investigating direct and indirect effects of variables in marketing

LIST OF TABLES Table Page 2.1 Model Description ...35 2.2 Coefficient Estimates for Homogeneous Regression Model Simulated Data...36 2.3 Coefficient Estimates for Normal Mixture Model Si

INVESTIGATION OF DIRECT AND INDIRECT EFFECTS

ABSTRACT

The idea of hierarchical, sequential, or intermediate effects has long been posited

in textbooks and academic literature Hierarchical effects occur when relationships among variables are mediated through other variables Despite the attractive theoretical properties of these models, their practical existence has been difficult to show in

empirical studies This thesis comprises of three essays where we demonstrate the presence of hierarchical effects and propose methods for detecting and measuring these effects The first two essays use empirical data to demonstrate our methodology and its extensions, while the third essay uses three experimental studies to demonstrate the hierarchical effects and role of memory associations impacting consideration sets

In the first essay, we propose an approach to studying hierarchical effects using sets of conditional relationships among affected variables while allowing for

heterogeneous response segments, and using Bayesian variable selection to deal with the high dimensional parameter space often resulting in applied empirical studies Cross-sectional data from a national brand-tracking study is used to illustrate our model, where

we find empirical support for a hierarchical relationship among media recall, brand beliefs, and intended actions We find these effects to be insignificant when measured with standard models and analyses The proposed model is useful for understanding the

influence of variables that lead to intermediate, as opposed to direct effects on brand choice

The second essay proposes a methodological extension to the first essay by

extending it to panel data We investigate through a series of quantitative models the role played by customer wait times at a teller and its relationship with the overall satisfaction

in a retail banking environment We demonstrate that accounting for heterogeneous segments of branches provides a better understanding of the drivers of overall

satisfaction Customer wait times impact the drivers of customer satisfaction that result

in impacting overall satisfaction We provide managerial insights by incorporating a threshold parameter in the model that determines average time that a customer is willing

to spend waiting at a bank and its impact on overall satisfaction

The third essay incorporates the benefits sought by consumers into network models of memory Prior consumer research in network models of memory has primarily focused on the association between brands and attributes The concept of benefits sought

by consumers has not been integrated into these models We propose a model of memory organization that explicitly recognizes the distinction between brand attributes and desired benefits and study the impact of advertising on this proposed network The model

we advance includes nodes representing benefits sought by consumers that are linked to brand attributes and brand names We demonstrate, using three studies, that advertising effectiveness increases when the advertising message taps into an individual's desired

benefits Understanding the cognitive associations between desired benefits and brand attributes can help marketers design more effective communications

This thesis contributes new methodological approaches for exploring hierarchical effects among variables in marketing Essay one proposes a Bayesian approach for analyzing hierarchical effects in cross-sectional data which can easily be extended and applied to mediation analysis Essay two demonstrates the importance of our proposed modeling approaches with application in services literature Essay three contributes to the existing literature on associative networks by incorporating an additional layer that accounts for desired benefits and demonstrates the significant role played by the

associations in a hierarchical memory network on forming consumer consideration sets

ACKNOWLEDGMENTS

I wish to express sincere thanks to my adviser, Dr Greg M Allenby, for the time and effort he put into my doctoral education I truly believe that I have benefited both academically and personally from my association with Greg He has instilled in me something he truly believes in, to be rigorous in research

I would also like to thank Dr H Rao Unnava for his invaluable help and patience in guiding me through entire experimental design research I am grateful to Dr Robert E Burnkrant for his insightful comments that helped fine tune my research I would also like to thank Dr Thomas Otter for his encouragement during my doctoral program

I could not have completed my doctoral studies without the consistent support of

my family and friends and I am indebted to them I would also like to thank all the current and past doctoral students who helped me through my research work Finally, I would like to thank Cindy Coykendale and Lisa Gang for their help in navigating through all the administrative details

