The Great Equalizer?

Consumer Choice Behavior at Internet Shopbots






Erik Brynjolfsson


Michael D. Smith


MIT Sloan School of Management

Cambridge, Massachusetts




July 2000
















Acknowledgements: We thank Il-Horn Hann, John D.C. Little, Thomas Malone, Allen Montgomery, Nancy Rose, Robert Zeithammer, and seminar participants at Boston University, Carnegie-Mellon University, Indiana University, the University of Maryland, MIT, the University of Michigan, the University of Texas at Austin, Stanford University, The Wharton School, the NBER E-Commerce Project (July 2000), the Brookings conference on "Measuring E-Commerce" (September 1999), and the Workshop on Information Systems and Economics (December 1999) for valuable comments on this research. We thank for generously collecting the data necessary to conduct this research and for providing valuable insight into the shopbot market. Thomas Cheng and Frederic Mahoue provided excellent research assistance. The Center for eBusiness@MIT provided generous financial support under a grant from Fleet Bank.




The Great Equalizer?

Consumer Choice Behavior at Internet Shopbots





Our research empirically analyzes consumer behavior at Internet shopbotsó sites that allow consumers to make "one-click" price comparisons for product offerings from multiple retailers. By allowing researchers to observe exactly what information the consumer is shown and their search behavior in response to this information, shopbot data has unique strengths for analyzing consumer behavior. Furthermore, the method in which the data is displayed to consumers lends itself to a utility-based evaluation process, consistent with econometric analysis techniques.

While price is an important determinant of customer choice, we find that, even among shopbot consumers, branded retailers and retailers a consumer visited previously hold significant price advantages in head-to-head price comparisons. Further, customers are very sensitive to how the total price is allocated among the item price, the shipping cost, and tax, and are also quite sensitive to the ordinal ranking of retailer offerings with respect to price. We also find that consumers use brand as a proxy for a retailerís credibility with regard to non-contractible aspects of the product bundle such as shipping time. In each case our models accurately predict consumer behavior out of sample, suggesting that our analyses effectively capture relevant aspects of consumer choice processes.




(Internet; Choice Models; Brand; Service Quality; Partitioned Pricing; Intermediaries)

  1. Introduction
  2. "The Internet is a great equalizer, allowing the smallest of businesses to access markets and have a presence that allows them to compete against the giants of their industry."

    Jim Borland, Knight Ridder (1998)

    "The cost of switching from Amazon to another retailer is zero on the Internet. Itís just one click away."

    Thomas Friedman, New York Times (1999)

    "Shopbots deliver on one of the great promises of electronic commerce and the Internet: a radical reduction in the cost of obtaining and distributing information."

    Greenwald and Kephart (1999)


    Two decades ago information technology and bar code scanners radically reduced the cost of tracking and recording consumer purchases. A pioneering paper by Guadagni and Little (1983) used these data to estimate a multinomial logit model to analyze attribute-based consumer decision making in a retail environment. The results and extensions of their research (e.g., Kamakura and Russell 1989; Fader and Hardie 1996) have since been widely applied by academic researchers and by industry analysts for market forecasting, new product development, and pricing analysis.

    Today continued reductions in computing cost and the rise of commercial uses of the Internet augur a similar revolution in retailing and consumer analysis. Our research seeks to apply multinomial logit models as a first step in understanding consumer behavior in Internet markets.

    A better understanding of Internet markets could be particularly important in markets served by Internet shopbots. The Internet has been called "The Great Equalizer" because the technological capabilities of the medium reduce buyer search and switching costs and eliminate spatial competitive advantages that retailers would enjoy in a physical marketplace. Internet shopbots are emblematic of this capability.

    Shopbots are Internet-based services that provide one-click access to price and product information from numerous competing retailers. In so doing, they substantially reduce buyer search costs for product and price information. They also strip away many of the accoutrements of a retailerís brand name by listing only summary information from both well- and lesser-known retailers. Further, every retailer at a shopbot is "one click away," reducing switching costs accordingly. In each instance these factors should serve to increase competition and reduce retailer margins in markets served by shopbots ó an effect that should be felt most strongly for homogeneous physical goods (e.g., Bakos 1997).

    One wonders, then, what will happen to a retailerís brand equity and consumer loyalty in the presence of shopbots. has invested hundreds of millions of dollars in developing its online brand position. Likewise, brick-and-mortar retailers such as Barnes & Noble and Borders are attempting to transfer the value of their existing brand names to online markets.

    Our research addresses these questions by analyzing consumer behavior through panel data gathered from an Internet shopbot. We use these data to study four major aspects of Internet shopbot markets. First, we analyze how consumers respond to the presence of retailer brand names. Second, we analyze consumer response to partitioned pricing strategies (separating total price into item price, shipping cost, and sales tax). Third, we use Internet cookie data to analyze consumer loyalty to retailers they had visited previously. Fourth, we use the responses of observable groups of consumers to analyze how consumers respond differently to contractible aspects of the product bundle versus non-contractible aspects such as promised delivery times. In addition, we analyze the correspondence between predicted and actual consumer behavior to assess the reliability of our models and the potential for retailers to use shopbot data to facilitate dynamic or personalized pricing strategies.

    We find that branded retailers and retailers a customer had dealt with previously are able to charge $1.13 and more than their rivals, ceteris paribus. Furthermore our models demonstrate that consumers use brand name as a signal of a retailerís reliability in delivering on promised non-contractible aspects of the product bundle. Consumer loyalty can also provide pricing power; consumers are willing to pay an average of $2.49 more to buy from a retailer they have visited previously. Potential sources for the importance of brand and loyalty include service quality differentiation, asymmetric quality information, and cognitive lock-in. We also find that shopbot consumers are significantly more sensitive to changes in shipping cost than they are to changes in item price, in contrast to what would be expected from a straight-forward application of utility theory and rational consumer behavior. Lastly, we find a high correspondence between predicted and actual consumer behavior in our data suggesting that our models capture relevant aspects of consumer decision-making. We also note that retailers may be able to use the predictability of consumer behavior demonstrated in these models to facilitate personalized pricing strategies.

    Our approach to analyzing electronic markets differs from recent empirical studies in that it examines the responses of actual consumers to prices set by retailers, not just the retailersí pricing behavior. Research analyzing retailer pricing strategies has been used to characterize the relative efficiency of electronic and physical markets (Bailey 1998; Brynjolfsson and Smith 2000), retailer differentiation strategies (Clay, Krishnan, Wolff, Fernandes 1999), and price discrimination strategies (Clemons, Hann, and Hitt 1998). However, retailer pricing strategies provide only second-order evidence of consumer behavior in electronic markets.

    In this regard, shopbots provide Internet researchers with a unique opportunity to analyze actual consumer behavior in Internet markets. At Internet shopbots, thousands of consumers a day search for product information on different books. Their searches return comparison tables with a great deal of variation across retailers in relative price levels, delivery times, and product availability. Consumers then evaluate the product information and make an observable choice by clicking on a particular product offer. The result is a powerful laboratory where Internet researchers can observe snapshots of consumer behavior and, by tracking cookie numbers, consumer behavior over time.

    The data available at Internet shopbots have several natural parallels to grocery store scanner data. First, shopbot data present consumer decisions made in response to a choice between several alternatives. Second, salient product attributes are observable by both consumers and researchers. Third, consumer behavior can be tracked over time. The relative strengths and weaknesses of shopbot data when compared to scanner data are discussed in more detail below.

    The remainder of this paper is organized in four parts. Section 2 addresses the data we collect how it was collected and its strengths and limitations. Section 3 discusses the empirical models we use to analyze our data. Section 4 presents our results. Section 5 concludes, discusses implications of our results, and areas for future research.

  3. Data
    1. Data Source
    2. We use panel data collected from to analyze consumer behavior at Internet shopbots. We selected EvenBetter for four reasons. First, EvenBetter sells books ó well-defined homogeneous physical goods in a relatively mature Internet market. By analyzing shopping behavior in markets for homogeneous goods, we are able to control for systematic differences in the physical products through our methodological design. Additionally, homogeneous physical goods provide a useful reference point for the importance of brand and retailer loyalty because they should experience strong price competition in the presence of markets with low search costs (Bakos 1997). Examining relatively mature Internet markets ensures a sufficient number of consumers and retailers to draw meaningful conclusions.

      A second reason for choosing EvenBetter is that their service offers consumers a more detailed list of product attributes than most other shopbots for books. This information includes separate fields for the total price, item price, shipping cost, sales tax, delivery time, shipping time, and shipping service. Third, EvenBetter does not offer priority listings to retailers who pay an extra fee (as do some other shopbots; e.g., An unbiased listing of retailers provides a clearer interpretation of the factors driving consumersí choices. Fourth, has a revenue sharing arrangement with many of its retailers allowing us to compare descriptive statistics for the relative sales conversion ratios of the different retailers.

      A disadvantage of using data gathered from Internet shopbots is that our analysis is restricted to consumers who choose to use a shopbot. Consumers who choose to use a shopbot are likely to be systematically different than consumers who visit Internet retailers directly. Thus, our logit model predictions must be understood as being conditioned on a consumer choosing to use a shopbot. Conditioning on prior consumer choice in this way does not bias multinomial logit results (Ben-Akiva and Lerman 1985). Furthermore, in analyzing the effect of this self-selection bias on our results, it seems reasonable to assume that shopbot consumers are more price sensitive than typical Internet consumers are. Thus, our estimates of brand and loyalty effects are likely to be lower bounds on the importance of brand and loyalty among the broader population of Internet consumers.

