The hypotheses regarding the existence, direction, and magnitude of the relationships posited in Figure 1:

Hypothesis 1a:

Previous site usage is negatively associated with a decision to purchase.

Hypothesis 1b:

Previous site usage is negatively associated with bounce rate.

Hypothesis 1c:

Previous site usage is positively associated with exit rate.

Hypothesis 2a:

Site content and quality are positively associated with a decision to purchase.

Hypothesis 2b:

Site content and quality are negatively associated with average exit rate.

Hypothesis 3:

Association between site content and exit rate is heterogeneous at the previous site usage group level

Hypothesis 4a:

Previous site usage is negatively associated with variability in exit rate.

Hypothesis 4b:

Previous site usage is negatively associated with variability in bounce rate.

Hypothesis 5a:

Technological factors are associated with variability in exit rate.

Hypothesis 5b:

Technological factors are associated with variability in exit rate.

Hypothesis 6:

The amount of viewed product content is negatively associated with variability in exit rate.

Proper analytical treatment of the outcome variables begins with an appropriate selection of the model structure. Exit rate, bounce rate, and revenue variables are

all bounded. To avoid misspecification of the model for bounce and exit rates, empirical distributions were examined to detect which model for the conditional distribution would be most appropriate. Values for exit and bounce rates were scaled according to a min-max scaling so that observed values were bounded in [0, 1]. Densities for both bounce and exit rates across subpopulations of visitors are displayed in Figure 2. The data is bimodal with peaks near zero and a smaller peak near one. This bimodality suggests the possibility of two distinct data generating processes that govern exit and bounce behavior.

To improve the selection of a distributional model, scaled third and fourth moments (skewness and kurtosis) were plotted for a set of different theoretical distributions with maximum-likelihood estimation used to compute these moments. Bounce and exit rate exhibited shapes consistent with a beta distribution. The third and fourth moment evidence is shown for exit rate in Figure 3 but a highly similar result was found for bounce rate. Further maximum-likelihood estimation was used to fit the bounce and exit data to beta distributions. Removal of observations making up the right peak in both the bounce and exit data

resulted in beta fits with greater suitability as displayed in Figure 4 and Figure 5. Considering these observations, it was decided to remove observations in the 99^th percentile for both the exit and bounce rate data. In both, this amounted to about 5.5% of observations being taken out. This process is equivalent to winsorization. Doing this does ignore a source of information but enables more accurate modeling of the other 94.5% of observations.

With the assumption that the decision to purchase or not follows the random utility model from Section 5.2.1, the following logistic regression model was used to determine if the available clickstream variables captured the process generating the revenue response data.

log R e v e n u e i 1 − R e v e n u e i = A d m i n i s t r a t i v e i + A d m i n i s t r a t i v e _ D u r a t i o n i + I n f o r m a t i o n a l i       + I n f o r m a t i o n a l _ D u r a t i o n i + P r o d u c t R e l a t e d i       + P r o d u c t R e l a t e d _ D u r a t i o n i + E x i t R a t e i + B o u n c e R a t e i       + V i s i t o r T y p e i + B r o w s e r i + T r a f f i c T y p e i + O p e a r t i n g S y s t e m i       + R e g i o n i + M o n t h i + W e e k e n d i + S p e c i a l D a y i (12)

The first six variables are theorized to convey site content and quality information. Visitors to the website are assumed to be goal-directed utility maximizing agents and so time spent on certain pages should assist the visitor in deciding on what course of action is benefit-producing. Variables Browser, TrafficType, and OperatingSystem are included as they are surmised to encode technological preferences, technical knowledge, and technology-website incompatibility. Variables Region, Month, Weekend, and SpecialDay are control variables that should adjust for variability in purchase intention seen over various times and geographical contexts. ExitRate and BounceRate are included as it is surmised that both contain information independent from the other variables

Bounce rate is the probability a visitor traffics to the website but departs immediately. This response varies between pages on the website and its value is derived from previous arrival and departure events of other visitors which are divergent from visitor i. A flexible probability model of these probabilities which can incorporate non-symmetries, complex variance structures, and skewness is warranted. The inherent flexibility of the beta distribution with respect to symmetry, skewness, and variance structure motivated the choice of a beta regression model for bounce rate. As bounce rate is theorized to be a process external to the website content and quality, independent variables that correspond to internal aspects of the website were excluded.