VITA

October 16, 1975 Born – Hyderabad, India

1997 B.E., Instrumentation Engineering

Osmania University, Hyderabad, India

University of Texas, Dallas, TX, USA

2003-present Graduate Teaching and Research Associate,

The Ohio State University

FIELDS OF STUDY Major Field: Business Administration

Specialization: Marketing

TABLE OF CONTENTS

Page

Abstract ii

Acknowledgements v

Vita vi

List of Tables ix

List of Figures xi

Chapters: 1 Introduction 1

2 Essay 1: Bayesian Analysis of Hierarchical Effects 5

2.1 Introduction 5

2.2 Model 9

2.3 Simulation Study 17

2.4 Data 19

2.5 Results 20

2.6 Discussion 25

2.7 Conclusion 29

3 Essay 2: Bayesian Investigation of Service Wait Times 48

3.1 Introduction 48

3.2 Data 50

3.3 Model Specifications 51

3.4 Results 58

3.5 Discussion 62

3.6 Summary 65

4 Essay 3: Incorporating Desired Benefits into Network Models of Memory 74

4.1 Introduction 74

4.2 Product attributes and benefits 75

4.3 Proposed memory network 77

4.4 Study 1 81

4.5 Study 2 91

4.6 Study 3 96

4.7 Discussion 100

5 Conclusions and Future Research 111

Appendices 117

Appendix A: Estimation algorithm for Essay1 117

Appendix B: Estimation algorithm for HB threshold model 122

Appendix C: Ad for Study 1 125

Appendix D: List of statements and response scales (Study 1 and Study 2) 126

Appendix E: Ad for Study 2 129

List of references 130

LIST OF TABLES

Table Page

2.1 Model Description 35

2.2 Coefficient Estimates for Homogeneous Regression Model Simulated Data 36

2.3 Coefficient Estimates for Normal Mixture Model Simulated Data 37

2.4 Coefficient Estimates for Finite Mixture Model Simulated Data 38

2.5 Descriptive Statistics for Automobile Data (N = 6178) 39

2.6 Aggregate Regression Coefficient Estimates Automobile Data 40

2.7 Nạve Segment Regression Estimates 41

2.8 Coefficient Estimates for Nạve Aggregate Model using Multivariate Regression 42

2.9 Model Fit 43

2.10 Sub-model model Fit 43

2.11 Direct Effects of Media Exposure, Brand Beliefs and Intended Actions on Purchase Intention {βk} 44

2.12 Effects of Brand Beliefs on Intended Actions {Γk} 45

2.13 Effects of Media Exposure on Brand Beliefs {∆k} 46

2.14 Aggregate Effect of Media Exposure (Z) on Purchase Intention (y) 47

3.1 Branch level Descriptive Statistics for Retail Banking Data (N = 1748 branches) 70

3.2 Correlation matrix for the variables in retail banking data 70

3.3 Model fit comparisons for retail banking data 71

3.4 Influence of Wait Times on Perceived Service Drivers (Mean Effects) – Standard HB model 71

3.5 Influence of Wait Times on Perceived Service Drivers (Unobserved Heterogeneity) – Standard HB model 71

3.6 HB mixture model for Retail Banking Data (N = 1748 branches) 72

3.7 HB threshold model for Retail Banking Data (N = 1748 branches) 73

4.1 Variables Collected in the Initial Survey before Viewing the Advertisement 107

4.2 Number of Subjects Considering Puma for Purchase – Study 1 109

4.3 Ratings for Attributes Not Included in the Advertisement – Study 1 109

4.4 Number of Subjects Considering Puma for Purchase – Study 2 110

4.5 Number of Subjects Considering Puma for Purchase – Study 2 110

4.6 Mean Reaction Times for the Subjects Response to Key Statements – Study 3 110

4.7 Mean Reaction Times – Hierarchical Memory Organization – (Respondents from Study 1) 111

LIST OF FIGURES

Figure Page

2.1 Trace Plot of Segment Weights for Homogeneous Regression Model Simulated

Data 32

2.2 Trace Plots of Segment Weights for a Three-Component Mixture Model with K = 4 Simulated Data 33

2.3 Trace Plot of Segment Weights for Automobile Data with K = 4 34

3.1 Influence of Wait Times on Perceived Service Drivers Data and Posterior Distributions .67

3.2 Trace Plot of Segment Weights for Bank Data with K = 4 68

3.3 Trace Plot of Cutoff parameter for Bank Data 69

4.1 Proposed Hierarchical Memory Network 104

4.2 Subjects pool for studies 104

4.3 Associative Network for Respondents in Study 1: Before viewing the Ad 105

4.4 Associative Network for Respondents in Study 1: After viewing the Ad 105

4.5 Associative Networks for Respondents in Study 2 106

4.6 Associative Networks for Respondents in Study 3 106

CHAPTER 1

Introduction

Advertising variables, such as media exposure, are often introduced into models

of consumer behavior as regressors in linear models The role of advertising, however, is more subtle Advertising can initiate intermediate actions, like seeking additional

product information, impact brand beliefs and it can effect consideration sets that later lead to purchase Models that attempt to measure advertising relationships as the direct link to purchase may under-estimate effect-sizes by overstating its role Consumers at different stages of the buying decision may differ in the type and degree to which

marketing activities influence their behavior The purpose of this thesis is to better understand and develop models for measuring the direct and indirect or intermediate effects of commonly encountered variables in marketing data

There are two main themes to this dissertation First, to propose a methodology to capture hierarchical effects between various variables, extend this methodology and demonstrate using empirical applications the relevance and significance of the proposed approaches For example, in the first essay we demonstrate the direct and intermediate effects of media and brand beliefs on purchase intention Second, use an experimental setup to understand the impact of advertising on consumer memory associations (in a hierarchical network) that lead to changes in the consideration set In both these cases,

we find that advertising impacts the outcome variable (purchase intention in one, and brand consideration set in the other) through intermediate variables (consumer actions and brand beliefs in one and attribute-benefit associations in the other)