    3. Data Characteristics
    4. EvenBetterís shopbot operates similarly to many other Internet shopbots. A consumer who wants to purchase a book visits EvenBetter and searches on the bookís title or author, ultimately identifying a unique ISBN as the basis for their search. EvenBetter then queries 47 distinct book retailers checking to see if they have the book in stock and their price and delivery times. The prices and delivery times are queried in real-time and thus represent the most up-to-date data from the retailer. Because the prices are gathered directly from the retailers, they are the same prices that are charged to consumers who visit the retailer site directly.

      Prices are displayed in offer comparison tables (e.g., Figure 1). These tables list the total price for the book and the elements of price (item price, shipping cost, and applicable sales taxes) along with the retailerís name and the bookís delivery information. If a retailer provides multiple shipping options at multiple prices (e.g., express, priority, book rate) the table lists separate offers for each shipping option.

      Figure 1: Sample Screen from

      By default, the table is sorted by total price; however, the consumer can sort based on any of the 9 columns in the comparison table. After the consumer has evaluated the information, they can click-through on a particular offer and are taken directly to the retailer in question to finalize their purchase.

      We collect four categories of data from offer data, session data, consumer data, and choice data (Table 1). We define an offer as an individual price quote from a retailer ó or equivalently an individual entry in an offer comparison table. Our offer data include separate variables for each of the nine columns in the offer comparison table: total price, item price, sales tax (if applicable), retailer name, shipping cost, shipping time, shipping service, and total delivery time. Rank is the numerical position of the offer in the table.

      Table 1: Shopbot Data Collected

      Offer Data

      Total Price

      Total price for the offer (item price plus sales tax plus shipping cost)

      Item Price

      The price for the item

      Shipping Cost

      The price for shipping

      State Sales Tax

      Sales tax (if applicable)

      No Tax

      =1 if there is no sales tax on the offer


      Retailer Name (used to create dummy variables for each retailer)

      Shipping Time

      Time to ship product from retailer to consumer (Min, Max, Average)

      Acquisition Time

      Time for retailer to acquire product (Min, Max, Average)

      Delivery Time

      Shipping time plus acquisition time (Min, Max, Average)

      Shipping Method

      Priority (1-day or 2-day), Standard (3-7 day), Book Rate (>7 day)

      Delivery NA

      =1 if retailer canít quote acquisition time on book


      The position of the offer in the comparison table

      Session Data


      Date and time search occurred


      ISBN number of book searched for (used to calculate book type)

      Sort Column

      Identifies which column the consumer sorted on (default is total price)

      Consumer Data

      Cookie Number

      Unique identifier for consumers who leave their cookies on

      Cookies On

      =1 if the consumer has their cookies on


      Which country the consumer says they are from

      U.S. State

      Which state the consumer says they are from (U.S. consumers only)

      Choice Data

      Last Click-Through

      =1 if the consumerís last click-through was on this offer


      =1 if the consumer clicked on this offer

      Loyalty Data

      Prior Last Click-Through

      =1 if the consumer last clicked through on this retailer on most recent visit

      Prior Click-Through

      =1 if the consumer clicked through on this retailer on their most recent visit

      We also track a variable we call "delivery ĎN/A.í" In some instances, retailers are unable to determine how long it will take them to acquire the book from their distributor. When this occurs, EvenBetter lists "N/A" in the delivery time field (but still lists a numerical value in the shipping time field). We capture this situation with a dummy variable that takes on the value of 1 whenever "N/A" is listed in the delivery time column. We model this by assuming that the consumer infers the total delivery time as the quoted shipping time plus an unknown constant (captured by the dummy variable).

      From our offer data we impute two additional sets of dummy variables relating to the type of shipping associated with the offer and the position of the offer in the comparison table. To construct dummy variables associated with shipping service we use the fact that the shipping services offered by retailers generally fall into three categories: express shipping (typically a 1-2 day shipping time), priority shipping (3-6 day shipping time), and book rate (greater than 7 day shipping time). We generate dummy variables for each category of shipping service. We also generate dummy variables for the first offer in the comparison table and the first screen of offers displayed (i.e., the first 10 offers) in the comparison table.

      Our second type of data is session data. We define a session as an individual search occasion for a book, or equivalently data that is common to an individual offer comparison table. Our session data include the date and time the book search occurred, the ISBN the consumer searched for, and whether the consumer chose to sort the offer comparison table based on a column other than total price (the default).

      Our consumer data include fields for the consumerís unique cookie number, whether the consumer had turned their cookies off (which occurred for 2.9% of the sessions), and the consumerís state and country location. The state and country data are self-reported and to allow the shopbot to accurately calculate local currency, taxes, and delivery times.

      Our choice data are made up of two fields. A "click-through" field captures whether a consumer "examines" an offer from a particular retailer. Since 16% of the consumers in our sample look at multiple retailers, we use a separate field to record the last click-through made by each consumer during a session. We use this as a proxy for the offer selected by the consumer. As noted in section 2.4, the click-through variable does not appear to be biased with regard to sales in a way that would affect our conclusions.

      Using our consumer and click-through data we construct two additional variables to help us control for consumer heterogeneity (Guadagni and Little 1983) and to track consumer loyalty over time: Prior Click, and Prior Last Click. Prior Click is a dummy variable taking on the value 1 for retailers the consumer clicked on in the most recent visit but did not "last click." Similarly, Prior Last Click is a dummy variable taking on the value 1 for retailers the consumer "last clicked" on in the most recent visit.

    5. Data Advantages and Limitations
    6. It is important to note that shopbot data have unique advantages and notable limitations when compared to grocery store scanner data (see Table 2 for summary). One advantage of shopbot data is that a higher proportion of shopbot consumers use identification (cookies) than scanner data consumers (scanner cards). As noted above, 97.1% of the Internet consumers in our sample left their cookies on; whereas typically less than 80% of grocery store consumers use scanner cards to make their purchases. Likewise, the shopbot does not need to establish special incentives to have consumers identify themselves. Most consumers leave their cookies on out of ignorance, habit, or convenience. In a grocery store setting, consumers must be given incentives in the form of special discounts or coupons to apply for and use scanner cards.

      At the same time there are several limitations to the use of cookies to identify consumers. Internet consumers may have more than one computer, and thus more than one cookie. Further, some computers (e.g., pooled computers at Universities) may be shared by more than one user (while having a single cookie number). Consumers may also periodically destroy their cookies, making it difficult to track behavior from cookie to cookie. Lastly, we are unable to observe consumer behavior at other Internet sites (e.g., other shopbots or product retailers) or outside the sample window. However, these limitations bias our results in known ways. Specifically, they should not effect our calculations with regard to brand and should bias our loyalty results negatively as compared to a situation where we knew with certainty each consumerís prior behavior.

      Table 2: Summary of Data Advantages and Limitations




      Accuracy of consumer identification

      Higher proportion of Internet consumer use identification (cookies).

      Cookie data for consumer identification less reliable than scanner cards.

      Accuracy of offer data

      Highly reliable knowledge of competing offers and prices.

      Coupon availability and use not observed directly.

      Observability of consumer behavior

      Observe consumer search behavior (click-through versus last click-through).

      Purchases not observed directly (only click-through observed).

      Applicability to utility-based choice models

      Offers are presented with individual product attributes in sortable table.

      Model limited to factors driving click-through not necessarily purchase.

      Another advantage of Internet shopping data as compared to scanner data is the amount and quality of data that can be collected. With our data we know exactly which offers were shown to consumers and the order in which the offers were displayed. In scanner data sets, only the prices of products that are purchased are collected directly. Thus, the prices and stock characteristics of competing offers must be inferred from available data on purchases within the scanner data sample. This provides an imperfect signal of the prices and stock conditions for competing offers in scanner data sets (see Erdem, Keane, and Sun 1999 for a discussion of this problem and an approach to address it).

      However, a limitation of our data in this regard is that we do not observe the use of coupons in our Internet, whereas coupons are readily observable in scanner data sets. Thus, a consumerís knowledge that a particular Internet retailer had a $10 off coupon would increase the particular retailerís brand effect during the time frame the coupon was available. During our sample period we did not observe significant use of coupons (with one possible exception, noted in section 4). However, we did not track couponing systematically. Future research could track the availability of coupons by querying Internet coupon aggregation site (e.g.,,,,

      A third advantage of our data is that the manner in which offers are presented is particularly applicable to utility-based models of consumer behavior. Shopbot data are presented in a comparison matrix where the different attributes of each product are readily available and can be easily evaluated and compared. In contrast, the attributes of products in a scanner data context are more difficult to compare directly. Decreasing the effort necessary to compare the different attributes of a bundle should improve the accuracy of a consumerís latent utility calculations (Morwitz, Greenleaf, and Johnson 1998).

      A final advantage of our data is that by comparing the click-through field to the last click-through field (see Table 1) we can analyze consumer search behavior: which retailers do consumers examine before they make their final selection. In a grocery store setting, this would be equivalent to observing a consumer pick up a particular item, look at it, but ultimately put it down and choose a different item ó data that could only be gathered at a very high cost in physical stores.

      However, as above, these advantages come with limitations. In our data set we only observe the consumerís click-through choices ó we do not observe their final purchase directly. This is a significant limitation as compared to scanner data settings where purchases are readily apparent. However, because of associate program relationships between the shopbot and most of its retailers we are able to determine whether purchase behavior is biased in a way that would impact our empirical analysis. We discuss this issue in more detail in the methodology section.

    7. Descriptive Data

    Our data set was gathered over 69 days from August 25 to November 1, 1999. To simplify interpretation, we limit our analysis to prices for U.S.-based consumers (75.4% of sessions), sessions that lead to at least one click-through (26.3% of remaining sessions) and sessions that return more than one retailer (99.9% of remaining sessions). The resulting data set contains 1,513,439 book offerings from 39,654 searches conducted by 20,227 distinct consumers. Included in this data set are 7,478 repeat visitors, allowing us to track consumer behavior over time.

