Competitor influence on marketing mix effectiveness

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Competitor influence on marketing

mix effectiveness

How do competitor actions influence marketing campaigns of a focal

brand?

Master Thesis

MSc. Marketing Intelligence & Marketing Management Faculty of Economics and Business

Department of Marketing University of Groningen Supervisor: Dr. P.S. van Eck

By

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Acknowledgement

In the past six months I have dedicated most of my time to finishing my master’s degree. These were no easy times, especially due to the pandemic, which was definitely not a great motivator. But there were some factors that made it a lot easier. First of all, I would like to thank my supervisor Dr. Peter van Eck for his professional and dedicated guidance during this process. His feedback sessions and comments have helped me in achieving what is laying in front of you. Besides that I would also like to express my gratitude to some of my friends, in particular Tom, John, and Vincent. Our favorite new hobby was going for walks or having online meetings, all to mind the severe Corona measures. These moments have given me several epiphanies and ‘Eureka-moments’ regarding my thesis. I would like to thank them for that.

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Abstract

One of the fundamental issues marketers have to account is the issue of competition. The success of a brand can be decided by how managers deal with competitor effects. Whereas a lot is known already about how marketing mix elements influence firm performance, less is known about how competitor actions influence the effectiveness of these marketing instruments. This study at hand aims to deliver insights on how competitors influence marketing mix effectiveness. The empirical results of this study have been based on a dataset by GFK containing 51633 observations from 5 brands across 6 major retail chains in the Spanish coffee market. This study found evidence that competitor actions most certainly influence marketing mix effectiveness, but the magnitude of this interference depends on retail chain type. Overall we found that the price reductions are moderated by competitor price reductions. The same goes for affiliate marketing and display marketing. We found for those instruments that traditional competitive television advertising reduces their positive effects.

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1. Introduction

Throughout the history of marketing research, much attention has been spend towards marketing mix effectiveness. Many managers are feeling the need to account for their spending within firms (Morgan, 2012). The statement as said already in the 19th_{century by the late John Wanamaker: “Half the money}

I spend on advertising is wasted; the trouble is I don’t know which half.” is still very relevant for managers even these days. Marketers have to account for their efforts even more these days because measurement possibilities have drastically increased.

One tool that is at hand for marketers these days is marketing mix modeling. According to Lilien and Kotler (1990), these models help firms in making decision on how to distribute their marketing spending according to each channel’s effectiveness. It has been shown that modeling based on a firm’s own assets is fairly easy, but taking external variables into account makes it more difficult. One of these external variables is competitor influence.

Dealing with competition lies at the heart of marketing strategy. It is the one task for any marketer to be better than any competing firm (Easton, 1988). Only by creating a sustainable competitive advantage, firms are able to outperform their competition. This topic has already seen a lot of attention in marketing literature. From the generic competitive strategies by Michael Porter (1980) to game theories like the prisoners’ dilemma.

Another well-known competitive theory is the Resource Advantage Theory. Hunt and Morgan (1995) state that firms are able to create an edge over competition by having a resource-based advantage. These resources can be any tangible or intangible assets available to a firm and firms should use these to create products and marketing strategies (Hunt & Morgan, 1995). Resources can be found in many shapes and sizes. Examples are financial capital, access to raw materials, possession of patents or copyrights and many more. To create a marketing offering these resources are translated into the marketing mix. This mix serves as a manifestation of the combination of resources (Thoeni, Marshall & Campbell, 2016). However, there is more to it than just being able to leverage a resource-based advantage. To be successful, firms also have to take into account how their competitors behave and what they do. Hunt (2015) states that some strategies can be perfectly executed in certain markets, but once the competitive context changes, the results might not be the same. Thus, it is of utmost importance to base your strategy not only on your own capabilities, but also on competitive circumstances.

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2 Even though these authors have given attention to the underexposure to competitive orientation, we did find several studies that come close and study several issues regarding competition (see: Moorthy (1985); Shai, Gupta & Lonial (2016)). For example, Gatignon (1984) already found that advertising effectiveness is moderated by competitor intensity in the travel industry. Massy & Frank (1965) state that competitor price promotions within the Fast-Moving Consumer Goods market decrease a focal firm’s own marketing effectiveness. Another interesting school of thought is the idea of category demand increase of price promotions. Nijs, Dekimpe & Steenkamp (2001) did however not find any evidence that this is the case withing the FMCG-market.

Most of the studies mentioned in the foregoing paragraphs have been executed in the FMCG-market. So what about the market for durable goods? In 2018 consumers spent 14 trillion dollars on durable goods in the United States alone. These expenditures account for 68% of the US gross domestic product (Kenton, 2019). This is just one indication for the importance of this market. Due to the lack of previous research we want to advance into this avenue and study competitor influence in the market for durable goods. The goal of this study is to address the question of how competitors influence marketing mix effectiveness and how marketers should account for this. Resulting in the main research question:

“How does the competitor marketing mix influence the marketing mix effectiveness of a focal firm?” In this study we have obtained data from both a focal firm and several competitors in the market for coffee machines in Spain. The competitor mix data consists of two parts. On the one hand we have price variables and on the other we have traditional media variables. In terms of the focal firm data we have pricing variables as well but regarding to advertising, we only have digital media spending. This makes for an interesting case to study the effects of competitive traditional media on a firm’s own digital efforts. To the best of my knowledge this has not been studied before in this capacity.

This paper will firstly dive into marketing mix effects of a focal firm. This will be done to confirm earlier studies by providing new evidence. Beyond a firms’ own marketing activities we will take a look at competitor influences on marketing mix effectiveness. By adding to the existing literature, managers gain a broader understanding of how competitors influence their own decision making. This study will subsequently give several propositions on how to deal with competitor marketing activities. Managers can use these to improve their own marketing efforts.

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2. Literature Review

2.1 The optimal marketing mix

The marketing mix that is available to firms consists in its classical form out of four marketing decisions: product, price, place and promotion (McCarthy, 1964). To have a successful marketing strategy marketers need to make the right decisions within the mix (Mintz, Ofer; Currim, Imran, 2013). Within this study we will specifically look at the marketing decisions: price and promotion.