The thesis comprises three essays The first essay demonstrates the problems with ignoring the impact of media exposure on intermediate intervening consumer

actions The analysis of media effects in the presence of a staged decision process requires models that allow for response segments affected by different variables We propose a method that simultaneously pools respondent data into segments that differ in the likelihood of purchase and its association to intermediate actions, brand beliefs and media exposure Models that acknowledge the presence of response segments with different behavior patterns and associated variables are known as models with structural heterogeneity Our proposed method accounts for structural heterogeneity by using a normal mixture model While the intermediate consumer action variables are related to brand beliefs and brand beliefs to media exposure variables using auxiliary multivariate regressions We deal with the issue of model dimensionality using Bayesian multivariate variable selection We demonstrate the significance of our methodology using an

empirical application from a national brand tracking study (cross-sectional data) for luxury automobiles

The second essay proposes an extension to the Bayesian hierarchical model of essay 1 to panel data in a retail banking environment We propose three different model

specifications to understand the impact of customer waiting times on drivers of

satisfaction and overall satisfaction in the context of retail banking The first model, Standard HB model, investigates the moderating effect of mean waiting time before and after reaching a teller on drivers of satisfaction (like courtesy and friendliness, undivided attention of the teller etc.) and overall satisfaction This model accounts for preference heterogeneity only The second model, HB mixture model, incorporates preference and structural heterogeneity where different heterogeneous segments are determined by the relationship between the drivers of satisfaction and overall satisfaction We account for structural heterogeneity in the data by modeling a mixture of likelihoods as opposed to a single likelihood function We determine whether, overall satisfaction or waiting times, differentiate the different response segments The third model, HB threshold model, extends the second model by incorporating a threshold parameter that determines the average cutoff time that consumers are willing to wait beyond which it has a significant impact on overall satisfaction This model has significant managerial implications

because it provides a concrete measure of a cutoff time that branch managers can actually use as guidance for taking appropriate actions to help improve the overall satisfaction of the bank Thus, in essay 3 we study the indirect effects of wait times on overall

satisfaction

The third essay focuses on understanding how advertising works based on

associative memory networks We integrate the concept of benefits sought by consumers

along with attributes and brands into a network model of memory We propose and test the presence of a memory structure linking benefits with attributes and brands, and show that advertising effectiveness increases when the advertising message taps into an

individual's desired benefits or concerns Understanding the cognitive associations between benefits and brand attributes can help marketers design more effective

communications The implications of such a representation of brand information in memory are studied in two experiments

This thesis is geared toward understanding and developing models for measuring direct and indirect effects of variables In: essay 1, impact of media exposure on

purchase intention, essay 2: impact of wait times on overall satisfaction and essay 3: impact of attribute efficacy associations on consideration set The common underlying finding in all the essays is: not accounting for indirect effects of variables can mask the true impact and underestimate the effects of commonly encountered variables in

marketing The remainder of this thesis is organized as follows In chapter 2, the first essay “Bayesian Investigation of Hierarchical Effects” is discussed The second essay, an extension to essay 1, “Bayesian Investigation of Service Wait Times” is discussed in chapter 3 Chapter 4 presents the third essay “Incorporating Benefits into Network Models of Memory” Conclusions and future extensions of this thesis is presented in chapter 5

or sequential process (e.g., Vakratsas and Ambler 1996; Assael 1993) The AIDA

framework (E St Elmo Lewis 1898; Strong 1925) is one of the earliest and best known examples, where advertising impacts choice through a specific, sequential process: from attention to interest to desire to action Lavidge and Steiner (1961) extend this process to include knowledge, liking, preference, conviction, and ultimately, purchase Recent work has attempted to generalize these early advertising effects models by couching them in terms of cognition, affect, experience, and action (Vakratsas and Ambler 1999; Holbrook and Batra 1987) Although they differ in form, most models adhere to the general notion that consumers first learn, and then know, feel and do

These extended models of behavior point to the idea of hierarchical effects, where

knowing on doing are assumed to be mediated, at least in part, by variables that reflect feelings and affect This chapter proposes a Bayesian approach to studying hierarchical effects such as these Hierarchical effects are modeled by expressing the joint

distribution of variables under study as a set of marginal and conditional distributions Thus, for three sets of variables (A,B,C), we can write the joint distribution [A,B,C] in terms of various factorizations The model [A,B,C] = [A|B][B|C][C] indicates that B mediates the influence of C on A, whereas the model [A,B,C] = [A|B,C][B][C] indicates that both B and C directly influence A In these expressions, the vertical bar "|" stands for the conditioning argument, and the bracket notation implies a distribution