    These data show a significant dispersion in prices, even for entirely homogeneous physical goods. The average difference in total price between the lowest priced offer and the tenth lowest priced offer is $10.77 in our data. In percentage terms, the tenth lowest priced offer is typically 32.3% more expensive than the lowest priced offer. These results are very similar to Brynjolfsson and Smith (2000, p. 575) who report an average range of 33% between the highest and lowest book prices obtained from 8 different Internet retailers in 1998-1999.

    Table 3 lists selected descriptive data statistics for our data from the 6 most popular retailers at EvenBetter. Column 1 lists estimates of market share in the broader Internet market and column 2 lists the share of last click-throughs for EvenBetterís consumers. Comparing these two columns yields two insights into the Internet shopbot market. First, shares of last click-throughs are significantly less concentrated than estimates of market share in the broader Internet market for books. Second, click-through shares strongly favor low priced retailers when compared to share estimates in the broader Internet market. For example,, a relatively high priced retailer, has approximately 75% of the total Internet book market yet holds only an 8.6% click-through share for EvenBetterís consumers. At the same time the share positions for three low priced, and relatively unknown, retailers are dramatically enhanced at

    Table 3: Comparison of Retailers at a Shopbot


    Internet Market Share (Est.) *

    Shopbot Last Click Share

    Proportion of Lowest Prices

    Click-Sales Conversion Ratio



























    * Internet market share is compiled from press reports and an analysis of click-through data from prior research (Brynjolfsson and Smith 2000).

    One explanation for this difference is that the lower search costs offered by shopbots make it easier for consumers to locate and evaluate unbranded retailers and this changes their choice behavior from what it would have been if no shopbots were available. To the extent that this explanation holds, it supports the hypothesis that shopbots are a "great equalizer" in Internet markets, putting small retailers on a more equal footing with their larger and more well known competitors. It is also possible that because EvenBetterís consumers are highly price sensitive they are more inclined to shop at low priced retailers than consumers in the broader market.

    However, while shopbot consumers appear to be price sensitive, 51% of them choose an offer that is not the lowest price returned in a search. Although the books offered are completely homogeneous, factors other than price influence consumer choice in this setting. Our descriptive data suggest that retailer brand identity is at least one of the factors influencing consumer behavior. This can be seen by comparing columns 2 and 3 in Table 2. These columns show that while branded retailers have the lowest price for only 15% of the book searches they make up 27% of consumer choices. Likewise, the top three unbranded retailers, who have the lowest price 36% of the time, make up only 26% of consumer choices. The advantage held by branded retailers can also be seen by examining the offer price premium, the difference between the lowest priced offer and the price of the offer actually selected. For branded retailers this difference averages $3.99 while for unbranded retailers it averages $2.58, a difference of $1.41.

    Our descriptive statistics also give insight into consumer purchase behavior. Because our choice data only track click-throughs, our empirical results only predict factors that drive traffic to a site ó not necessarily factors that drive sales. However, the descriptive statistics in column 4 of Table 3 suggest that traffic is a relatively unbiased indicator of actual sales. These ratios are constructed by comparing the number of sales at a particular retailer during September and October 1999 to the number of last click-throughs recorded for that retailer during the same time period. These statistics do not vary significantly across branded and unbranded retailers ó supporting the interpretation of our results with regard to the behavior that influences sales.

    Descriptive statistics provide a useful first step in analyzing consumer choice data. However, definitive conclusions are only possible through systematic empirical models that control for the effect of other aspects of the product bundle. In the next section we discuss two systematic empirical models that can be used to analyze our research questions.

  4. Methodology
  5. As noted above, our research goal is to analyze how consumers respond to different aspects of a product bundle including brand name, retailer loyalty, partitioned prices, and contractible and non-contractible product characteristics. There are a variety of choice models available to analyze these questions in a multidimensional choice setting. We discuss the two most prominent models below ó the multinomial logit and nested logit models ó as an introduction to our analysis. We also provide brief descriptions of multinomial probit as an alternate empirical model and Hierarchical Bayesian Estimation as an alternate estimation technique.

    As discussed below, the availability of a nested logit model to control for concerns about the independence of irrelevant alternatives, the applicability of aggregate response in the shopbot market, and the limited availability of longitudinal individual-level choice data leads us to conclude that logit-based models and maximum likelihood estimation techniques are the most appropriate analysis techniques for our research questions.

    1. Multinomial Logit Model
    2. Given the parallels between our data and scanner data, the multinomial logit model ó the workhorse of the scanner data literature (e.g., Guadagni and Little 1983, Kamakura and Russell 1989, Fader and Hardie 1996) ó provides a natural empirical starting point for our analysis. We describe the nature of this model briefly below and refer the interested reader to Ben-Akiva and Lerman (1985) or McFadden (1974) for more detailed treatments of the model.

      In a choice setting, the multinomial logit model can be motivated by assuming consumers make choices by first constructing a latent index of utility (Uit) for each offer (t) in each session (i) based on the offerís characteristics and the consumerís preferences. We model the consumerís utility for each offer as the sum of a systematic component (Vit) and a stochastic component ():


      The stochastic disturbance can be motivated from a variety of perspectives (Manski 1973); for our purposes the two most natural motivations are (1) unobserved taste variation across consumers and (2) measurement error in evaluating offers.

      We further express (Vit) as a linear combination of the productís attributes () and the consumerís preferences for those attributes (). Equation (1) then becomes


      To justify this starting point we note that, while modeling consumer choices in terms of latent utility indexes is accepted practice in the marketing and economics literature, its use may be particularly applicable in our setting. By listing offers in a comparison matrix with separate values for a variety of product attributes EvenBetterís comparison matrix lends itself to a rational, attribute-based evaluation by consumers.

      The coefficients in (2) could be readily estimated using standard least squares techniques if the researcher could observe directly. Unfortunately, this is not generally the case in practice. Instead we typically observe only the resulting choice in session i: . However, under the assumption of utility maximization, we can infer that if and only if . Thus, we can write the probability that offer t is chosen in session i as:


      Using (2) this can be rewritten as:


      The multinomial logit model assumes that the disturbance terms are independent random variables with a type I extreme value distribution


      where m is an arbitrary scale parameter. This distribution is motivated, in part, because it is an approximation to a normal distribution. However, the assumption has the even more desirable property that it dramatically simplifies (4) to the following form (McFadden 1974):


      This formula has all the desirable properties of a purchase probability: it is always positive, it sums to 1 over all the offers in session i, and it is invariant to scaling.

      Our goal is to determine the b vector ó the weights on the consumersí evaluation of offers. Unfortunately, we estimate m b . Since m is present in each of the b terms it is not identifiable. However, since its purpose it to place a scale on the utility of the model, we can arbitrarily set it to any real number (Ben-Akiva and Lerman 1985, p. 107) to identify the b coefficients. While this is a benign assumption in the multinomial logit model, it has implications for our ability to compare coefficients in the nested logit model, which we now discuss.

    3. Nested Logit Model

The parsimony of the multinomial logit formula comes at a cost. The assumption that errors are independent across offers gives rise to the Independence of Irrelevant Alternatives (IIA) characteristic in the multinomial logit model. Simply put the IIA problem is that the probability ratio of choosing between two offers depends only on the attributes of those two offers and not on the attributes of any other offers in the choice set. Using equation (6) this can be expressed as:


This restriction is violated if the error independence assumption does not hold. The error independence assumption might be violated if subsets of alternatives in the consumerís choice set are similar to one another. This problem may impact our data if consumers perceive different branded (or unbranded) retailers as offering similar service levels. For example, a consumer who placed a high value on offers from may also place a high value on offers from or In this case, the cross-elasticity between offers is not equal but rather is much higher among branded retailers than it is between branded and unbranded retailers (and potentially vice-versa).

The solution to this problem is to place similar offers in common groups ó or nests ó such that the IIA assumption is maintained within nests while the variance is allowed to differ between nests. Thus, the consumer can be modeled as facing an initial choice S (e.g., S={branded retailers, unbranded retailers}) followed by a restricted choice R (e.g., R={{amazon, barnesandnoble, borders}, {a1books, kingbooks, 1bookstreet,Ö}).

Given this decision model we represent the choice set for consumer n as the Cartesian product of the sets S and R minus the set of all alternatives that are infeasible for individual n, or . We further define the marginal brand choice set, Sn, to be the set of all brand options corresponding to at least one element of Cn and the conditional retailer choice set, Rns, as the subset of all retailers available to consumer n conditional on the consumer making brand choice s.

We then model the utility associated with a choice of brand category and retailer as


where Vs and Vr are the systematic utilities associated with the choice of brand and retailer respectively and Vsr is the systematic utility associated with the joint choice of brand and retailer. The error terms are defined similarly as the random components of utility associated with the choice of brand, retailer, and the joint choice of brand and retailer.

We additionally assume that

  1. var(er)=0, which is equivalent to assuming independence of choice alternatives in the bottom level nest (Guadagni and Little 1998);
  2. es and esr are independent for brand and retailer selections in the consumerís choice set;
  3. the esr terms are independent and identically Gumbel distributed with a scale parameter , and
  4. the es terms are distributed such that is Gumbel distributed with a scale parameter of

Given these assumptions, the choice of retailer conditional on the choice of brand at the lower level nest becomes


which is simply the standard logit model.

Similarly, the choice of brand category becomes




As in the multinomial logit model, the coefficients we estimate are convoluted with the scale parameter (m r). Because the m r is constant within nests, it is possible to analyze the b parameters within nests. However, the scale parameter will not be constant across nests in general, making it impossible to directly compare coefficients across nests (Swait and Louviere 1993). However, it is possible to compare shared coefficients by normalizing to a common reference point. We discuss this in more detail in the analysis section.