According to Blythe (2009) decisions regarding to price include: pricing strategy, tactics and settings, discounts and all else that is related to the price of a marketing offering. With regards to promotion the following decisions have to be taken: communication strategy, advertising strategy, ad platform decisions, message frequency and many more (Blythe, 2009).

For many years scholars and practitioners have been trying to find ways to the optimal marketing mix to achieve the best results for any firm. One of these methods is by using marketing-mix models (Lilien & Kotler, 1983). Within these models several marketing decision variables are taken as explanatory variables as to predict a performance variable, often depicted as sales, market share or profitability. This method entails a statistical analysis to predict future impact of marketing instruments based on results of the past (Nielsen, 2014). It is often used to measure past marketing performances and transform that knowledge into guidelines for future investments. Marketing mix modeling has proven its worth over time, however, the models are usually not set up properly for the digital marketing channels (Thinkwithgoogle, 2019). That finding is quite shocking as per 2019 the digital ad spending covers half of total advertising spending worldwide and this ratio is only expected to become higher (emarketer, 2019).

Besides the individual marketing effects, it has also been widely accepted that there exist interaction effects between the marketing mix elements. For example, advertising effectiveness is increased by a higher or lower price based on the advertising medium (Prasad & Ring, 1976).

2.2 Price effects

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4 Already since the early 1970’s, price promotions have been immensely popular as a tool for marketers to generate sales (Currim & Schneider, 1991). Firms use this strategy to stimulate purchases by giving consumers an incentive to buy (Daws, 2004). According to Gupta (1988) the effect of price promotions can be decomposed into three effects: higher sales because brand switching, because of purchase time acceleration and because of stockpiling. He found in his study for a FMCG good that 84% of sales increased due to brand switching behavior, 14% due to purchase time acceleration and only 2% due to stockpiling (84/14/2). These are mostly short-term effects (Gupta, 1988). Bell, Chiang and Padmanabhan (1999) find a similar, albeit lower, effect. Respectively they report a 75/11/14 effect. In terms of consumer responses to pricing strategy there can usually be made a distinction in either short-term or long short-term effects (Pauwels, Hanssens, & Siddarth, 2002). In their 2002 study they do however find no evidence of long-term effects of prime promotions. They only find that temporary price reductions have an effect on the short-term. All the above findings result in the following hypothesis: H1: Price reductions have a positive effect on product sales.

H1a: Base price has a negative relation with sales.

2.2.1 Competitive Pricing

Besides the overall price elasticity and the effect of price reductions of a focal firm, we should also have a look at how these marketing actions from competitors influence this. As firm performance also depends on competitor (re)actions and not only on how well a company in itself is able to create an advantage with its own resources (Moorthy, 1985). Thus we expect that the strategic decisions concerning the price of competing brands also influences the effectiveness of a firm’s marketing mix effectiveness.

If we follow the reasoning that a firm’s own sales increases due to price promotions because it stimulates consumers to switch brands, we can extend on that by saying that if a competitor uses a price promotion, it might eat away revenue that the focal firm would have generated otherwise. In the past this was also pointed out by Frank and Massy (1967) and also by McAlister and Totten (1985). They demonstrate that price promotions can generate sales by luring in customers from other brands. They also suggest that there exists an interaction effect between promotional activities of the competitor brand and performance of the focal brand and vice versa.

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5 H2: Competitor price discounts have a negative effect on product sales.

H2a: The positive effect of price discounts is negatively moderated by competitor discounts H2b: The negative effect of base price is positively moderated by competitor base price

2.3 Advertising effects

Advertising is one of the most important instruments within the marketing mix. De Haan, Wiesel and Pauwels state that advertising creates revenue by introducing a (potential) customer to start the process of purchasing at a specific firm (de Haan, Wiesel, & Pauwels, 2016). But over the years there have been many discussions on its effectiveness. A lot of the doubt arises because there is a limited amount of studies that really quantifies the effect of advertising on sales (Samuel, 1970). This is mostly because of the fact that it is difficult to isolate the effect of advertising.

A popular belief is that advertising alters consumer behavior. This statement was introduced by Galbraith (1967). He states that corporations use advertising to create wants and desires among consumers that did not exist before. This is also known as the dependence effect. There have been many studies trying to prove or disprove this statement. For example, Metwally and Tamaschke (1981) found evidence to support Galbraiths’ statement. They concluded, based on Australian data, that the level of advertising expenditures has a positive and significant effect on sales. In 1975 Peel also found the same effect for the UK.

Then there is also the debate whether advertising is the most effective on the long or short term. Being able to impact the long-term with advertising is important to create a sustainable competitive advantage (Nijs, Dekimpe, Steenkamp, & Hanssens, 2001). In a more recent study by Ouyang, Zhou and Zhou (2002), evidence has been brought to the table that advertising indeed has a long-term effect on sales of durable goods. This can be attributed to the mechanism that consumers have a higher involvement level when purchasing durables, as means to reduce risk. Because of that, advertising is able to have an impact in the memory of the consumer for a long period, because the viewer is more cognitively active during this period (Vaughn, 1980). Hence, consumers are likely able to remember advertising concerning this product or brand and develop goodwill towards the advertising firm, given that their experience with the brand is positive (Givon & Horsky, 1990).

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2.4 The modern promotion mix

In the last few decades we have seen major changes in how most firms divide their marketing budgets across all available channels. As mentioned before, the share of digital marketing becomes ever larger. With the rise of digital, many new marketing channels have come to life. Among these are affiliate marketing and display marketing

2.4.1 Affiliate marketing

The arrival of affiliate marketing gave marketeers a new way to make their marketing activities more accountable. In the past, many marketers have been struggling with the effectiveness of their marketing campaigns. They had to invest funds into marketing campaigns upfront, without having any assurance that these investments would return profits. Affiliate marketing offers a change in this perspective. With this method advertisers only pay when a sale has occurred (Edelman & Brandi, 2015).