A challenge in the analysis of hierarchical effects is the large numbers of

variables present that reflect diverse aspects of behavior Consider, for example,

individuals engaged in the process of buying a new car When first entering the market, they may engage in an extensive information search to identify available products and their corresponding attributes The variables at this stage include media viewership and advertising recall As preferences develop and consideration sets are formed, individuals may become increasingly sensitive to direct appeals attempting to initiate purchase Possible variables include the use of electronic and direct postal mail These variables may also influence a set of intended actions, such as dealer visits, and may influence the formation of brand beliefs, all of which may precede actual vehicle purchase

Our approach to analyzing hierarchical effects in extended models of behavior is

to employ three known aspects of modern Bayesian analysis First, as stated above, we express hierarchical effects in terms of probability statements about the joint distribution

of the data In the model [A,B,C] = [A|B][B|C][C], the variable A is conditionally

independent of C given B All information from C that affects A must flow through B Conditional independence is a basic assumption of modern Bayesian analysis (Bernardo and Smith 1994), including hierarchical Bayes models (Rossi, Allenby and McCulloch 2006) Our approach, however, differs from the typical hierarchical Bayes model in marketing, where interest focuses on explaining variation in effect sizes using random-effects models Instead, we propose tools to investigate hierarchical effects among variables, not among coefficients

Second, our model allows for heterogeneous segments that differ in terms of response coefficients and error variance We employ the Bayesian method of data augmentation (Tanner and Wong 1988) to identify respondent segment memberships that greatly simplify high-dimensional calculations associated with these models Third, our model uses Bayesian variable selection (McCulloch and George 1993) to help reduce the high-dimensional mapping between sets of variables We show that both model aspects are needed for our data

Our model generalizes a statistical procedure commonly known as "mediation analysis" (Baron and Kenny1986), where a series of estimated regression relationships is

used to assess the presence of a hierarchical relationship Traditional mediation analysis involves using standard regression procedure and comparing effect sizes across different combinations of variables More recently (Iacobucci et al 2007), propose using

structural equation models to be a superior option than traditional approaches in that it can handle additional construct into the mediating system Our approach is more flexible

in that it can be used to compare hierarchical effects across multiple levels and across models that differ by more than the inclusion of a regression variable

We investigate the relationship among purchase likelihood, intended consumer actions, brand beliefs and media exposure using cross-sectional data for a high-end luxury automobile We find the presence of response segments that differ in their

likelihood of purchase and its association to the other variables Results from our model indicate that media effects, after accounting for the presence of heterogeneous response segments, are large and change in magnitude as the likelihood of purchase increases We also find evidence supporting a decision process in which media has direct and indirect (through brand beliefs) effects on likelihood of purchase Analysis that fails to account for heterogeneous response segments is shown to grossly under-estimate the effectiveness

2.3 to demonstrate key features of the proposed method Section 2.4 describes the data used to investigate different hierarchical effects, and results are presented in Section 2.5 Section 2.6 contains a discussion of the results, and Section 2.7 offers concluding

remarks and discusses limitations of our analysis

2.2 Model

Hierarchical effects models of consumer behavior and advertising are particularly important in the context of high-involvement goods and services where substantial, prolonged consideration occurs prior to purchase An initial stage of information search

is typically posited as a set of considered brands is formed, and then additional

information is sought as preferences are developed, brands are ranked and choices are made If consumers do engage in a staged decision process, it is likely that their

sensitivities to advertising and other, experiential, activities differ according to their relative stage in that process

The analysis of media effects, brand beliefs and consumer actions in the presence

of a staged decision process requires models that allow for response segments affected by different variables Models that acknowledge the presence of response segments with different behavior patterns and associated variables are known as models with structural heterogeneity Structural heterogeneity models have been used in marketing to study the order in which different consumers process attributes in purchasing grocery items

(Kamakura, Kim and Lee 1996), the evaluation of credit card offers and its relationship to

a consumer's current balance (Yang and Allenby 2000), and the presence of conjunctive versus disjunctive screening rules in conjoint analysis (Gilbride and Allenby 2004) Structural heterogeneity models employ a finite mixture of likelihoods, in contrast to standard heterogeneity models that assume one likelihood function is sufficient for

describing all respondents

Our models for investigation of hierarchical effects relates an intent-to-purchase measure (y) to a series of intended consumer actions (X), brand beliefs (B) and media exposure variables (Z) We use capital letters (e.g., X) to denote a set of responses by collections of individuals, and lower-case letters (e.g., xi) to denote the response from a specific individual indexed by the subscript "i." The intent-to-purchase measure, y, is a single item and is represented in lower-case (y and yi) We consider a variety of

relationships among these variables as described in table 2.1 The second column of table 2.1 provides a symbolic description of the model using the bracket notation described above The third column of table 2.1 highlights the conditional relationship for the intent-to-purchase variable, and column four indicates variables for which a marginal distribution is assumed