    1. Alternate Models and Estimation Techniques

The multinomial probit model (Hausman and Wise 1978) is the most recognized alternative to the logit-based models of choice described above. This model assumes that the discrete choice errors are normally distributed. The advantage of this assumption is two-fold. First it allows for more realistic correlation structures for the error components, eliminating the IIA problem. Second, and similarly, it allows for flexible modeling of taste variation across consumers (or other subsets of choice actors).

However, the normality assumption comes as a high cost. It is computationally intensive to evaluate the higher-order multivariate normal integrals used in the multinomial probit model. Several advances have been made in the evaluation these integrals. Hausman and Wise (1978) use a transformation of variables to reduce the dimensionality of the variance-covariance matrix by one. McFadden (1989) employs a method of simulated moments using Monte Carlo simulation to eliminate the need for direct estimation of the likelihood function. However, in spite of these advances, standard multinomial probit estimation using these techniques remains computationally infeasible for large samples or models with more than a handful of choice alternatives making it impractical in our setting. In its place, our use of the nested logit model should control for IIA concerns across branded and unbranded retailers.

Hierarchical Bayesian Estimation (McCulloch and Rossi 1994) provides an individual-level estimation alternative for both logit- and probit-based models. Hierarchical Bayesian Estimation uses Bayesian techniques to estimate individual-level responses for each consumer in a sample (along with aggregate level responses). Moreover, the model makes probit estimation feasible by using the Gibbs sampler to generate an exact posterior distribution of the multinomial probit model. This avoids the computational problems associated with estimation of the multinomial probit likelihood function while still allowing for a correlated error structure.

However, hierarchical Bayesian techniques are typically used to analyze individual level consumer response (e.g., Rossi, McCulloch, Allenby 1996; Montgomery 1997). Given the separation between shopbots and retailers, individualized pricing strategies are not currently used in shopbot markets making Hierarchical Bayesian techniques less appropriate for our analysis. Additionally, most of the customers in our data set make only a single purchase or have relatively short purchase histories, making individual level estimation less reliable. However, with longer purchase histories Hierarchical Bayesian Estimation may make a potentially useful area for future analysis, especially if shopbots develop individualized pricing regimes in the future.

  1. Empirical Results
  2. Our analysis addresses four empirical questions: consumer response to the presence of brand, consumer response to partitioned pricing strategies, consumer loyalty to retailers they have visited previously, and consumer response to contractible and non-contractible aspects of the product bundle. We also use the predictive characteristics of our models to assess their reliability of our results and to explore the potential for retailer-based personalized pricing strategies. We address each of these questions in turn below using multinomial logit and nested logit models.

    1. Consumer Response to Brand
    2. Retailer brand might matter to consumers of homogeneous physical goods if branded retailers provide objectively better service quality or if consumers are asymmetrically informed regarding individual retailerís service quality and are using brand as a proxy for quality. To analyze consumer response to brand, we capture brand name in two ways: first with a dummy variable that takes on a value of 1 for branded retailers, and second with separate dummy variables for each of these three retailers (,, Results for these models are presented in Columns 1 and 2 of Table 4 along with other variables that may impact consumer choice: total price, average delivery time, and delivery "N/A."

      As noted above, the coefficients listed in Table 4 should be interpreted as preference weights in a latent utility function. Thus, the negative coefficient on price indicates that higher prices, ceteris paribus, lead to lower latent utilities and, as a result, to fewer consumer click-throughs. Likewise, longer delivery times and not being able to quote a specific delivery time (Delivery "N/A") lead to lower latent utility in the consumerís evaluation.

      Table 4: Basic Models of Brand Choice







      Total Price

      -.252 (.001)

      -.253 (.001)


      Item Price


      -.193 (.001)

      -.194 (.001)

      -.194 (.001)

      Ship Price


      -.367 (.002)

      -.368 (.002)

      -.369 (.002)

      Sales Tax


      -.438 (.014)

      -.432 (.014)

      -.214 (.020)

      No Sales Tax (0/1)


      .504 (.039)

      Average Delivery Time

      -.011 (.001)

      -.011 (.001)

      -.018 (.001)

      -.019 (.001)

      -.019 (.001)

      Delivery "N/A"

      -.417 (.015)

      -.420 (.015)

      -.368 (.015)

      -.374 (.015)

      -.370 (.015)

      Branded Retailers

      .284 (.014)


      .315 (.014)




      .467 (.020)


      .477 (.020)

      .463 (.020)



      .179 (.023)


      .177 (.023)

      .185 (.023)



      .186 (.020)


      .266 (.020)

      .254 (.020)

      Log Likelihood






      Adjusted U2






      * Standard Errors listed in parenthesis. All results are significant at p<.05. Adjusted U2 = 1-(LL(*)-# of variables)/LL(0) (Ben-Akiva Lerman 1985, p. 167). N=39,654 sessions.

      At the same time, consistent with the descriptive data presented in section 2, we find that even after controlling for price and delivery time brand still has a significant positive effect on latent utility. Each of the coefficients on brand in specifications 1 and 2 are positive and highly significant suggesting that consumers are willing to pay more for offers coming from branded retailers.

      Following Guadagni and Little (1983), we can use the absolute value of the ratio of the coefficient to the standard error (the t-statistic) to interpret the relative importance of each variable in the consumerís evaluation of an offer. This comparison is motivated by observing that larger coefficients indicate factors that are more important in the consumerís evaluation of the offer and more accurately estimated coefficients indicate factors where there is a high degree of uniformity in response to the variable. Using this comparison we note that the total price variable has a t-statistic of 176, which is nearly 10 times larger than the next closest t-statistic. This indicates that an offerís total price is by far the most important factor consumerís use to evaluate offers ó supporting the inference that consumers are highly price sensitive in the shopbot setting.

      We can use the relative sizes of the coefficients to gain an idea of the importance of brand name in dollar terms. This comparison exploits the fact that coefficients in the multinomial logit are product attribute weights in the consumerís latent utility function. Thus, we can construct counter-factual comparisons of varying offer characteristics to evaluate the importance of characteristics in dollar terms. For example, we can ask: Given two offers that are exactly the same with respect to all product attributes, if we added brand to one offer, how much would we need to decrease the price of the other offer to keep the latent utility constant? The answer, derived from equation (2) above is:


      Using this equation we can use the results from Table 3 column 1 to calculate that offers coming from one of the three branded retailers have a $1.13 price advantage over unbranded offers. From column 2, we further infer that offers from have a $1.85 advantage over unbranded retailers, ceteris paribus, and offers from Barnes and Noble and Borders have an advantage of approximately $0.72 over unbranded retailers. Considering that the average total price of the books chosen by customers in our sample is $36.80, these figures translate into 3.1% margin advantage for branded retailers (and a 5.0% margin advantage for in head-to-head comparisons with unbranded retailers.

      There are several possible explanations for the price advantage among branded retailers in Internet markets for homogeneous physical goods. First, branded retailers may provide objectively better service quality with regard to product delivery, web site ease-of-use, privacy policies, product return policies, or other service attributes. Retailer differentiation in these service characteristics is consistent with their strategic goal to mitigate direct price competition (de Figueiredo 2000).

      Delivery service is likely to be one of the most important aspects of a retailerís service quality. While our empirical methodology will control for the quoted delivery time by each retailer, it is possible that branded retailers are more reliable in meeting their quoted delivery times. To investigate this possibility, we ordered 5 books, using various shipping services, from the 6 most popular retailers listed at and compared their actual and promised delivery times. Our results are displayed in Table 5 below. The first column displays the number of books (out of 5) that were delivered before the first day in the retailerís quoted delivery range. The second column displays the number of books that were delivered within the quoted delivery time (out of 5) including those that were delivered early. The third column displays the delivery rating (out of 5) for each retailer. While each of the first three ratings is an imperfect measures of the actual service quality delivered by these retailers, they do not indicate a dramatic differences in service quality between branded and unbranded retailers, suggesting that heterogeneity in this aspect of service quality may not explain the majority of brand response observed in our data.

      Table 5: Retailer Delivery Accuracy


      Early Delivery

      On-Time Delivery (including early) Delivery Rating

























      A second possible explanation for the importance of brand concerns the information available to consumers in electronic markets. It is possible that service quality should be modeled as an experience good where consumers are asymmetrically informed, ex ante, regarding the quality they will receive for a particular order.

      Erdem and Swait (1998) use an information economics framework to demonstrate that in markets with asymmetric information about quality, consumers use brand names as a signal of product quality. These signals reduce consumersí information acquisition costs, lower the risk they must incur when making purchases, and ultimately increase their expected. Brand signals can be communicated to consumers through advertising (Milgrom and Roberts 1986) and through prior personal evaluation (Erdem and Keane 1996).

      Extending the information economics model of brand value to the Internet, Erdem et al (forthcoming), argue that the Internet may have a differential effect on brand value depending on the nature of the product: "We expect that for search goods the Internet reduces the importance of brand in its role of reducing perceived risk. For experience goodsÖwe expect that the Internet will not reduce (and may well increase) the importance of a brand in its role of reducing perceived risk" (p. 269).

      However, as noted above, the importance of service quality for physical products ordered over the Internet may cause these products to behave more like experience goods than search goods. This aspect of Internet markets may differ conceptually from physical world markets to the extent that the spatial and temporal separation between consumers, retailers, and products in Internet markets increases the importance of service quality and reduces consumersí ability to evaluate quality prior to making a purchase (Smith, Brynjolfsson and Bailey 2000). Under this explanation, retailer branding may remain an important source of competitive advantage for Internet retailers ó even in markets served by shopbots.