The use of affiliate marketing brings many benefits to a firm. Akçura (2010) found that in general it is a way for firms to increase their profits. This is a result of these programs because they help increase traffic to the firm’s website. Another benefit for the affiliate that is introduced by Duffy (2005), is the fact that through affiliate marketing, firms can create extra revenue streams without investing in inventory or infrastructure. This makes it a very attractive option for entrepreneurs to become an affiliate, which in turn increases the worldwide network and reach of these programs.

We expect the following effect in our study:

H3: Affiliate marketing has a positive effect on the focal firm’s sales.

2.4.2 Display advertising

Another tool available to marketers is display advertising. In the broadest sense, display marketing is advertising on websites, apps or social media using graphical banners or other advertising formats (Marketing Land, 2014). Hoban & Bucklin (2015) found that display advertising effectiveness differs per stage in the purchase funnel. But for 3 out of 4 stages the effect is significant and positive (Hoban & Bucklin, 2015). Moreover, it was also found that even though customers actively avoid looking at banners, the ads still do have a positive effect on brand awareness and ad recall (Dreze & Hussherr, 2003). Manchanda et al. (2006) went even further and linked display advertising directly to purchase behavior. They found that exposure to these ads increases the purchase frequency of existing customers. All these findings indicate that display advertising should have a positive effect on sales. Thus, we expect the same results in this study.

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2.4.3 Competitive Advertising

Besides the effects of own firm marketing efforts, it is also likely that the marketing efforts of competitors have an influence on the results of one firm. According to Danaher and Dhar (2008), competitor advertising can influence a brand’s sales in two ways. Firstly, through a direct cross-brand effect. And secondly through ways that competitor advertising influences the advertising elasticity of the focal brand in a negative way.

Albeit obvious, Burke and Srull (1988) found evidence that when competition advertises at a higher level, competitor interference increases as well. Additionally, Anderson (1998) and Keller (1987, 1991) found that this same effect also increases with the number of competitors advertising at the same time. In their study on FMCG advertising effects, Danaher and Dhar (2008) do find empirical proof of these effects. They show that when one or multiple competitors advertise in the same week, advertising elasticity of the focal firm significantly diminishes. Meaning that for every percentage of ad expenditure increase, the results become less. We expect that competitive advertising influences the advertising tools of the focal firm. Our formal hypotheses regarding this expectation will be explained in the next paragraph.

2.5 Digital versus traditional media

Now that we have made a distinction between the several types of media, it is interesting to take a look at how both these types affect each other. Previous studies have already shown that when marketers combine multiple media within one campaign, its effectiveness increases (Edell & Keller, 1989; Dijkstra 2002; Naik & Raman, 2003). The reason as to why this is more effective was still unknown until Voorveld, Neijens and Smit (2011) paid specifically attention to the underlying mechanisms (Voorveld, Neijens, & Smit, 2011). They found that this effect is caused by three processes, specifically: forward encoding, image transfer and multiple source perception.

However, all these studies look at how one firm can combine both digital and traditional media to increase its effectiveness. In our own specific search for studies that looked into the effect of competitive traditional media on digital media effectiveness of the focal firm we have found none.

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8 company are negatively moderated by competitive traditional media, resulting in the following hypotheses:

H5: Competitive traditional media advertising has a negative effect on the focal firm’s sales

H5a: The positive effect of affiliate marketing is negatively moderated by traditional competitive advertising.

H5b: The positive impact of display advertising is negatively moderated by traditional competitive advertising.

H5c: All other digital advertising activities are negatively moderated by traditional competitive advertising

H6: All other digital advertising activities have a positive effect on

2.6 Overview of studies

Authors Main topic Market Data Limitation

Ibrahim, Harrison (2020)

Model impact of competitor actions

B2C car market Uses competitor MM as explanatory variable

Gatignon (1984) Competitive reactivity as moderator on advertising effectiveness

Travel data Only uses advertising. Measures DV in price sensitivity.

Massy & Frank (1965) Effects of competitor price promotions

Fast-Moving Consumer Goods

Panel data

Nijs, Dekimpe & Steenkamp (2001)

Effect of price

promotions on category demand

FMCG Study is limited to price promotions. Models competition, but only the effect of number of competitors.

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2.7 Conceptual Model

The proposed hypotheses led to the following conceptual model:

Figure 2.1 Conceptual model

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3. Methodology

In this chapter we will give an overview of the data that has been used in answering our research questions. Besides that we will also discuss how the study will be executed, in terms of what type analyses are used and why.

3.1 Data

Our main goal is to investigate what the effect of competitor actions is on a firm’s own marketing mix effectiveness. To test our propositions we analyze data from the Spanish coffee market. More specifically, we will analyze data on sales in the durable/technological market, namely coffee machines. The data was collected and provided by GFK, which has the largest point-of-sale retail panel in durables and tech. The data in our set spans over a time period from 14-05-2017 until 05-05-2019 and consists of point-of-sale observations among Spanish retailers. In the dataset we have access to 51.633 observations from 5 brands across 6 major retail chains over 670 outlets. These are weekly observations where every observation contains sales as dependent variable. From the dataset we can use the following variables for modeling:

Table 3.1 Overview of used variables

Variable: Description Scale Expected effect

Sales Depicts number of units sold in period T. Ratio x

Price Reduction Price reduction of an article in € in period T Ratio +

Base Price Base price of an article in € in period T Ratio -

Competitor Price Reduction

Depicts how much competitor articles were reduced in price in period T.

Ratio -

Competitor Base Price Depicts the competitor base price in period T. Ratio + Affiliate Marketing Depicts how many affiliate impressions were

registered in period T.

Ratio +

Display Marketing Depicts how many display advertising impressions were registered in period T.

Ratio +

Other Media Depicts how many impressions were registered by other media, which could not be classified as either affiliate or display ads, in period T.

Ratio +

Competitor TV Sponsorship

Depicts how much was spend on TV sponsorship by competitors in period T.

Ratio -

Competitor TV Traditional

Depicts how much was spent on traditional TV advertising by competitors in period T.