Model 1 posits a conditional relationship between purchase intent (y) and

intended consumer actions (X), with marginal distributions for actions (X), brand beliefs (B) and media exposure (Z) Thus, brand beliefs and media exposure data are not

assumed to have a direct or indirect affect on purchase intention Model 2 includes brand

beliefs (B) with actions (X) in the model for purchase intentions, and model 3 also

includes media exposure information (Z) Thus, models 2 and 3 assume direct

relationships between purchase intent and its antecedents Model 4 posits a series of conditional relationships among the variables where media exposures (Z) influence beliefs (B), which in turn influence actions (X), and then actions affect purchase intent (y) Models 5 and 6 reflect two variations on the hierarchical effects model, with model 5 removing the hierarchical influence of media exposures (Z) and model 6 assuming the media has a direct affect on actions (X)

Consider model 4, where hierarchical effects are assumed to exist among each set of variables: [y|X][X|B][B|Z][Z] We introduce heterogeneous response segments in the first factor in the model by assuming a finite mixture of likelihoods:

k Our model differs from a traditional finite mixture model (Kamakura and Russell 1989) by allowing the error variance to be

segment-specific We illustrate the importance of this assumption in our simulation study below

Equation (1) is used to identify the K response segments using a hierarchical Bayes model that augments the parameter space with latent indicator variables, si, used to simplify calculations (see Rossi, Allenby and McCulloch 2005 chapter 5) At each iteration of the Markov chain used to estimate the parameters in equation (1), latent indicator variables {si} are drawn from multinomial distributions These latent variables are used to assign each observation to a response segment k = 1,…, K Given these indicator variables, the regression coefficients { 2}

,

k k

β σ are estimated using a series of

independent models for each of K datasets Ak, k=1,…,K where A = A1∪ A2∪ … ∪ AKdenotes the entire set of data Details of the estimation procedure are provided in the appendix A

The brand belief variables (B) are related to intended consumer action variables (X) through independent auxiliary multivariate regression models for each response segment:

k k i

Similarly, media exposure variables (Z) are related to brand belief variables (B), through independent auxiliary multivariate regression models for each segment:

( i ) ( k i k)

k k i

where the regression coefficients (Γk and ∆k) and error covariance matrix (Σk and Ωk) are segment-specific All models (except model 2 and model 3), assume that the response segments (k) are determined entirely by the relationship between consumer actions (X) and purchase intention (y) in equation (1) Equations (2) and (3) are only used to

characterize these segments This assumption, however, is not a requirement of our general approach to study hierarchical effects, and is made in anticipation of our

empirical results

An advantage of our assumed segment structure described by equations (1), (2) and (3) is that it does not necessarily require the presence of media effects (∆) for a staged decision process to exist Some media may be ineffective at driving some of the brand beliefs and some of the brand beliefs may be ineffective in driving the consumer actions, and we believe this lack of relationship (i.e., elements of Γ and ∆ equal to zero)

should not be used as a basis for identifying the latent segments We recognize that this

is a strong assumption and therefore propose two alternate models (models 2 and 3) in which the assumption is relaxed In model 2, we assume that the response segments are determined not only by consumer actions and purchase intent but by brand beliefs as well Model 3 assumes that response segments are determined by consumer actions,

brand beliefs, media exposure and purchase intent Thus model 2 and model 3 capture the direct effects of brand beliefs and media on purchase intent and indirect effects

through auxiliary multivariate regressions Our approach thus identifies direct and

indirect effects of media and brand beliefs on consumer actions and purchase intent after accounting for heterogeneous segments

Models that attempt to draw a direct relationship between media exposure and purchase likelihood can be seen to miss important relationships in the data by considering the expected change in purchase intentions due to changes in media exposure Using Equations (1) – (3) and the chain rule of differentiation we have:

1

1

K k

K

k k k k k

intermediate beliefs and behavior Our model can reflect intermediate effects through the coefficient matrices Γk and ∆k

Our approach to studying hierarchical effects involves comparison of the joint distribution of the data, [y,X,B,Z], under alternative factorizations Comparison among factorizations can be done in terms of the marginal density of data, a Bayesian measure of model fit Computing the joint marginal density requires the specification of the

marginal density of model factors that are not conditionally related to other variables For example, the model [A,B,C] = [A|B][B|C][C] requires specification of the marginal density of C, [C] The fourth column of table 2.1 lists the variables that require marginal specifications for each model We propose simple specifications based on the

multivariate normal distribution:

where the µ's denote the mean vectors and the Ψ's are covariance matrices associated

with the marginal distributions, which are assumed to be multivariate normal

The proposed model is highly parameterized due to the response segments (k) and the segment-specific coefficient matrices Γk and ∆k characterizing the conditional relationships among variables We deal with the issue of model dimensionality using Bayesian variable selection developed by George and McCulloch (1993) for univariate regression (equation 1) and by Brown et al (1998) for multivariate regression (equation 2) Bayesian variable selection is implemented by assuming a prior distribution for the

model coefficients that places mass close to zero, corresponding to the situation in which the variable is not selected Thus, posterior estimates based on these priors are centered away from zero if the data provides fairly strong support of a non-zero effect Otherwise, the posterior is centered near zero