      It is also possible that our brand name results derive from unobserved loyalty. Because we do not observe consumer behavior for visits directly to the retailer or for visits to the shopbot outside of our sample window, consumers have prior unobserved relationships (and therefore loyalty) that disproportionately resides with branded retailers. In this case the loyalty effects discussed in section 4.2 will also apply to our brand coefficients.

    3. Consumer Response to Partitioned Pricing
    4. We also consider consumer response to the elements of total price: item price, shipping cost, and sales taxes. Prices that are comprised of a base cost and various surcharges are referred to as partitioned prices in the marketing literature. Morwitz, Greenleaf, and Johnson (1998) analyze partitioned prices in environments where it is difficult for the consumer to calculate the total price from the presentation of the base price and surcharge. They find that consumers are less sensitive to the amount of the surcharge (and therefore surcharges can be an effective pricing strategy for retailers). These results may explain why Internet retailers commonly use partitioned prices for their web-site direct consumers. Waiting to present the cost of surcharges such as shipping cost until the final step of a purchase may decrease the Internet consumerís perception of total price during their evaluation of the product.

      However, shopbots present consumers with a very different environment with regard to partitioned prices. To analyze consumer response to partitioned prices in this setting, columns 3 and 4 of Table 4 separately model consumer response to the elements of total price: item price, shipping price, and sales tax. In contrast to Morwitz, Greenleaf, and Johnson, these results suggest that consumers are nearly twice as sensitive to changes in shipping price than they are to changes in item price. Column 5 adds a "no tax" dummy variable that takes on the value 1 when there are no tax charges assessed by the retailer for that particular consumer. The addition of this variable suggests that conditional on tax being charged, consumers are no more sensitive to changes in tax than they are to changes in item price. However, they respond very strongly to the presence of any tax at all in a price (c.f. Goolsbee 2000) and they are still nearly twice as sensitive to changes in shipping price as they are to changes in item price and sales tax.

      The source of the difference between our results and those of Morwitz, Greenleaf, and Johnson is likely due to the difference in consumer cognitive processing costs when associating the base price and surcharge at a retailerís web site and at a shopbot. As noted above, partitioned prices are typically used in a situation where it is computationally difficult for the consumer to compute the total price from the separate base price and surcharge information. In contrast, at most shopbots shipping cost and tax are included in the total price and identified separately in the offer comparison table, making the effect of shipping cost and tax on the offer price fully observable to the consumer.

      Still, finding a higher sensitivity to shipping costs than item price is surprising insofar as it conflicts with the most straightforward application of utility theory and rational consumer behavior. We would expect that if there were no cost to calculate the total price, the effect of a $0.01 increase in price would be the same whether it enters total price through item price or through shipping cost or sales tax. Apparently this is not the case for at least some of EvenBetterís consumers. There are several possible explanations for these findings. First, consumers may be considering the fact that shipping and handling charges are non-refundable in the event that they return the book. In this case, the expected cost of a book would be


      where a is the probability of returning the book. However, for this to explain all of the observed difference in response to item price and shipping costs, consumers would have to estimate that the probability of making a return is 48% (i.e., 1-/). This is much higher than the 3-5% return rate observed in the monthly sales reports from EvenBetter.comís associate program relationships with its retailers.

      A second explanation for the increased sensitivity of consumers to shipping prices is that consumers are simply opposed to paying for costs they perceive to be unrelated to the product. A consumer may perceive that a dollar paid to a publisher (and eventually, in part to the author) is different than a dollar paid to a store, a shipper, or to the government (in the case of taxes). Similarly, consumers may object to prices they believe to be "unfairly" high (Kahneman, Knetsch, Thaler 1986) such as handling charges typically added to shipping costs.

      Prospect theory (Kahneman and Tversky 1979; Thaler 1985) offers third possible explanation. Consumers may be using different reference prices for shipping costs and item prices. For example, consumers may be using a low (possibly zero) reference price for shipping charges and a higher reference for item price, having strong negative reactions to increases in price above their reference price for each price category. A fourth, and closely related, possibility is that consumers evaluate percentage changes in prices ó responding more strongly to an increase in shipping cost from $3 to $4 than an increase in item price from $30 to $31.

      A fifth possibility is that consumers are planning to make multiple purchases from the retailer over several shopping visits, and are taking into account how lower shipping costs will effect their total purchase price over multiple items.

      There may also be other explanations and this finding deserves more study. It would be interesting to focus on differences in consumer response to partitioned prices between a typical Internet retailerís web site where base prices and shipping costs are presented separately and a shopbot where they are presented together. Such an investigation could reveal that retailers should adopt differential pricing strategies with respect to shipping charges for shopbot consumers and web site direct consumers. Similarly, one could analyze price comparison behavior among web shoppers from a prospect-theoretic or cognitive processing context. As noted above, a possible explanation for our results is that customers respond non-linearly to price changes and have separate mental accounting functions for the different elements of price. Non-linear response is also seen in the importance of an offerís position in the price comparison table reflected in Table 8 columns 2-6 and may be explained by prospect theory or the cognitive processing costs of evaluation additional offers.

    5. Retailer Loyalty
    6. Our data can also be analyzed to determine the effect of retailer loyalty. Consumers may be loyal to retailers for a variety of reasons. As noted above, in a setting with asymmetric information regarding retailer service quality, consumers may use prior experience with a retailer as a signal of service quality in subsequent purchase occasions. Consumers may also factor in the cost of time to learn how to use a new retailer site or to enter in the information necessary to establish an account with a new retailer. Johnson, Bellman, and Lohse (2000) refer to this effect as cognitive lock-in and find that it is a significant source of web site "stickiness."

      We use the two variables Prior Click and Prior Last Click to analyze the effect of retailer loyalty in our setting. To simplify interpretation of the coefficients, we limit our analysis to repeat visitors. Our results adding these two variables to the previous models are shown in Columns 1 and 2 of Table 6. Here we find that consumers are much more likely to choose a retailer they have selected on a prior search (Prior Last Click). In dollar terms, retailers that a consumer had selected previously hold a $2.49 advantage over other retailers. We also find that consumers who had evaluated, but not selected, a brand (Prior Click) are statistically no more likely to select that brand on a subsequent visit. This suggests that, what they learned about the brand by visiting the retailerís site has, if anything, a negative effect on subsequent offer evaluations (consistent with their observed behavior on the initial visit).

      Table 6: Basic Models of Brand Choice with Loyalty for Repeat Visitors






      Total Price

      -.232 (.002)

      -.233 (.002)


      Item Price


      -.179 (.002)

      -.180 (.002)

      Shipping Price


      -.342 (.003)

      -.343 (.003)



      -.163 (.023)

      -.164 (.023)

      No Tax (0/1)


      .615 (.048)

      .603 (.048)

      Average Delivery Time

      -.011 (.001)

      -.010 (.001)

      -.019 (.001)

      -.018 (.001)

      Delivery "N/A"

      -.368 (.018)

      -.373 (.018)

      -.328 (.018)

      -.332 (.018)

      Branded Retailers

      .296 (.017)


      .314 (.017)




      .499 (.024)


      .482 (.024)



      .252 (.028)


      .254 (.027)



      .130 (.025)


      .197 (.025)

      Prior Last Click

      .577 (.028)

      .579 (.028)

      .547 (.028)

      .548 (.028)

      Prior Click

      -.096 (.064)

      -.082 (.064)

      -.114 (.063)

      -.105 (.063)

      Log Likelihood





      Adjusted U2





      * Standard Errors listed in parenthesis. Italicized results are insignificant at p<.05. N=26,390 sessions.

      These findings are consistent with the importance of cognitive lock-in, web site convenience, and asymmetric information as sources of competitive advantage in electronic markets. They also help to quantify the importance of first mover advantage among Internet retailers. Moreover, these results are obtained from consumers who are likely to be among the least loyal consumers in Internet markets. According to shopbot managers, many customers use shopbots to locate retailers they are happy with and, after a period of good service, begin to visit the retailers, directly, bypassing the shopbot (and regrettably our data set. Thus, our loyalty results constitute a lower bound on loyalty among typical Internet customers.

      The importance of loyalty in this setting also suggests that shopbots may provide an effective and low cost avenue for retailers to acquire new consumers and gain competitive advantage against their rivals. This factor may be particularly important for lesser-known retailers as reflected in the market and click-through share statistics presented in Table 2.

    7. Contractible and Non-contractible Product Characteristics
    8. Another aspect of competitive behavior in Internet markets pertains to how consumers respond to contractible and non-contractible aspects of the product. Contractible aspects of the product bundle include aspects where consumers have clear avenues of recourse if the retailer does not deliver what they had promised such as the characteristics of the physical product or the productís price. Other aspects of the product bundle, such as delivery time, are non-contractible. It is difficult, if not impossible, to force the retailers to deliver a product within the time frame quoted to the customer.

      In the presence of non-contractible product characteristics, economic theory predicts that consumers will use a retailerís brand name as a proxy for their credibility in fulfilling their promises on non-contractible aspects of the product bundle (e.g., Wernerfelt 1988). Moreover, consumers who are more sensitive to non-contractible aspects of the product bundle should disproportionately use brand in their evaluation of product offers.

      To investigate how customers respond to non-contractible aspects of the product bundle we assume that consumers who sort the offer comparison tables based on elements of shipping time (e.g., shipping service, shipping time, and total delivery time) are more sensitive to accuracy in delivery time than consumers who sort on total price or item price. We then compare the responses of these two sets of consumers to selected aspects of the product bundle (Table 7).