Ratio -

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3.2 Plan of analysis

To make any inferences based on our data, we need to use models. In scientific marketing research there is a wide range of models available which each its own set of limitations and goals. Formal models can either be descriptive, predictive and normative (Leeflang, Wieringa, Bijmolt, & Pauwels, 2015). In our case we want to model the sales variable based on several explanatory independent variables and moderating variables. We are interested in how effective several marketing instruments are and how this effectiveness is being influenced by competitors. We also want to be able to predict what will happen when changing values of the variables. Thus, we need a descriptive and predictive model. Descriptive models allow researchers to study how effective certain instruments are (Leeflang et al., 2015). Beyond the basic goal of the model we have to decide on the functional form. This form is based upon the mathematical relationships between the variables. One of the most simple forms of a model is the linear additive model. This type of model assumes that the relation between the variables is linear (Leeflang et al., 2015). It has several major drawbacks, for example: this model assumes that there are no implicit interactions between the variables. However, this model does allow for including moderating effects explicitly. By adding the product of the variables that are likely to have interaction effects, we can accommodate the moderators.

3.2.1 Linear regression

Linear Additive Model

As mentioned before, to accommodate for moderating effects we need a linear additive model. A simple linear model has the following structure:

𝑦𝑡 = 𝛼 + 𝛽

₁

𝑋

_1𝑡

+ 𝛽

₂

𝑋

_2𝑡

+ … + 𝛽

_𝐾

𝑋

_𝐾𝑡

+ 𝜀𝑡

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In our case we want to include moderating effects, which takes the basic form as:

𝑦𝑡 = 𝛼 + 𝛽1𝑋1𝑡+ 𝛽2𝑋2𝑡 + 𝛽3 (𝑋1𝑡𝑋2𝑡) + 𝜀𝑡 (4)

With our envisioned effects the model will look like this:

𝑆𝑎𝑙𝑒𝑠𝑡=

𝛼 +

𝛽1𝐵𝑃𝑡+ 𝛽2𝐵𝑃_𝐶𝑡+ 𝛽3(𝐵𝑃𝑡𝐵𝑃_{𝐶 𝑖𝑡}) +

𝛼 +

𝛽4𝐷𝑆𝐶𝑡+ 𝛽5𝐷𝑆𝐶_𝐶𝑡 + 𝛽6(𝐷𝑆𝐶𝑡𝐷𝑆𝐶_𝐶𝑖𝑡) + 𝛽7𝐴𝐹𝑀𝑡+ 𝛽8𝑇𝑉_𝐶𝑡+ 𝛽9(𝐴𝐹𝑀𝑡𝑇𝑉_𝐶𝑖𝑡) + 𝛽10𝐷𝐼𝑆𝑡 + 𝛽11(𝐷𝐼𝑆𝑡𝑇𝑉_𝐶𝑖𝑡) + 𝛽12𝐷𝑂𝑡+ 𝛽13(𝐷𝑂𝑡𝑇𝑉_𝐶𝑖𝑡) + 𝛽14𝐶𝐵𝑡+ 𝛽15𝐼𝑆𝑃𝑡+ 𝛽16𝐿𝐹𝑡 + 𝛽17𝐿𝐹𝑃𝑡 + 𝜀𝑡 (5) Where:

𝐵𝑃𝑡 = Base Price of focal brand in period t

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12 𝐷𝑆𝐶𝑡 = Price reduction of focal brand in period t

𝐷𝑆𝐶_𝐶𝑡 = Price reduction of competitor i in period t

𝐴𝐹𝑀𝑡 = Number of affiliate marketing impressions of focal brand in period t

𝑇𝑉_𝐶𝑡 = Expenditure level of competitor TV advertising of competitor i in period t

𝐷𝐼𝑆𝑡 = Display advertising impressions of focal brand in period t

𝐷𝑂𝑡 = Other digital marketing number of impressions of focal brand in period t

𝐶𝐵𝑡 = Number of cashbacks of focal brand in period t

𝐼𝑆𝑃𝑡 = Number of in-store-promotions of focal brand in period t

𝐿𝐹𝑡 = Number of leaflets per store of focal brand in period t

𝐿𝐹𝑃𝑡 = Availability of leaflets per store of focal brand in period t.

3.2.2 Linear regression estimation

As this model is linearizable we can use the Ordinary Least Squares (OLS) method to estimate the parameters. To be able to use OLS, several assumptions need to be met (Leeflang et al., 2015). These assumptions are:

1. E(𝜀𝑡) ≠ 0 for all t or the nonzero expectation;

2. Var(εt) = σ2 for all t or heteroscedasticity; 3. Cov(εt,εt) = 0 for t t or correlated distributions; 4. εt is normally distributed or nonnormal errors; 5. Variables are nonstochastic

6. Variables are linearly independent.

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Violated assumption How to detect? How to solve?

E(𝜀𝑡) ≠ 0 ▪ Plot each IV residual against each other

▪ RESET-test ▪ White test

▪ Modify functional form ▪ Add relevant predictors ▪ Allow parameters to vary Var(𝜀𝑡) ≠ 𝜎2 ▪ Plot each IV residual against each other

▪ Goldfeld/Quandt test, Breusch-Pagan test, White test

▪ Modify specification ▪ Use

Heteroscedasticity-consistent estimation

Cov(𝜀

𝑗

, 𝜀

𝑡

′) ≠ 0, 𝑡 ≠ 𝑡′

▪ Plot residuals against time

▪ Durbin Watson test ▪ Durbin’s h-test

▪ See 1

Nonnormal errors ▪ Plot Distribution of residuals ▪ 2_-test ▪ Kolmogorov-Smirnov ▪ Bera-Jarque ▪ See 1 ▪ Robust Regression ▪ Box-Cox-transformation Stochastic predictor correlated with the disturbance term

▪ Diagnose Specification ▪ Simultaneous equations ▪ Instrumental variable

estimation

Multicollinearity ▪ Inspection of the correlation matrix ▪ Inspect VIF values

▪ Reformulate model ▪ Create new predictors ▪ Obtain more data ▪ Apply other estimation

methods

▪ Eliminate predictor variables

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3.2.3 Bayesian regression

Another way of modeling our problem is by using Bayesian methods, in particular we will use Bayesian regression to model sales based upon our proposed explanatory variables. Bayesian regression has only recently seen its rise in popularity in practical application. Even though this method has been studied a long time before, the computational power that is needed has only become widely available in the last two decades (Bishop, 2003).