The prior distribution used in equation (1) is:

N d By setting c small and d large, the prior is flat except for a spike

in mass near zero Posterior estimates based on this prior have the effect of shrinking small values of β to zero (the prior), and leaving larger values of β alone As discussed

by George and McCulloch (1993) we choose a value of c = 0.001 and d = 5.0 so that effect-sizes below 0.05 are shrunk to zero The multivariate extension of this approach as proposed by Brown et al (1998) uses a latent vector of binary values to identify

parameters that are either close to 0 or away from zero This approach is computationally efficient and works really well for large dimensions of variables The specification for

the multivariate regression model as demonstrated in Brown et al (1998) is discussed in more detail in the appendix A

2.3 Simulation Study

Two simulation studies are used to demonstrate the ability of our model to

recover parameters and identify segments using cross-sectional data In the first study,

we investigate the performance of our model when data are generated with no latent segments In the second study, we investigate the ability of our model to correctly

identify the number of latent segments and segment-specific parameters

For the first study, 1000 observations were generated according to a homogeneous linear regression model y i =x i′β +εi with εi ~ N(0,1) Parameter estimates were

obtained using a standard Bayesian regression model with diffuse priors, and our normal mixture model (Equation 1) with two latent segments Results are presented in Table 2.2 and include estimates of the posterior mean, posterior standard deviation (in parenthesis), and a 95% credible interval (in brackets)

Results of the first simulation study indicate that both methods are able to

successfully recover the true simulation parameters from the simple model Bayesian estimation of the normal mixture model correctly indicates the absence of heterogeneous segments in the population, and successfully shut down draws from one of the two

mixing distributions This is illustrated by the trace plots in figure 2.1 The vertical axis displays the values of the segment size parameters φ across iterations of the Markov

chain used for parameter estimation, and described in the appendix A After an initial burn-in period, the estimated size of one of the latent distributions goes to zero while the weight for the other converges to one Thus, the estimation procedure is sensitive to absence of latent segments, and will find just one segment in data generated with K = 1

The second simulation study generated 1000 observations using equation (1) with three latent segments (K = 3) Parameter estimates with their corresponding true values are presented in Table 2.3 Given the linear nature of the model described above, the parameter estimates using a standard regression model are a convex combination of parameter estimates for the normal mixture model, reflecting the marginal effect of x on

y Estimates based on the normal mixture model correctly identify the existence of the three segments, and successfully recover the true parameters

Figure 2.2 illustrates the ability of the Bayesian estimation procedure to

successfully identify the number of latent mixing distributions when we incorrectly assume that four latent segments are present (K = 4) As illustrated by the trace plot in figure 2.2, the procedure correctly shuts down one of the series In the analysis reported below, we employ an approach where we over-specify the number of latent segments in the data, and let the estimation routine shut down redundant segments by estimating small segment weights (i.e., φk = 0) where appropriate

Results reported in table 2.4 illustrates the effect of incorrectly assuming equal error variance across segments, an assumption made in finite mixture models For our

simulated data, we estimate a common variance (σ2 = 1.8) across all segments The

assumption of a common variance leads to incorrect segment weights and parameter estimates – our results indicate that two of three segments weights, and six of 15

parameters converge to wrong values Table 2.4 displays the posterior mean, standard deviation and 95% credible intervals for all the parameters Entries in bold indicate the presence of the simulated true value in the 95% credible interval of the parameter

estimates The assumption of common error variance across segments needs to be

relaxed to correctly identify the segments and parameter values

2.4 Data

We investigate the presence of hierarchical effects using data from a national brand-tracking study of a leading luxury automobile Study participants completed an extensive questionnaire designed to elicit their attitudes and opinions toward the focal brand, their likelihood of purchasing a vehicle (y), intended consumer actions (X) such as taking a test drive in the next six months, brand beliefs (B) such as durability,

manufacturing quality and their exposure to the focal brand through a variety of distinct media sources (Z) such as television, radio, Internet and direct mail A total of 6178 observations were available for analysis

Descriptive statistics for the data are reported in Table 2.5 Likelihood of

purchase (y), intermediate actions (X) and brand beliefs (B) were collected on an eleven

point scale, with zero indicating "not at all," and ten indicating "extreme" likelihood of purchase or action within the next six months Media exposure variables (Z) were self-reported recall measures of the number of exposures to the brand via the indicated media during the prior six months The summary statistics reported in Table 2.5 suggest there is sufficient variation in the data for analysis In addition, the data contain a broad set of media variables under partial control of management The goal of our analysis is to explore conditional relationships between the batteries of variables X, B and Z and their impact on likelihood of purchase (y)