      The selected variables include the differential response of consumers who sort on shipping columns to the productís item price, shipping price, average delivery time, and a dummy variable identifying whether the product is sold by a branded retailer. These variables were chosen using a likelihood ratio test to compare the restricted model (in Table 7) to an unrestricted model where all variables are allowed to vary between consumers who sort on shipping and consumers who sort on price. The likelihood ratio test failed to reject (p<.01) the null hypothesis that there is (jointly) no difference in the response of consumers who sort on shipping and consumers who sort on price to tax, the no tax dummy variable, delivery "N/A," prior last click, and prior click.

      Table 7: Sorting Based on Shipping versus Price



      Item Price

      -.194 (.001)

      Shipping Price

      -.370 (.002)


      -.207 (.020)

      No Tax (0/1)

      .524 (.039)

      Average Delivery Time

      -.019 (.001)

      Delivery "N/A"

      -.369 (.015)

      Branded Retailers

      .291 (.014)

      Prior Last Click

      .545 (.028)

      Prior Click

      -.126 (.064)

      Differential Coefficients for consumers who sort on shipping

      Sort on Shipping * Item Price

      .080 (.014)

      Sort on Shipping * Shipping Price

      .296 (.019)

      Sort on Shipping * Average Delivery Time

      -.053 (.013)

      Sort on Shipping * Branded Retailers

      .986 (.222)

      * Standard Errors listed in parenthesis. All results are significant at p<.05. N=39,613 sessions (39,487 sessions sort on total price or item price, 126 sessions sort on shipping time, delivery time, or shipping service).

      Our results show that consumers who care about accuracy in delivery time are, not surprisingly, less sensitive to item price and shipping price and more sensitive to average delivery time. However, these consumers are also more than four times more sensitive to the presence of brand in an offer than consumers who sort in price. These results confirm the economic intuition above. Consumers who care about non-contractible aspects of the product bundle appear to use retailer brand as a proxy for credibility.

      This result may also explain a comparison of our results for frequent versus infrequent visitors. It is possible that frequent book purchasers are more likely to be sensitive to quality service as a function of their motivation for making the frequent purchases. To analyze this we classify cookies that only appear only once in our 69-day sample as infrequent visitors and cookies that appear multiple times in our sample as frequent visitors. We present multinomial logit model results for these two groups of consumers in Table 8.

      Table 8: Comparison of Frequent and Infrequent Visitors


      Frequent Visitors

      Infrequent Visitors

      Item Price

      -.179 (.002)

      -.228 (.003)

      Shipping Price

      -.343 (.003)

      -.423 (.004)


      -.422 (.017)

      -.473 (.025)

      Average Delivery Time

      -.018 (.001)

      -.019 (.001)

      Delivery "N/A"

      -.330 (.018)

      -.448 (.026)

      Branded Retailers

      .344 (.017)

      .260 (.024)

      * Standard Errors listed in parenthesis. Italicized results are insignificant at p<.05. N=26,390 sessions.

      As noted in section 3.1, each model has a unique and unidentified scale parameter, which prevents the direct comparison of coefficients across model specifications. However, it is possible to compare coefficients across model runs after normalizing to a common variable within each specification. Normalizing in this manner cancels the scale parameter and provides a common basis for comparison. In our case, we normalize each coefficient in Table 8 as follows


      where j is item price and s={frequent visitors, infrequent visitors}. Thus, as in equation 12 in section 4.1, we express each coefficient in terms of its dollar value impact on a consumerís evaluation of the product bundle. Our results from this normalization are shown in Table 9.

      To allow for statistical comparison of our normalized coefficients we use the fact that for two random variables a and b, the variance of is given by (Bevington 1992) as


      For and using our unbiased estimates of standard deviation this simplifies to


      The resulting standard errors () are listed in parenthesis in Table 9.

      Table 9: Comparison of Frequent and Infrequent Visitors, Normalized by Item Price


      Frequent Visitors

      Infrequent Visitors

      Shipping Price/Item Price

      -1.911 (.024)

      -1.853 (.030)

      Tax/Item Price

      -2.355 (.095)

      -2.073 (.111)

      Avg. Delivery Time/Item Price

      -.101 (.004)

      -.083 (.005)

      Delivery "N/A"/Item Price

      -1.840 (.101)

      -1.960 (.117)

      Branded Retailers/Item Price

      1.916 (.097)

      1.136 (.108)

      * Standard Errors listed in parenthesis. Italicized results are insignificant at p<.05. N=26,390 for frequent visitors and 13,264 for infrequent visitors.

      In each case, we test the null hypothesis that the normalized coefficients are equal using the standard t-test for with and unknown and


      with degrees of freedom given by (Satterthwaite 1946)


      Under this test, we reject the null hypothesis for average delivery time and the presence of brand at p=0.05, finding instead that frequent visitors are more sensitive to average delivery time and the presence of brand. We fail to reject the null hypothesis for the normalized coefficients on shipping price, tax, and delivery "N/A". Consumer response to these coefficients is statistically the same for frequent and infrequent visitors. One possible explanation for this finding is that, consistent with the results in Table 7, frequent purchasers are more sensitive to elements of service quality and this is reflected in using brand as a proxy for this non-contractible element of the product. We also note that this finding does not support the conventional wisdom that regular users of shopbots will, over time, rely on brand less in their purchase behavior.

    9. Model Predictions
    10. An additional aspect of understanding shopbot markets relates to how well the predictions of our models fit actual consumer behavior both within and outside the time sample. Accurate predictions of consumer behavior both confirm the validity of our findings and have implications for retailers considering differential pricing strategies for shopbot markets.

      To avoid overfitting, it is important to analyze model predictions using a different data sample than the one used to estimate the model. To account for this, we divide our data into calibration and holdout samples. Our calibration sample is made up of 15,503 sessions conducted by consumers with odd numbered cookies between August 25, 1999 and October 18, 1999. We have two types of holdout samples. An intra-temporal holdout sample is made up of 15,503 sessions conducted by consumers with even numbered cookies between August 25, 1999 and October 18, 1999. The inter-temporal holdout sample is made up of 8,648 sessions conducted during the last two weeks of the data set: October 19, 1999 through November 1, 1999.

      Table 10: Extensive Model of Consumer Behavior










      Total Price


      -.062 (.002)

      -.061 (.002)


      Total Price/Min


      -2.254 (.059)


      Item Price


      -.049 (.002)


      Item Price/Min


      -.092 (.022)

      Shipping (Fast)


      -.131 (.005)

      -.109 (.004)

      Shipping (Priority)


      -.092 (.007)

      -.074 (.007)

      Shipping (Bk Rate)


      -.046 (.005)

      -.015 (.004)

      Sales Tax


      .007 (.026)

      -.025 (.021)

      No Tax


      .180 (.063)

      .036 (.058)

      Position in Table


      First Price Listed

      2.507 (.019)

      2.256 (.022)

      2.257 (.022)

      2.054 (.024)

      2.181 (.023)

      2.390 (.022)

      In First 10 Prices

      2.923 (.032)

      2.358 (.035)

      2.359 (.036)

      2.117 (.036)

      2.147 (.037)

      2.544 (.036)

      Delivery Time


      Delivery Avg.


      -.029 (.001)

      -.029 (.001)

      -.028 (.001)

      -.035 (.001)

      -.037 (.001)

      Delivery "N/A"


      -.344 (.035)

      -.362 (.036)

      -.474 (.037)

      -.417 (.036)

      -.472 (.035)

      Retailer Brand


      1.079 (.039)

      1.018 (.045)

      .988 (.045)

      .980 (.046)

      1.038 (.050)

      .895 (.048)


      .787 (.042)

      .591 (.049)

      .560 (.050)

      .565 (.050)

      .623 (.054)

      .477 (.052)


      .212 (.039)

      .194 (.047)

      .166 (.047)

      .186 (.048)

      .264 (.052)

      .145 (.050)


      .126 (.039)

      .115 (.047)

      .090 (.047)

      .164 (.047)

      .217 (.051)

      -.009 (.050)


      -.491 (.039)

      -.335 (.044)

      -.354 (.044)

      -.339 (.045)

      -.360 (.048)

      -.596 (.047)


      -.143 (.046)

      -.081 (.050)

      -.117 (.050)

      -.370 (.053)

      -.147 (.059)

      -.435 (.059)


      -.036 (.048)

      .012 (.051)

      .018 (.051)

      .129 (.052)

      .153 (.055)

      .020 (.055)


      -.847 (.049)

      -1.087 (.057)

      -1.095 (.058)

      -.666 (.056)

      -.864 (.058)

      -.377 (.053)

      -.203 (.051)

      -.356 (.055)

      -.367 (.055)

      -.301 (.056)

      -.283 (.059)

      -.430 (.058)

      Fat Brain

      -.021 (.052)

      -.261 (.061)

      -.274 (.061)

      -.296 (.062)

      -.182 (.066)

      -.287 (.064)

      .587 (.056)

      .368 (.069)

      .344 (.070)

      .348 (.067)

      .098 (.073)

      -.234 (.069)

      -.739 (.056)

      -.550 (.059)

      -.548 (.059)

      -.490 (.060)

      -.576 (.061)

      -.732 (.060)

      Other Retailers







      Prior Choices


      Prior Last Click


      .729 (.049)

      .644 (.051)

      .723 (.049)

      .727 (.048)

      Prior Click


      -.112 (.113)

      -.154 (.114)

      -.114 (.113)

      -.107 (.111)

      Log Likelihood







      Adjusted U2




























      * Standard Errors are listed in parenthesis. Italicized results are insignificant at p<.05. (N=15,503 sessions)

      Table 10 presents the results from applying our calibration sample to an extended model specification. Column 1 presents a minimal model specification using only attribute specific dummy variables (Fader and Hardie 1996) to model different offers (alternatives). Our attribute specific dummy variables include the position of the offer in the comparison table and the retailer brand name for all retailers with greater than 3% last click-through share (12 retailers).

