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4.1. A Predictive Analysis with State Changes at the Page, Session, and User Level
Our model permits a great deal of flexibility with regards to changing the underlying
browsing state, since the state may potentially change with every page viewing. For example, a
user may begin their session in a state where purchase is unlikely, but then switch later in the
session to a state where purchase is likely. However, allowing state changes at the viewing level
may result in too much variability. Hence we consider two additional formulations of our model
that restricts state changes to the session or user level. Restricting viewings within a session to
share a common state reduces the potential of a user switching states in the midst of a session.
Restricting all of a user’s viewings to a single state permits heterogeneity across users (although
not within a user), which can capture departures from the normality assumption in our hierarchy.
We estimate our model using the assumption that states that are allowed to change at the
page and session level with both a zero and first-order Markov model, and another set of models
where the state is constant for all of a user’s viewings (only a zero-order Markov process is
estimated, since there is no pre-user information necessary for a first-order Markov process).
The question of how many states should be included is an empirical one, hence we estimate our
model for one, two, and three states (S=1, 2, or 3) to allow the data to inform about this
parameter. This yields a total of 15 models from which to investigate the amount of within user
heterogeneity. We report the fit and out-of-sample prediction validation in Table 5.
First, notice transitions defined at the page-level outperform models estimated at a
session or user level. This supports the notion that users are likely to change states in the midst
of a session. Hence it is inaccurate to describe a user or an entire user session simply being
either purchase or non-purchase oriented. Secondly, notice when the hidden states are governed
by a first-order Markov model the fit is superior to a zero-order process. This suggests that the
goals, to the extent they are reflected in a state, show some persistence. It also suggests that the
VAR process cannot fully capture a user’s behavior, perhaps due to abrupt changes in a
consumer’s goal, e.g., a user changes from a browsing orientation to a purchase orientation. We
also compute Bayes factors following Kass and Raferty (1995) for three of our page-level
proposed models: a one-state, two-state and three-state version of the hidden Markov model.
The two-state model is favored over the one-state model by odds of 117.1. Also, the two-state