2.5 Results

We begin analysis using an aggregate model that assumes one response segment (K = 1) and then compare estimates to a model with multiple segments (K > 1) Table 2.6 reports coefficient estimates for the one segment model in which intended actions (X) and media exposure (Z) are directly related to likelihood of purchase (y) The left side of Table 2.6 is for the model of purchase intention regressed on intended actions alone (i.e.,

y | X), and the right side of the table is for the model that includes the media variables (i.e., y | X, Z) Reported are posterior means, standard deviations, and the 95% credible interval Entries in bold correspond to variables with at least 95% of their posterior mass centered away from zero The results indicate a fairly strong relationship between

intended actions and purchase likelihood, but that the media variables add little to

improve model fit The media coefficients are estimated to be small in magnitude, with all estimates being near zero

We continue the nạve analysis of our data in two parts First, we attempt to identify response segments using the marginal distribution of purchase intentions (y) Table 2.7 provides coefficients estimates of this model where response segments are formed by partitioning the dependent variable (segment 1: y = 0 – 2; segment 2: y = 3 – 5; segment 3: y = 6 – 7; segment 4: y = 8 – 10) We recognize that partitioning based on the dependent variable is not the right approach But, it is done to demonstrate the

method shortcomings and contrast it with what we believe is the right modeling

approach The coefficients displayed in table 2.7 are estimated to be small in magnitude, with almost all estimates being near zero

The second part of our nạve analysis attempts to investigate hierarchical affects

in an aggregate analysis of the X, B and Z variables Table 2.8 displays coefficient estimates for a Bayesian multivariate regression of X given B and B given Z without accounting for heterogeneous segments The results indicate that brand beliefs have a significant impact on consumer actions Media coefficients, however, are estimated to be small in magnitude, with almost all estimates being near zero Thus, the impact of media

on brand beliefs is estimated to be insignificant The results of our nạve analysis of the data is that media effects are estimated to be insignificant in any kind of aggregate

analysis, and that brand beliefs and consumer actions do not have large affects on

purchase intent Moreover, the nạve analysis does not provide measures of model fit needed to assess alternative hypothesized model structures

We now turn to our proposed analysis based on alternative factorizations of the joint distribution of the data Table 2.9 reports the log marginal density of the various factorizations discussed in table 2.1 Our preliminary analysis indicates that model 3, which postulates direct effects between intended actions (X), brand beliefs (B) and media recall (Z) on purchase intention (y) fits the data best Based on this finding, we further investigate a series of sub-models for the relationship among X, B and Z The results of this search across various sub-models that allow for the presence of direct effects are reported in Table 2.10 The fit statistics indicate that the joint distribution of X, B, and Z

is best factored hierarchically: [X,B,Z] = [X|B][B|Z][Z] Thus, we find evidence for both direct and indirect media effects – direct in the sense that media (Z) directly influences purchase intention (y), and indirect through the influence of media on brand beliefs, and brand beliefs on intended actions (see also Orth and Marchi, 2007) Measuring the influence of media on purchase intentions must account for both direct and indirect effects

Parameter estimates for our best-fitting model, model 4, are displayed in tables 2.11 – 2.13 We report parameter estimates that have more than 95% of posterior mass away from zero The 95% credible interval and the posterior standard deviation of the parameters in tables 2.11 – 2.13 can be obtained from the authors and have been omitted

to avoid clutter Table 2.11 reports parameter estimates {βk} for the normal mixture model in Equation (1) with brand beliefs (B) and media recall (Z) also included as

explanatory variables We find support for four latent segments of respondents (K = 4), where the explanatory variables are estimated to have different effects across segments, and are found to be much larger than those estimated in the aggregate analysis with K = 1 (table 2.6) We also find differences in the variance of the error terms, σ2

k, for each of the

segments, justifying the need for the proposed model relative to simpler specifications such as a finite mixture model Also reported at the bottom of table 2.11 is the average value of purchase intention for each segment This statistic is computed across iterations

of the Markov chain: the latent indicator variables {si} used to classify observations to

the latent segments are used to average purchase intention (y) across iterations The latent segments are ordered in the table so that segment 1 has the smallest average

purchase intention, and segment 4 has the largest A detailed examination of the results

is offered in the discussion section below

Figure 2.3, displays the trace plot of the draws of weights, φk, k=1 ,…, 4 These plots indicate that the Markov chain used to estimate the parameters converges quickly to the posterior distribution, and that initial conditions are quickly dissipated in this model

We find that analyzing k > 4 leads to small weight φk thus indicating that k = 4

Table 2.12 reports multivariate Bayesian variable selection parameter estimates {Γk} for the auxiliary regression of the consumer actions (X) on brand beliefs (B) We

only report estimates that have more than 95% of the posterior mass away from zero Displayed are results for the four segments Overall, we find large coefficient estimates Consider, for example, the effect of "overall impression of the make" (OIM) on consumer actions The OIM coefficients are found to have a large effect on the intended actions, with an increase of just one exposure associated with an increase on the intention scale of approximately 0.50 for all actions in segment 4 Also, OIM has differential impact in different segments Thus, we find that the effects of brand beliefs on intended consumer actions are large and are segment specific These intermediate effects are masked in aggregate analysis