      Column 2 adds coefficients for total price, average delivery time and delivery "N/A". Column 3 adds coefficients for prior last click and prior click behavior. Column 4 replaces the coefficient on total price with total price as a percentage of the lowest price available in the search. Allowing price to enter as a percentage of the lowest price in a search controls for prospect theoretic effects (Kahneman and Tversky 1979) ó in this case the possibility that consumers may respond differently to a $1 price increase on a $5 book than on a $50 book.

      Column 5 includes the separate partitioned price variables and the "no tax" dummy variable. To control for the possibility that our shipping price sensitivity results arise from sensitivity across as opposed to within shipping service types we include separate variables for the shipping price associated with express (1-2 day), priority (3-6 day), and book rate (>6 day) shipping types.

      Results from these more complete models are ostensibly the same as the results from the basic models in section 3.3.1. Consumers respond strongly to branded retailers, exhibit loyalty to retailers they have visited before, respond strongly to the presence of sales tax, and remain more sensitive to price changes in the express and priority shipping categories than they are to changes in item price. However, sensitivity to changes in book rate shipping is statistically the same as sensitivity to changes in item price. This may support the inference that consumers respond negatively to shipping charges they perceive to be above a retailerís marginal cost since book rate shipping charges are typically priced near cost.

      In evaluating the reliability of these models we note the standard errors are generally stable across specifications suggesting that collinearity is not a significant problem in our model specifications. This inference is confirmed in other standard tests of data collinearity. In the next section we discuss how to choose among these different specifications to determine the model that best combines explanatory power and parsimony.

      1. Model Selection and Model Fit
      2. Table 6 presents six different model specifications containing different independent variables. Various alternatives have been offered to choose among model specifications to best combine fit and parsimony. The most common model selection criteria fall into two categories. The first, Log likelihood-based criteria such as U2 measures of fit (McFadden 1974; Ben-Akiva and Lerman 1985, p. 167) select the model that minimizes the log-likelihood value in maximum likelihood estimation, either ignoring issues of parsimony or accounting for parsimony by subtracting the number of parameters in the model. The second category, information theoretic criteria, selects models based on the amount of information in the data that is explained by the model. By using information theory, these models better account for both the fit and parsimony of the different candidate models. Notable information theoretic measures include the Akaike Information Criterion or AIC (Akaike 1973), Bayesian Information Criterion or BIC (Schwartz 1987, Raferty 1997), and information theoretic measure of complexity or ICOMP (Bozdogan 1990; Bearse, Bozdogan, Schlottmann 1997, a more recent test, which uses the Fisher information matrix. These criteria are discussed in more detail in Appendix C.

        For each model in Table 10, we present the resulting log-likelihood values; Ben-Akiva and Lermanís adjusted U2; and the AIC, BIC, and ICOMP information based measures of model selection. In spite of the very different nature of these selection criteria, they are unanimous in choosing specification 4 as the "best" specification. These results are better than even the results for the components of price in columns 5 and 6 suggesting that consumers focus their comparison on total price and that they are more sensitive to percentage changes in total price than they are to absolute changes. In the next section we use specification 4 to analyze various measures of the fit and predictive qualities of this model.

        Once a model has been selected as providing the best combination of explanatory power and parsimony, we can evaluate how well the predictions made by that model match observed behavior. To conduct this evaluation, we first calculate the hit rate ó the proportion of times the prediction made by the model is the same as a choice made by the consumer (for the holdout sample) as


        where is a vector which takes on the value of 1 for the offer that has the single highest predicted choice probability in each session and 0 otherwise, and y is a vector that takes on the value of 1 or 0 for the actual choices made by consumers.

        Using this definition, we find a hit rate of .4873 intra-temporally and .4694 inter-temporally for specification 4 above. These hit rates compare very favorably to hit rates reported in the scanner data literature. While there is a slight drop in the hit rate for the inter-temporal holdout sample during the 2-week period following out estimation the hit rate during this 2-week period is still quite high.

        Furthermore, this drop in hit rate can be explained by analysis of week-by-week predicted and actual choice share for EvenBetter.comís consumers. To analyze choice share in this way we use the holdout sample to calculate predicted share for each brand j in each week k as:


        (Guadagni and Little 1983, p. 224) where pi is the predicted probability that the brand is chosen in each session and in each week and nk is the number of sessions in each week. We also use the fact that the predicted offer selection is a binomially distributed random variable to calculate a standard error for the predicted share as


        We then graph the predicted and actual choice behavior along with a 90% confidence interval band () for each of the brands with more than 3% share. The graphs are presented in Appendix A. The vertical line in the graphs between weeks 8 and 9 represents the difference between the intra- and inter-temporal holdout samples.

        As with the hit rate calculations above, these graphs show a strong consistency between predicted and actual share across retailers. Within the time period covered by the calibration sample, our predicted share is within a 10% error bound of the actual share 98% of the time. During the subsequent two weeks, the predicted share accuracy declines to 79% accuracy.

        There are two aspects of the graphs that deserve further explanation. First, there is a strong decline in the actual (and predicted) share of during weeks 5 and 6. This drop in share is due to the fact that did not query BarnesandNoble during a significant portion of these two weeks because of concerns about the accuracy of BarnesandNoble.comís tracking of sales through their site. After talking with BarnesandNoble managers, EvenBetter realized that the discrepancy was due to an upgrade at BarnesandNobleís site and that all the data had been recorded correctly and they reinstated the retailer.

        Second, there is a dramatic increase in Bordersí actual share during week 10. Further analysis shows that on the last three days of the month of October, Bordersí averages 21% of last click-throughs (see Figure A.13). During the first 65 days, Bordersí share had averaged 10% (with a daily high of 13% and a low of 6%). This is displayed in Figure A.13, which shows the consistency of Bordersí share until the end of the month and the return to a "normal" share value on November 1, the last date in our data sample. (Investigation of the data from November 2 to November 13 shows that Bordersí share remained between 6-8%.)

        These statistics, combined with the fact that there is no significant difference in Borders participation in sessions, pricing strategies, or shipping policies during this week, suggests that the source of the share jump is possibly a special temporary promotion on the part of that we do not observe in our data. Unfortunately, efforts to verify this have been unsuccessful. Searches of press articles in Lexis-Nexis and USENET newsgroup messages during this time period have not revealed any mention of a special Borders promotion.

        However, this change does highlight an interesting fact about this shopbot market. The increase in Bordersí share appears to come at the expense of only and BarnesandNoble.comís shares. This suggests that there is a high cross-elasticity among the three branded retailers indicating that the IIA assumption, mentioned above, may be too restrictive for our market environment. In the next section, we attempt to address this concern by modeling the branded and unbranded retailers in separate nests of the nested logit model.

      3. Nested Logit Models

    As noted in section 3, the nested logit model offers an alternative modeling technique to control for correlation between the errors of different offers. Our results in section 4.4 suggest that there exist different error correlation structures for branded and unbranded retailer groups. Thus, a consumer who places a high value of offers from may also place a high value on offers from and Borders. To explore this possibility, we construct a nested logit model by supposing that consumers first choose whether to purchase from a branded or unbranded retailer and then choose which offers to select from the subset of offers in their choice set (Figure 2).

    Figure 2: Nested Logit Decision Model


    At the top level, we model the choice between branded and unbranded retailers as arising from four variables. First, the difference between the lowest priced branded offer and the lowest priced unbranded offer when branded retailers have the lowest price and the analogous value when unbranded retailers have the lowest price. Second, whether the consumer last clicked (or clicked without last clicking) on a branded or unbranded retailer on their most recent visit. Third, a dummy variable for the lowest priced category (branded or unbranded). And fourth, a dummy variable for branded retailers. The variables in the bottom level nests are the same as those in column 4 of table 8, except that we add a dummy variable for the offer with the best price in each nest ("Best Price In Nest").

    We estimate our nested logit model sequentially as described in Ben-Akiva and Lerman (1985, pp. 297-298) and Guadagni and Little (1998). Sequential estimation produces consistent but asymptotically inefficient estimates, causing the standard errors to be too small (Amemiya 1978). However, it has been shown that in many applications the resulting standard errors are not significantly different from those resulting from Full-Information Maximum Likelihood estimation (Bucklin and Gupta 1992, p. 205). Given the strong significance of nearly all our coefficient estimates it is highly unlikely that Full Information Maximum Likelihood estimation would change our results.

    Table 11: Nested Logit Model: Top Nests



    Price Difference if Brand Lowest Price

    .033 (.009)

    Price Difference if Unbranded Lowest Price

    .060 (.004)

    Prior Last Click Brand

    .358 (.056)

    Prior Click Brand

    -.323 (.097)

    Lowest Priced Category

    1.012 (.037)

    Branded Retailer

    .358 (.056)

    Unbranded Retailer


    * Standard Errors are listed in parenthesis. Italicized results are insignificant at p<0.10. n=39,654 sessions

    Our results using the nested logit model are presented in Tables 11 and 12 for the top and bottom level nests respectively. These results are consistent with the results presented above for the multinomial logit model: consumers are very sensitive to price (as evidenced by the coefficients on "lowest priced category," price, and position in table), but still respond strongly to the presence of brand and retailer loyalty.

    Table 12: Nested Logit Model: Bottom Nests


    Branded Retailers

    Unbranded Retailers



    Total Price/Min Total Price

    -5.735 (.246)

    -1.841 (.066)

    Position in Table


    First Price Listed

    1.013 (.080)

    1.296 (.096)

    In First 10 Prices

    1.054 (.076)

    2.366 (.049)

    Best Price In Nest

    .634 (.068)

    .897 (.095)

    Delivery Time


    Delivery Average.