B o u n c e R a t e i = exp ( η ) 1 + exp ( η ) (13)

η = V i s i t o r T y p e i + B r o w s e r i + T r a f f i c T y p e i + O p e a r t i n g S y s t e m i       + R e g i o n i + M o n t h i + W e e k e n d i + S p e c i a l D a y i (14)

Φ i = exp ( V i s i t o r T y p e i + B r o w s e r i + T r a f f i c T y p e i ) (15)

where η is the linear predictor for the mean bounce rate and Φ i is the precision parameter for visitor i

A beta regression model was chosen to represent dependencies between the exit rate and the explanatory variables. The argument to do so closely matches that made for the bounce rate. Unlike the bounce rate, a visitor’s observed exit probability is posited to be more dependent on the user interface and user experience of the website. It was decided to include ProductRelated in the precision model as this is seen as a proxy for commitment to a goal on the website and it is reasoned a visitor should exhibit less variable exit rates when more committed.

E x i t R a t e i = exp ( η ) 1 + exp ( η ) (16)

η = A d m i n i s t r a t i v e i + A d m i n i s t r a t i v e _ D u r a t i o n i + I n f o r m a t i o n a l i       + I n f o r m a t i o n a l _ D u r a t i o n i + P r o d u c t R e l a t e d i       + P r o d u c t R e l a t e d _ D u r a t i o n i + V i s i t o r T y p e i + B r o w s e r i       + T r a f f i c T y p e i + R e g i o n i + M o n t h i + W e e k e n d i + S p e c i a l D a y i (17)

Φ i = exp ( V i s i t o r T y p e i + P r o d u c t R e a l a t e d i ) (18)

where η is the linear predictor for the mean exit rate and Φ i is the precision parameter for visitor i

Any model of user behavior should possess the qualities of being interpretable, valid, and useful. Interpretability and practical usefulness are coupled as any loss of interpretability will erode how useable the model is. Validity here refers primarily to the predictive accuracy and support of the model on the available data. It is for these reasons that variable selection was included in the analysis so that the resulting models were as simple as possible yet capable of explaining the appearance of the observed data.

To improve interpretability of the revenue model, the least absolute shrinkage and selection operator (LASSO) method was employed to filter out independent variables (IV’s) that do not contribute to model accuracy. Regularization with LASSO was used as a first step for two primary reasons. First, fitting a model against the available IV’s would yield non-unique solutions. Second, the model inferred should not include parameters that are not justified by the data. Details of how LASSO performs variable selection can be found in several sources [51] [52] . Cross validation was used to select a value for the lambda parameter for which the revenue logistic model achieved the smallest mean cross validation error. Mean cross validation error was defined in two ways as either binomial deviance or area under the receiver operating characteristic curve. Results of this process are shown in Figure 6. Deviance is minimized, and AUC is maximized at the models with optimal complexity fitted to an 80% subset of the data. Model 1 was a full complexity model with all available IV’s included whereas Model 2 included the variables identified in the variable selection phase.