One of the biggest issues with classical, non-Bayesian, models is that when models become complex and flexible, the model will be overfitted to the data. The least squares estimation for a model is able to achieve a one-on-one fit to the training data. This causes issues for generalizing the results provided by the model (Bishop, 2003). Bayesian modeling tries to overcome this issue and thus that is why we also build a Bayesian model alongside a classical model.

Another main differences between linear regression and Bayesian regression is that the latter gives us estimations based on probability distributions instead of point estimates. Estimation will give us a posterior distribution for all the model parameters. This is supposed to give a more accurate result (Koehrsen, 2018). A Bayesian regression model, based on a normal distribution looks like the following model:

𝑦 ~ 𝑁(𝛽

𝑇

𝑋, 𝜎

2

𝐼)

The posterior part of the model is calculated as following:

𝑃(𝛽|𝑦, 𝑋) =

𝑃(𝑦|𝛽, 𝑋) ∗ 𝑃(𝛽|𝑋)

𝑃(𝑦|𝑋)

In words, a Bayesian prediction is estimated as follows:

𝑃𝑜𝑠𝑡𝑒𝑟𝑖𝑜𝑟 =

𝐿𝑖𝑘𝑒𝑙𝑖ℎ𝑜𝑜𝑑 ∗ 𝑃𝑟𝑖𝑜𝑟

𝑁𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑎𝑡𝑖𝑜𝑛

Thus, the core idea of a Bayesian regression model is that you can use prior data to make predictions. This prior data is knowledge on shapes of the probabilistic distributions of a model. However, in many cases there is only limited prior information available, and in some cases there is no prior data at hand. In those cases we need a prior distribution, called a noninformative prior (Bishop, 2006). In those cases the posterior will depend only on the given data and not from the prior.

3.2.4 Bayesian regression estimation

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15 our posterior. This methods creates a Markov Chain that has a stationary distribution which is equal to the probability distribution of our model. Thus, this will allow us to estimate the effects of our predictors by averaging over the generated sample (Elster, Klauenberg, & Walzel, 2015).

3.3 Data preparation

The dataset that was used for this study originally contained over more than 9000 variables. Most of these were iterations of a so-called ad stock variable. Ad stock variables are a way to accommodate marketing dynamics in modeling. Marketing dynamics for example capture the effect of lagged variables. In marketing literature it is widely accepted that advertising effects are not generally limited to only one period in time. Often it is the case that these effects are still visible in future periods. To accommodate for this, marketers need to incorporate lagged effects (Leeflang et al., 2015).

Within our GFK dataset, all media variables contained ad-stock transformations. This adstock transformation was based upon two transformations. Firstly, the half-life parameter. This value states in how many weeks the value of a medium is halved. Secondly, the data is transformed in order to create a S-curve. It is assumed that in order to get a minimum effect of a medium, a certain level of investment is needed. It is reasonable to assume that for example broadcasting an advertisement once does not yield any results. However, at a certain point the effect diminishes as well. Similar to the previous example, broadcasting one ad a thousand times would likely not have a larger impact than broadcasting it 900 times. In order to create this variable a logit transformation was used which was based on two parameters: the saturation point and the steepness factor. The former states at what point the increasing effect starts to decrease and the latter states how steep the middle part of the curve is.

However, it is not set in stone what the ideal value is for each of the parameters. Hence, over 9000 iterations of these variables were present in our data, each iteration displaying a different adstock effect. To find the optimal levels for the parameters we ran a regression model for all parameters. Where we modeled sales on only that specific set of adstock parameters. After running these models we picked the optimal adstock levels based on the highest adjusted R2. In table 3.3 the final variables can be found.

Variable Saturation point Steepness Half-life

TV_Spons_Comp 0.3 0.75 7

TV_Comp_total 0.5 1.25 4

Affiliate impressions 0.3 1.25 1

Display impressions 0.3 0.75 3

Other Digital Impressions 0.7 1.25 1

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16 Furthermore we also combined several variables to make their interpretation in a later stage more practical. Firstly, we created one variable that captures the total effect of competitive traditional advertising. This was done by summing both the tv sponsoring and tv traditional variables.

The dataset also contained two variables capturing the effect of discounts. The first was the pure discount variable. This data was based on input from the outlets that took part in the data collection period. The second, price reductions, was produced by the GFK company itself. This second variable aimed to detect price promotions that initially were not mentioned by the companies that were observed. To create one overarching variable that captures the effect of discounts we combined aforementioned variables into one by summing the observations: ‘Discounts’. This transformation was both executed for the discount variables of the focal firm as well as for the competitor firms.

Finally, to make our estimates better interpretable we rescaled several variables. In some cases variable observations take on extreme high or low values. To accommodate this we divided the variables by using a factor that was more fitting with the actual size of the observations. This changes the interpretation of the variables in the sense that the effect is not per one unit increase, but per a thousand, a hundred thousand or a million. In the table below we display which variables have been rescaled and with what factor.

Table 3.4 Overview variable scale transformations

Variable Divided by

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17

4. Results

In this chapter we will discuss the results of our study. The results from all models will be given and discussed thoroughly. Per model we will first check the accompanying assumptions. After that the empirical results will be reported.