    -.024 (.003)

    -.028 (.002)

    Delivery "N/A"

    -.576 (.121)

    -.534 (.043)

    Retailer Brand


    1.267 (.067)



    .753 (.069)







    .130 (.054)



    -.381 (.050)



    -.420 (.059)



    .173 (.056)



    -.645 (.060)


    -.341 (.062)

    Fat Brain


    -.293 (.067)


    .267 (.075)


    -.548 (.064)

    Other Retailers



    Prior Choices


    Prior Last Click

    .338 (.119)

    .712 (.070)

    Prior Click

    -.199 (.237)

    -.424 (.160)

    * Standard Errors are listed in parenthesis. Italicized results are insignificant at p<.05. (Branded Retailer n=4,023, Unbranded Retailers n=11,480)

    In addition the fit and predictive power of these models are quite good. Our hit rates for the nested logit results are slightly higher intra-temporally (.4880) and significantly higher inter-temporally (.4855) than those for the multinomial logit models reported above. The increase in inter-temporal hit rate reflects the fact that placing the branded retailers in a separate nest improves the predictions for branded retailers during week 10 when Bordersí share increases. The model still does not predict the increase in Borders share. However, because the nested logit models elasticity within nests, the actual shares for Amazon and BarnesandNoble fall within a 10% error bound of the predicted shares during week 10. Predicted and actual share for branded retailers under the nested logit model are shown in Appendix B. Because the share predictions for the unbranded retailers are similar to those shown in Appendix A, we suppress the graphs for these retailers. The similarity in the multinomial and nested logit results with regard to coefficients and predictions also provides confirmation that the IIA problem does not significantly impact our previous results.

    One implication of the quality of our inter- and intra-temporal share predictions is that retailers may be able to use information gathered from Internet shopbots to create personalized prices for shopbot consumers. Shopbots could arrange to pass information regarding the consumerís prior search behavior and product characteristics for competing offers to retailers, allowing them to calculate a personalized price for this consumer to maximize their profits.

    Using this information, the retailers could use the multinomial logit equation (equation 6) to calculate the probability that their offer would be chosen as a function of their price (), their product characteristics (), the prices and product characteristics of competing offers (, ), and the consumerís characteristics ():


    With this knowledge, the retailer could then choose a price to maximize their profit for this transaction:


    With an estimate of the annual frequency of the consumerís visits to the shopbot () and the marginal loyalty advantage from being chosen on this purchase (), and a discount rate for future revenue (i), the retailer could instead maximize the net present value of being chosen in the current transaction:


    In implementing a personalized pricing system involving one or multiple retailers, the shopbot would have to be mindful of the overhead in processing time such a system would impose on their ability to return prices to their consumers and the privacy concerns of their consumers. Still, employing such a system would allow shopbots to build lock-in among their consumers and leverage their most important source of competitive advantage ó knowledge of consumer behavior.

  3. Conclusions

As Internet shopbot technologies mature, consumer behavior at shopbots will become an increasingly important topic for consumers, retailers, financial markets, and academic researchers.

With regard to consumer behavior, our findings demonstrate that, while shopbots substantially weaken the market positions of branded retailers, brand name and retailer loyalty still strongly influence consumer behavior at Internet shopbots. These factors give retailers a 3.1% and 6.8% margin advantage respectively over their competitors in this setting. Our findings also suggest that consumers use brand name as a signal of reliability in service quality for non-contractible aspects of the product bundle. These results may derive from service quality differentiation, asymmetric market information regarding quality, or cognitive lock-in among consumers.

With regard to retailers, our results suggest several differential-pricing strategies for shopbot markets. First, it is likely that a consumerís willingness to take the extra time to use a shopbot is a credible signal of price sensitivity. Thus, retailers may use this information as part of a price discrimination strategy ó charging lower prices to shopbot consumers than consumers who visit their web site directly. Second, our findings suggest that partitioned pricing strategies that increase demand among web site direct consumers may decrease demand among shopbot consumers. Because of this, retailers should adopt different pricing strategies for shipping cost for shopbot consumers than they would for web site direct consumers. Lastly, the reliability of our models when compared to actual consumer behavior suggests that retailers may be able to use shopbot data to provide personalized prices to consumers.

For financial markets, our findings may help to focus the debate on the size and sustainability of market valuations for Internet retailers. Using as an example, our shopbot data indicate that the retailer maintains a 5.0% margin advantage over unbranded retailers and a 6.8% margin advantage among repeat visitors. Both of these statistics are likely to represent lower bounds on the actual margin advantages among their entire consumer base. A margin advantage of this magnitude, if sustainable and applicable across their entire product line, implies a very large capital value. The relevant questions then become whether companies such as can sustain current positions of competitive advantage, how much it will cost to sustain these positions, and whether they can transfer competitive advantage in one product category to other product categories to expand their revenue base.

Finally, for academic researchers, our results demonstrate the feasibility of using Internet shopping data to better understand consumer behavior in electronic markets. Future research in this regard may be able to extend these results to better understand how web-site direct and shopbot consumers respond to partitioned prices, to evaluate the cognitive processing costs of shopbot consumers, and to empirically analyze the application of personalized pricing strategies to shopbot consumers. Moreover, our results suggest that the quantity and quality of data available in Internet markets may introduce a revolution the analysis of consumer behavior rivaling that of the scanner data revolution in the 1980s.



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Appendix A: Week-by-Week Predicted to Actual Choice Share, Multinomial Logit Model


Figure A.1:

Figure A.2:


Figure A.3:

Figure A.4:


Figure A.5:

Figure A.6:


Figure A.7:

Figure A.8:


Figure A.9:

Figure A.10:


Figure A.11:

Figure A.12:


Figure A.13: Borders Last Click-Through Share ó 10/19/99 - 11/1/99



Appendix B: Week-by-Week Predicted to Actual Choice Share, Branded Retailers, Nested Logit Model

Figure B.1:

Figure B.2:

Figure B.3:


Appendix C: Model Selection Criteria

This appendix presents several of the most common model selection criteria applied to multinomial logit models. As noted above, these criteria fall into two general categories: log likelihood-based measures and information theoretic measures. Significant criteria from each category are presented in turn below.

The most common model selection criterion is the likelihood ratio test. Likelihood ratio tests can be used to evaluate multiple restrictions on a model (e.g., Guadagni and Little 1983). Likelihood ratio tests in this setting are based on the observation that with degrees of freedom equal to the number of restrictions between model A and B.

Applied to our model, likelihood ratio tests reject at any reasonable confidence level the restrictions on specification 1 above with respect to all other specifications and on specification 2 with respect to specification 3. However, these tests are only applicable where one model can be expressed as a restricted subset of the second model. Therefore we cannot use likelihood ratio tests to compare specification 3 to specification 4, for example.

Another technique to choose among multinomial logit model specifications is to use a measure of fit analogous to R2 in multivariate linear regressions. McFadden (1974) proposes to measure this value as


where is the likelihood associated with the specification in question and is the likelihood of the null model (the constrained model excluding all regressors).

Ben-Akiva and Lerman (1985, p. 167) note that this measure will always (weakly) increase when new variables are added to the model whether or not these variables contribute usefully to explaining the data. Therefore, this measure does not adequately account for desired parsimony in the selected specification. For this reason, the Ben-Akiva and Lerman adjust McFaddenís U2 measure to penalize the addition of variables


where k is the number of independent variables in the model. Using either measure, the best model is the one with the largest U2, corresponding to the model that explains the most variation in the data. Further, unlike the likelihood ratio presented above, these tests can be used to compare models that cannot be expressed as restricted subsets of each other.

A variety of model selection measures have been proposed based on concepts of information theory. The most well known of these measures, the Akaike Information Criterion or AIC (Akaike 1973) is specified as


where P is the number of parameters in the model (the number of independent variables plus the slope coefficient) and N is the number of observations. Intuitively, for models with better fit, should increase and should decrease. The 2P term will decrease with more parsimonious models. Thus, the "best" model minimizes the AIC criterion.

The Bayesian Information Criterion or BIC (Raferty 1986, Schwartz 1987) provides a similar measure, based on Bayesian statistical theory. In a Bayesian setting, we compare two models based on the ratio of their posterior probabilities. If Model 2 is preferred over Model 1 this odds ratio will be greater than 1. The posterior odds ratio of Model 2 to Model 1 can be written as


where the first factor on the right hand side of the equation is called the Bayes factor for Model 2 against Model 1 and the second factor is the ratio of the prior probability for Model 2 against Model 1. In the general case where there is no prior probability for choosing Model 2 against Model 1, this ratio will be 1 and the posterior odds ratio will be equal to the Bayes factor. Unfortunately, calculating the Bayes factor is computationally prohibitive.

However, the Bayesian Information Criterion (BIC) presents a useful, and easily calculated, approximation to the Bayes Factor. BIC is defined as


where and N are defined as above, and k is the number of regressors. Relating this to the Bayes factor, it can be shown (Raftery 1995) that

. (C.6)

Thus, as with the AIC measure above, the best model is the model that minimizes BIC.

The information theoretic measure of complexity or ICOMP (Bozdogan 1990; Bearse, Bozdogan, Schlottmann 1997) provides an alternate model selection criteria. ICOMP uses the Fisher information matrix to measure (penalize) complexity in the model. The measure is defined as


where is the inverse Fisher information matrix. The advantage of ICOMP is that, instead of viewing complexity as arising from the number of parameters (e.g., , AIC, BIC), it evaluates model complexity from the correlation structure of the parameter estimates (through the inverse Fisher information matrix).