To assess the relative quality of the two models, a series of goodness-of-fit (GOF) tests were performed. Examination of GOF must involve determining whether the fitted model’s residual variation is minor, shows no systematic patterns, and follows variability assumed by the fitted model. Hosmer and Lemeshow’s (HL) C and the le Cessie-van Hourwlignen-Copas-Hosmer (CHCH) unweighted sum of square test were used to evaluate global GOF. Both tests specify a null hypothesis that the tested model does not need to be more complex. Details will not be explored but can be found in the literature [53] [54] . Judgements on the power of each model to explain the phenomena were based on McFadden’s adjusted pseudo-R² which is based on the log likelihood ratio of the fitted

model to the null, intercept only model. It is a relative merit of how close each model can approximate the DGP [55] . Communication of each model’s model fitting and complexity tradeoff is given by reporting the Bayesian information criterion (BIC) and performance of a log likelihood ratio test on the two models. Results for each are in Figure 7.

At the 5% significance level, the HL and CHCH tests indicate that there is insufficient evidence to rule out the null hypothesis, thus concluding that the addition of interaction terms or nonlinearity to the models is not supported. The data did support the conclusion that the more complicated model results in a better fit to the data when measured by likelihood. However, the difference in McFadden’s R² between the two models is not considerable with the BIC for model 2 being 2.8% lower than Model 1. Therefore, it was concluded that the addition of extra variables is not supported by the data and Model 2 was pursued with estimated effects given in Table 3. Estimates greater than one on site content variables provides support for Hypothesis 1a whereas the estimate for visitor type less than one provides support for Hypothesis 2a.

Examination of the odds ratio column in Table 3 provides access to an interpretation of the estimates. For the Administrative, Informational, and ProductRelated variables, an increase in one more page view would correspond to an increase in odds of purchasing by 1.0183, 1.0369, 0.9995. In other words, a one-page increase in Administrative would result in about a 1.8% increase in odds to purchase. The number of pages regarding account management (Administrative) and web site, communication, and address information (Informational) would be important for new visitors to the site. The estimated effect of the duration spent on product related pages appears small, but when considering that the maximum observed value for this variable was 63,973 seconds (about 18 hours) and the standard deviation was 1912 seconds (about 32 minutes), a small effect could easily become magnified. Exit rate exhibited the most influence on revenue probability where a unit increase in it yields a 99% reduction in odds of purchasing. As visitors who visit more pages with higher exit rates can be anticipated to not select the action to purchase. It is important to keep in mind that the exit rate is itself influenced by the other predictors and any statement of causal effect would require mediation analysis. Month and TrafficType were included as control variables as these are less in control space of a web designer. Surprisingly, the nearness to a special day had a negative impact on the odds ratio of making a purchase as the odds of making a purchase decrease by 56% as the closeness to a special day increases by one day. This may be due to collinearity with the Month or the fact that any companies may offer incentives during holidays that elevate competition and lower propensity for any visitor to convert on the website. VisitorType had an estimated negative effect on the odds ratio of making a purchase with a 24% reduction in odds of making a purchase for a returning visitor. This is consistent with the supposition that returning visitors are more informed consumers and are not susceptible to the conversion mechanisms that operate on websites to persuade visitors to buy.

Given that the predictors are correlated, a quick check of multicollinearity using variance inflation factors (VIF) was conducted. A large VIF value (>10) for a predictor indicates that much of its variation is predictable from the other predictors. In the presence of high multicollinearity, the precision in estimates is low. Table 4 contains all VIF greater than two and shows that issues of major multicollinearity are absent.

The decision to purchase on the website was framed as discrete choice, utility maximization problem. Under the assumptions that the decision to purchase had a binary choice set, the choice set was mutually exhaustive, and irrelevant alternatives did not impact utility calculus, then the estimates for the logit model can be formulated as contributions to utility those variables confer, conditional on the correctness of the assumptions and the current level of other variables and the visitor’s utility. The following were estimated to contribute positively to utility on the website—site content and quality (Administrative, Informational, ProductRelated_Duration)—whereas factors that are estimated to contribute to lower utility—exit decisions, temporal factors (SpecialDay, Month), previous site usage (ReturningVisitor).