4.1 Linear Additive Model

Firstly, we ran a linear additive model to estimate the competitor effects on our own marketing mix.The following model was estimated:

𝑆𝑎𝑙𝑒𝑠𝑡=

𝛼 +

𝛽1𝐵𝑃𝑡+ 𝛽2𝐵𝑃_𝐶𝑡+ 𝛽3(𝐵𝑃𝑡𝐵𝑃_{𝐶 𝑖𝑡}) +

𝛼 +

𝛽4𝐷𝑆𝐶𝑡+ 𝛽5𝐷𝑆𝐶_𝐶𝑡

+ 𝛽6(𝐷𝑆𝐶𝑡𝐷𝑆𝐶_𝐶𝑖𝑡) + 𝛽7𝐴𝐹𝑀𝑡+ 𝛽8𝑇𝑉_𝐶𝑡+ 𝛽9(𝐴𝐹𝑀𝑡𝑇𝑉_𝐶𝑖𝑡) + 𝛽10𝐷𝐼𝑆𝑡

+ 𝛽11(𝐷𝐼𝑆𝑡𝑇𝑉_𝐶𝑖𝑡) + 𝛽12𝐷𝑂𝑡+ 𝛽13(𝐷𝑂𝑡𝑇𝑉_𝐶𝑖𝑡) + 𝛽14𝐶𝐵𝑡+ 𝛽15𝐼𝑆𝑃𝑡+ 𝛽16𝐿𝐹𝑡

+ 𝛽17𝐿𝐹𝑃𝑡 + 𝜀𝑡

4.1.1. Validation

As mentioned in chapter 3.2.2., several assumptions have to be met to be able to run a valid regression model using OLS estimation. That is why we will first check for these assumptions in order to obtain reliable coefficients for our models.

Nonzero expectation

First and foremost we will check the nonzero expectation. To test this assumption we used a RESET-test. The result of this test turned out to be significant, which means that we might have an omitted variable issue in our model. However, as we do not have extra data and already incorporate all the available variables in our dataset, we cannot extend the model even further.

Heteroscedasticity

Secondly, we want to test if the error term from our model is homoscedastic. This means that our error term has the same variance in all cases either cross-sectionally and/or over time. If this assumption is violated, our OLS estimation will be less efficient. Additionally, the covariance matrix of the estimates might be biased (Leeflang et al., 2015). This will hinder us in a later stage as well when we want to test the other assumptions. It has been shown that heteroscedasticity often occurs in studies using cross-sectional data. As this study also uses cross-cross-sectional data we expect this issue to arise.

To test for heteroscedasticity we used the Goldfeldt-Quandt test and split the dataset into two parts. One part containing only data from weeks where a promotional price was used, and one part with weeks where no price promotions were present. To calculate the corresponding F-statistic, we used the following calculation:

𝐹 = 𝑅𝑆𝑆1 / 𝑛2− 𝑘 𝑅𝑆𝑆2 / 𝑛1− 𝑘

= 518031 / 14335 − 12

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18 Searching for this F-statistic in the F-distribution results in an p-value of 1. Thus we cannot reject the null-hypothesis, meaning that we assume that the error term is homoscedastic, confirming the second assumption.

Correlated disturbances

We also need to check whether the residuals show a pattern. If this is the case, then some or all of the covariances will be nonzero. This will violate the assumption of uncorrelated disturbance terms (Leeflang et al., 2015). Violation of this assumption is also called correlation. Whenever auto-correlation occurs, the efficiency of OLS-parameter estimation is reduced. To test for autoauto-correlation we used the Durbin-Watson test. This test takes two consecutive disturbances and tests the difference in variance between these points (Durbin & Watson, 1950).

The Durbin-Watson test showed significant correlation among the disturbances (P < .05), which indicates that OLS estimation will be less efficient. To accommodate for this we used GLS transformation. This was done by multiplying the specific variable with the auto-correlation coefficient minus the previous observation. After transforming the data we performed the Durbin-Watson test again, which returned an insignificant results (P > .05), indicating that now we have met the assumption of uncorrelated disturbances.

Nonnormality

Furthermore we test for nonnormality issues in the dataset. To run an efficient regression we assume that the disturbances are normally distributed. If we cannot assume normality, then we cannot reliably interpret the significance values (Leeflang et al., 2015). To test this assumption we ran both a Kolmogorov-Smirnov and Jarque-Bera test. Both turned out to be significant which indicates nonnormality in the data.

Table 4.1 Overview of nonnormality tests

As both test report significant results, we assume that the fourth assumption has been violated. Meaning that we cannot assume a normal distribution among the disturbances. One way of resolving this issue is by using bootstrapping methods. While performing bootstrapping methods we encountered several issues, which made the bootstrapping of our model containing GLS variables impossible. This issue will be discussed in detail in chapter 5. For now we have to interpret the significance levels of our parameters with caution.

Test Test Statistic Significance

Kolmogorov-Smirnov 0.12077 P < 2.2e-16

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19

Multicollinearity

To test for multicollinearity we inspect the Variance Inflation Factor (VIF) values. Multicollinearity occurs when multiple predictors correlate perfectly with each other. This correlation will yield biased parameter estimates and thus a regression cannot be estimated correctly (Leeflang et al., 2015). Values above 5 indicate that variables correlate with each other. As can be seen from the table below, this threshold is exceeded in two instances: Other display impressions (ODI) and the interaction of ODI and Competitor traditional advertising. VIF-values of variables that are used in interactions tend to be inflated. Moreover, both values are still below, the more lenient, threshold of 10. Thus we continue with the variables as they are and do not conduct extra measures.

Table 4.2 Overview of VIF values

Predictor VIF-Value

Base price 1.108966

Price Reduction Affiliate impressions Display impressions Other digital impressions Number of Cashbacks 1.535278 2.434394 1.508090 7.163938 1.013954

Number of In-Store-Promotion days 1.022954

Presence of leaflets 1.058497

Competitor base price 1.092824

Competitor discounts 1.644015

Competitor traditional advertising spend 2.183759

Base price x Competitor base price 1.029364

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20

4.1.2. Empirical Results

Before we start discussing the empirical results of our models, it is important to note that within our data we might come across different entities. On itself this might not be a huge problem, however, it could mean that these different entities have unique estimates for the theorized effects. Within our data we observe many different entities. Firstly, on the lowest aggregation level, we have data on outlet level. In our sample we have observations of 670 outlets. One step higher we can aggregate on retailer level. We observed that our sample contains data on 14 retailers. Finally we notice that we can aggregate our data based on channel type. On this level we have three possibilities: hypermarkets, department stores and technical superstores. These three options vary quite a bit between each other in terms of type of store. We should expect that the main purpose of visiting a department store differs from one’s purpose of visiting a technical superstore. Hence, we expect the difference in effect sizes to be largest for this last aggregation level.

