topics for future
research.
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