Exit rate for a visitor is hypothesized to be an intermixture of several processes

including ones involved in the prediction of the intent to purchase. Departure behavior is also hypothesized to be a result of forces internal to the website and user experience. It is assumed that visitors that traffic to the website and do not immediately bounce have some goal that could be satisfied from usage of the web site. The web site is tasked with designing and implementing the web system such that any interest held by the visitor is channeled into conversion. The beta regression model will include only those predictors that correspond to site content and quality or are involved in the site-user interaction. The logit transformed expected value for the exit rate and the log transformed precision parameter are analyzed as linear functions of certain predictors. Using ( E x i t R a t e ∗ ( n − 1 ) + 0.5 ) and ( E x i t R a t e − min { E x i t R a t e } ) / ( max { E x i t R a t e } − min { E x i t R a t e } ) transformation made it so that exit rate was bounded in (0, 1). Testing of hypotheses 4, 5, 6 required VisitorType, Browser, and ProductRelated to be included in the linear predictor for the precision parameter. To ease interpretation, three separate models were examined whereby only one of the three precision parameter predictors was used (Model A: VisitorType, Model B: Browser, Model C: ProductRelated). Results for these three separate fits are provided in Table 5.

It is instructive to emphasize that the proposed DGP for exit rate is believed to be primarily a function of factors that are internal to the platform. The E-commerce platform serves as an interface between the visitor and personalized goals. Although there are numerous design features that are considered to contribute positively to human-computer interaction, a central premise of this work is that the usability and perceived usefulness of the web system is of utmost importance to user experience [56] [57] . This focus on a visitor’s viewpoint of the quality of a website is justified from three user experience principles: principle of predictive aiding, minimization of interaction cost, principle of multiple resources. Predictive aiding states that digital systems should forecast user needs and provide tools that ease cognitive burden before it occurs. Minimization of interaction cost asserts that a user should be able to accomplish his goal with the smallest investment of effort possible [58] [59] . The principle of multiple resources claims visitors can process multiple streams of information and this can be exploited to design an informative system [60] . Based on this theory, only site content variables, technology variables, and the visitor type variable were included in the model.

Viewing Table 5, it can seen that site content and quality variables – Administrative, Informational, ProductRelated - and the duration spent on each had a considerable influence on exit rate. With attention on Model A, an increase in a single page view for the three types of pages results in a reduction in the odds of visiting pages with high exit rate. For instance, if a visitor accesses an administrative page, the reduction in odds of exit rate is about 5.5%. Furthermore, the duration of time spent on administrative and product related pages also yields a reduction in odds of having a higher exit rate. Estimated values for duration variables are small but are measured in seconds and with large standard deviations

Note: *p < 0.1;**p < 0.05; ***p < 0.01.

in the variables, hence effects are magnified. Hypothesis 2b is supported by the data as increases in site content and quality demonstrates a negative association with average exit rate. This finding is consistent with expectations as pages that are most frequently visited are ideally the ones where the visitor should exit. If a visitor moves to a low frequency page and departs, this page will have a large exit rate. Superior site content and quality should facilitate behavior on the website that agrees with the site's objective. It can also be seen that previous site usage confers a positive influence on the average exit rate. According to Model A, if a visitor has had prior experience with the website, his odds of demonstrating an increase in expected exit rate increased by 108% compared to a user without experience. Hypothesis 1c is therefore supported by the data. Support for Hypothesis 1c and 2b appears to be contradictory but are compatible. Consider that returning visitors are assumed to have less uncertainty about their goals on the website and are therefore less likely to visit unnecessary pages. Because of this mechanism, the pages frequented by returning visitors would correspond to the ones where transactions are completed.

The precision parameter can be estimated using the technique of a generalized linear model (GLM). Examining Table 5, previous site usage (VisitorType) has a negative influence on the dispersion of exit rate, technological factors (Browser) have both positive and negative influences on dispersion in exit rate, and site content has a negative influence on dispersion in exit rate. It can be concluded that history of usage of the website is estimated to have a negative marginal effect, choice of technology in the form of a web browser is estimated to display both positive and negative marginal effects, and site content as represented by the number of product related pages viewed shows a positive marginal effect on exit rate. Thus, Hypotheses 4a, 5a, 6 are supported by the data.