To estimate the model we firstly create a pooled model. By pooling all data for one model we are able to make use of all the observations in our dataset. However, a pooled regression model assumes that both the intercept and parameters are the same. This is quite a strong assumption, as it is reasonable to assume that several differences exist within our dataset. As mentioned before we do expect differences to be mostly present between the channel types. It would not be surprising that these entities differ from each other in terms of base line level of sales or in the magnitude of effects from marketing activities (Leeflang et al., 2015). To formally test whether we can pool the data or should specify several models per channel, we perform the Chow-test. The Chow-test is a F-test which uses the Residual Sum of Squares and the degrees of freedom of both the pooled and unpooled models:

𝐹 = (𝑅𝑆𝑆_𝑑𝑓𝑝𝑜𝑜𝑙𝑒𝑑− 𝑅𝑆𝑆𝑢𝑛𝑝𝑜𝑜𝑙𝑒𝑑 𝑝𝑜𝑜𝑙𝑒𝑑− 𝑑𝑓𝑢𝑛𝑝𝑜𝑜𝑙𝑒𝑑 ) 𝑅𝑆𝑆𝑢𝑛𝑝𝑜𝑜𝑙𝑒𝑑 𝑑𝑓𝑢𝑛𝑝𝑜𝑜𝑙𝑒𝑑 = (1659921 − 1599238)/(51614 − 51582) (1599238/51582) = 61.16488

The corresponding p-value to this F-statistic is <.00001, which means that we can reject null-hypothesis. Thus, we can conclude the parameters are not homogeneous and that we cannot pool our date to create one model. In the following sections we will specify a model for each of the channels to accommodate for this.

4.1.2.1. Technical Superstores

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21 R2 as well. The accompanying adjusted R2 from our model does not deviate much from the regular coefficient of determination. The adjusted R2 of our model is 0.1289 or 12,89%, which is nearly identical. These values might seem rather low, but there are several explanations for why this might not be a bad thing necessarily. One of the reasons could be that we use an unaggregated modeling method. Aggregation tends to inflate the R2 values, hence why our model’s R2 may seem low.

Secondly, we take a look at the statistical significance of our model. As a first step we look at the significance level of the equation as a whole. Overall, our model shows high significance (P < 0.01). Then we take a look at the individual parameter estimates. Within our model most parameters, we have several variables that are insignificant, those being: competitor discount, affiliate impressions, competitive traditional advertising, other digital advertising, number of in-store-promotion days, interaction between discounts, interaction between traditional competitive advertising and the interaction between traditional competitive advertising and other digital ads. These insignificant variables will not be interpreted.

Then we look at the specific parameter estimates from which the full results are shown in table 4.3. Firstly, competitor base price has a significant and negative effect on our focal brand’s sales, β = - 0.925, P < .05. This is not in line with our initial expectation, as one would expect that when a competitor raises its price, demand for a substitute would increase. In our case it is the opposite. However, our own discount variable shows a highly significant positive effect β = 2.063, P < .001. Stating that whenever we increase our discounts with 1 unit, sales of the focal brand increase with 2.063 units, which confirms hypothesis 1.

Furthermore, we see that display advertising has a highly significant and positive effect β = 0.0129479207, P < .001. Indicating that whenever display impressions increase with one million units, sales increase with 0. 0129479207 unit, confirming H4.

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22 Table 4.3 Output Technical superstores model

4.1.2.2. Hypermarkets

Table 4.4 shows the results of the model created for the hypermarkets. This model shows overall significance (P < 0.01) and its explanatory variables explain 10,86% of the variance in sales (R2 = 0.1086). In interpreting the results we only observe the significant parameters. In this model base price, affiliate impressions, number of in-store-promotion days and the interactions containing base price, discounts and affiliate marketing show no significant effect. All other variables show high significance. We highlight the most important findings below.

First the effects of competitor pricing on our sales and the effectiveness of our pricing instruments. Competitor base price has a significant, negative effect β = - 1.521, P < .001, which is not in line with our expectations. Competitor discounts have a significant and negative effect β = - 0.415, P < .001. This finding confirms hypothesis 2.

In terms of media variables, competitive traditional advertising has a significant and negative effect on product sales β = - 0.849825, P < 0.001, confirming H5. Beyond that we look at the specific interaction effects between competitor advertising and our digital media channels. We find a significant and negative effect for the interaction between traditional advertising and display advertising β = -0.0093,

Coefficient Estimate Std. Error Significance

Intercept 2.498 0,049 < 2e-16 ***

Base price 0.900 0,443 0.0422 *

Competitor base price -0.925 0,359 0.0101 *

Discounts main 2.063 0,056 < 2e-16 ***

Competitor discounts -0.134 0,096 0.1617

Affiliate impressions 0.0061880694 0,000 0.9554

Competitor traditional advertising spend - 0.0001772591 0,000 0.2306 Display advertising impressions 0.0129479207 0,000 1.28e-13 ***

Other digital impressions 0.043 0,042 0.3002

Number of cashbacks 0.003 0,001 0.0162 *

Number of In-Store-Promotion days -0.182 0,125 0.1443

Base price main x Competitor base price 14.088 3.123 6.53e-06 *** Discounts mains x Competitor discounts -0.013 0,032 0.6723 Affiliate impressions x Competitor

traditional ad spend

-0.0009171417 0,000 6.33e-05 ***

Display advertising impressions x Competitor traditional ad spend

-0.0000008319 0,000 0.8009

Other digital advertising impressions x Competitor traditional ad spend

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23 confirming hypothesis 5b. The interaction between competitor advertising and other digital advertising is also significant and negative β = - 0.744, P < .001, which confirms H5c.