Table 2.13 reports multivariate Bayesian variable selection parameter estimates {∆k} for the auxiliary regression of brand beliefs (B) on media exposure (Z) We only report estimates that have more than 95% of the posterior mass away from zero

Displayed are results for the four segments We again find large coefficient estimates The effect of brochures, for example, are large for segment one where an increase of just one exposure is associated with an increase of approximately 0.62 to 1.02 across all brand beliefs

Finally, table 2.14 reports aggregated estimates of direct and indirect media affects across all segments The estimates for the best-fitting model are based on the relationship:

The first term in parenthesis on the right side of equation (7) is the direct,

segment-specific effect of media exposure on purchase intention (Z→y) The second term is the

indirect effect of media exposure that operates through an effect on brand beliefs

(Z→B→y) The third term is the indirect effect where media affects brand beliefs, which

then affect intermediate actions and purchase intentions (Z→B→X→y) We explore in

detail the implication of coefficient, direct and indirect effects estimates in the next section

in terms of the coefficient estimates reported in table 2.11 {βk: (X,B,Z)→y}, table 2.12

{Γk: B→X} and table 2.13 {∆k: Z→B}

Direct Effects on Purchase Intention {βk }

We begin our analysis by examining the segment-specific direct effects reported

in table 2.11, which indicate that media exposure (Z) and brand beliefs (B) have a direct effect on purchase intent (y) Respondents in segment 1 have the lowest levels of

purchase intention, averaging just 0.12 on the eleven-point scale On average, there is little chance these individuals intend to make a purchase in the next six months Yet, the effect of magazine and newspaper advertising is large, with effect sizes of 2.5 and 1.0, respectively Respondents in segment 2 have a higher likelihood of purchase, and are identified as being affected by a large number of media vehicles (magazine, newspaper, radio, direct mail etc.) Respondents in the second segment are therefore broader in terms

of the media that directly impacts them, as compared to the first segment, and do not rely entirely on a few media vehicles

Respondents in segment 3 have a relatively high average likelihood of purchase (3.65), and are characterized by a large effect-size of going to a dealer (0.92) Individuals

in this segment are influenced very little by either the media or band beliefs

Respondents in segment 4 have the highest average likelihood of purchase of 6.08, and are associated with the intended actions of making a recommendation to a friend in the next six months and seeking information directly We find that respondent purchase intent in this segment, unlike other segments, is impacted directly by their brand belief about the manufacturer’s quality Also, newspaper advertisement (0.15) and direct mail

(0.47) have larger direct impact on purchase intent as opposed to radio (0.06) or

television (0.05) advertisements

Overall, we find that media effects are largest for respondents least likely to make

a purchase in the next six months, and are smallest for respondents who are most ready to buy Thus, our results indicate that media advertising is most effective the initial stages

of the purchase process, possibly being associated with consideration set formation

Effects of Brand Beliefs on Intended Actions {Γk }

The effects of brand beliefs on consumer actions reported in table 2.12 indicate the presence of large and differential effects across response segments Respondents belief about the "overall impression of the make" is seen to be consistently associated with all of the intended actions examined in the study The influence of this belief on intended actions is weakest in segment 1, where respondents have the lowest likelihood

of making a purchase, and is largest in segments 3 and 4 where a respondent purchase is more likely Beliefs about overall impression therefore provide a useful measure for predicting consumer desire to take a next-step toward making a vehicle purchase

Respondent beliefs in segment 1 on brand innovation are also seen to be

positively associated with the intended actions of "recommending to a friend" and

"reading mail." There are negative associations in segment 2 between beliefs about manufacturing quality and the intent to go to a dealer and seek information directly

Respondents reporting strong, positive beliefs about quality apparently do not feel a need

to acquire first-hand knowledge

Significant coefficients are more abundant in segments 3 and 4 that comprise respondents who are more likely to make a purchase in the next six months For segment

3, numerous brand beliefs are found to play a significant role i.e OIM, security,

excitement and manufacturing quality However, belief about innovation does not play a significant role as with segment 1 If our model were only to account for structural heterogeneity [y | X, B, Z] without incorporating a hierarchical component [X | B], analysis of the data would suggest that brand beliefs are not significantly associated with purchase intent for these segments (see table 2.11) In contrast, we find in segment 3 that brand beliefs are significantly associated with going to a dealer (table 2.12), which in turn has a significant association on purchase intent (0.92 in table 2.11) Thus, an indirect, hierarchical effect of brand beliefs on purchase intent is present

Respondents in segment 4 demonstrate an interesting hierarchical effect

associated with manufacturing quality (MQ) The significant MQ coefficients reported in table 2.12 for segment 4 are all negative, implying that more positive beliefs of MQ are associated with a decrease in the likelihood of taking actions associated with seeking objective information, making recommendations, reading direct mail and taking a test drive It seems counter intuitive that higher MQ would have a negative impact This can

be partly explained by investigating our hierarchical model in more detail From table