Assessment of goodness-of-fit was performed by examining the pseudo-R² proposed by Ferrari and Cibari-Neto [35] , which is the squared correlation between the linear predictor for the mean and the logit-transformed response. BIC and a likelihood ratio test of the fitted models against the null intercept only model which assumes that the precision parameter is not a function of any covariates, were also used. Tests for calibration errors in the model were done with the Hosmer-Lemeshow and le Cessie-van Houwelingen-Copas-Hosmer tests. To further expose model specification issues, deviance residuals were plotted against unscaled predictor variables. Results of these tests can be found in Figure 8 and Figure 9. Model C was used for residual diagnostics as it demonstrated the largest log likelihood and smallest BIC.

Residual diagnostics in Figure 9 indicate the presence of bias in the estimated

model. This is consistent with the results of the le Cessie-van Houwelingen-Copas-Hosmer global miscalibration test which suggested that the model required the addition of bias reducing factors such as non-linear transformations of predictors or interaction terms between explanatory variables.

Unlike the exit rate model, the decision to bounce is hypothesized to be the result of factors external to the website. If the observed pattern of bouncing from pages is determined by external factors, then too much investment in mechanisms to decrease it could be wasteful. Three categories of variables were conjectured to have influence on bounce rate. Variables from each of these three categories were selected to test if bounce rate is dependent on them. Testing of relationships was conducted by fitting a beta regression model. Variability in bounce rate was hypothesized to be a function of two variables: technological variables (Browser) and previous site usage (VisitorType). Two separate beta regression models were fitted to the data where a linear predictor for the precision parameter included Browser (Model E) or VisitorType (Model D). Results of estimated effects are provided in Table 6.

Hypothesis 1b posited that as a visitor accumulated greater knowledge of the website and reduced his uncertainty about his goals, then observed bounce rate would decrease. Looking at the estimated for VisitorType in Table 6, the data does not support this hypothesis. The estimate is in the opposite direction. One might consider that visitors with a greater understanding of the layout and organization of a website may know how to traffic directly to the page they are interested in. Other websites or browsers may not link to the pages returning visitors enter at. Consequently, the page first seen by a new visitor may immediately contradict expectations, thus promoting a bounce. Hypothesis 4b is also not supported by the data as it proposed a negative association between previous site usage and dispersion in bounce rate. Looking at the results indicate that the estimate is in the opposite direction with an estimated positive marginal effect of being a returning visitor. It is worth noting that bouncing was hypothesized to be strongly dependent on factors exogenous to the website. It can be assumed that many of these are unobserved and could complicate the findings. Hypothesis 5b is supported by data which shows that technological factors do influence the dispersion in bounce rate. The two browser types with the largest positive and negative marginal effects are reported in Table 6. This is highly consistent with theory and literature as incompatibilities between browser output and visitor intention can engender immediate departure from the website.

Assessment of goodness-of-fit was performed by examining the pseudo-R², BIC, and likelihood ratio tests against the null intercept only model. Calibration errors in the model were tested for with the Hosmer-Lemeshow and le Cessie-van Houwelingen-Copas-Hosmer tests. Additional concerns with specification are documented in deviance residual plots. Results of these tests can be

found in Figure 10 and Figure 11. Model D demonstrated the smaller BIC and larger log likelihood and hence it was examined in the residual diagnostics.

The presence of bias in the deviance residual plots in Figure 11 are less pronounced and detectable than in the exit rate model, but the appearance of two clusters of residuals above and below zero conveys a bias that may be addressed with fitting a mixture model on the data. The appearance of gaps in the residual lines is consistent with the skewness of the data and is suggestive of the presence of a second mode in the data’s distribution.