Table 4.4 Output Hypermarkets model

Intercept 1.655 0.052 < 2e-16 ***

Base price -0.601 0.371 0.105032

Competitor base price -1.521 0.446 0.000661 ***

Discounts main 1.522 0.066 < 2e-16 ***

Competitor discounts -0.415 0.073 0.0000000159 ***

Affiliate impressions -0.115379 0.000 0.317204

Competitor traditional advertising spend

-0.849825 0.000 0.0000000163 ***

Display advertising impressions 0.003478 0.000 0.024848 *

Other digital impressions 0.368 0.062 0.0000000038 ***

Number of In-Store-Promotion days 0.0483 0.173 0.780299

LEAF_numstores 0.184 0.090 0.041561 * Base price main x Competitor base

price

1.439 26518360830971

10.000

0.587507 Discounts mains x Competitor

discounts

-0.008 0.007 0.235765

Affiliate impressions x Competitor traditional ad spend

-0.061230 0.000 0.800646

-0.009382 0.000 0.002268 **

Other digital advertising impressions x Competitor traditional ad spend

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24

4.1.2.3. Department stores

The full results of the model for department stores are shown in table 4.5. Firstly we take a look at the coefficient of determination or R2_{. The R}2_{of our proposed model has a value of 0.259 or 25,9%. The}

accompanying adjusted R2_{from our model does not deviate much from the regular coefficient of}

determination. The adjusted R2_{of our model is 0.2573 or 25,73%, which is nearly the same.}

Secondly we take a look at the statistical significance of our model. As a first step we look at the significance level of the equation as a whole. Overall, our model shows high significance (P < 0.01). Then we take a look at the individual parameter estimates. Within our model all parameters are highly significant (P < 0.001), except for competitor discounts, number of in-store-promotion days and the interaction between competitive traditional advertising and affiliate marketing.

In terms of the specific parameter estimates we first look at the pricing variables. Firstly, competitor base price has a significant and negative effect on our focal brand’s sales, β = -1.119, P < .05. This is not in line with our initial expectation, as one would expect that when a competitor raises its price, demand for a substitute would increase. In our case it is the opposite .

Furthermore, we see that competitive traditional advertising has a significant and negative influence on sales overall, β = - 1.092021, P < .001. This confirms our 5th hypothesis and shows that whenever a competitor increases its expenditures on television advertising on average with 1000 units, sales of the focal brand decrease on average with 1.092021 units.

Subsequently, we take a look at the interaction effects. Firstly, the effect of competitor base price on our own base price. This effect is significant and positive, β = 10.598, P < .001. Like our first model, this estimate is again extremely unrealistic. We have opted again to not interpret the estimate of this interaction. Then, we observe the effect of competitor discounts on our own discount effectiveness. We find a significant and positive interaction effect β = 0.272, P < .001. This means that on average when a competitor discounts its products our own product discounts will be more effective. This finding disconfirms hypothesis H2a.

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25 Table 4.5 Output Department stores model

4.2 Bayesian Regression

As specified in chapter 3.2.3. we also estimated a Bayesian regression model. With this model we will check the same hypotheses as with the linear additive model. To estimate this model the package ‘rstanarm’ in R was applied, which uses Stan. As mentioned before, Bayesian models require a prior to estimate the posterior. However, it is also possible to run a Bayesian regression without a prior. In that case the model uses a set of default priors, also called: non-informative priors. In this study we ran both a model containing noninformative priors and a model that includes informative priors. Due to the lack of actual prior data in this setting, we created priors based upon our earlier analysis. In specific, we took the mean and variance of all our parameters from the linear additive model to specify the priors.

4.2.1. Bayesian Regression with default priors

Firstly we ran a Bayesian regression without specifying priors. In theory this model should yield worse results than a model that uses specified priors (Van de Schoot et al., 2014). To compare, we first present the results of this model in table 4.6.

Most of the parameters of our model are shown to be significant, this was judged based upon the credibility intervals. For all parameters, except number of cashbacks and the interaction between traditional competitive advertising and other digital advertising, there is no zero-value in between the

Intercept 2.071 0.068 < 2e-16 ***

Base price -1.062 0.359 0.00312 **

Competitor base price -1.119 0.358 0.00179 **

Discounts main 3.212 0.117 < 2e-16 ***

Competitor discounts 0.083 0.082 0.30849

Affiliate impressions 0.398695 0.000 0.01969 *

-1.092021 0.000 1.22e-12 ***

Display advertising impressions 0.004183 0.000 0.00103 **

Other digital impressions 0.5845 0.082 9.39e-13 ***

Number of In-Store-Promotion days -0.0417 0.115 0.71728

Base price main x Competitor base price

10.598 2.72 9.94e-05 ***

Discounts mains x Competitor discounts

0.272 0.044 8.76e-10 ***

0.422285 0.000 0.15046

-0.018997 0.000 < 2e-16 *** Other digital advertising impressions x

Competitor traditional ad spend

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26 credibility intervals. Thus we can conclude that all parameters that do not contain a zero-value are significant. We also found that all R-hat values are around 1 (ranging from 0.999 – 1.003). This indicates that the chains from the MCMC method have properly mixed (Gelman, Hill, & Vehtari, 2020). Now that we have concluded that we can interpret our model we continue with the specific parameter estimates. For reporting we use median values. This was done because Bayesian methods do not generate a specific point-estimate for the parameters. Instead, posterior distributions are created for each explanatory variable. However, the median values paint a similar image as point-estimates created by OLS. Below we will report the estimates of the competitor explanatory variables, as those are the ones we are most interested in with this model.

First off, competitor base price. This effect is significant and negative M = -1.276. This indicates that whenever a competitor increases its price, sales for our focal brand decreases. Same as with OLS estimation this result is not in line with our expectation. On the other hand, competitor discounts have a negative effect on sales M = -0.394. Indeed, this effect has the direction we would expect and also confirms hypothesis 2. When we look at the interaction effect of competitor discount on our own discounting effectiveness we find a significant and negative effect M = -0.019. This indicates that whenever a competitor increases their discount value with 1 unit, our own discount generates 0,019 fewer units, which indicates H2a.

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27 Table 4.6 Output Bayesian Model with default priors

4.2.2. Bayesian Regression with informative priors

Now that we have estimated a Bayesian model with weak, or non-informative, priors, we turn to a model that does use prior data. Prior data can be retrieved from previous, similar, studies or other sources that would possess of data concerning our problem (Gelman et al., 2020). In our case we have not found prior data that aligns exactly with our problem. To accommodate for this we have chosen to use the results from our own analysis, the linear regression with OLS estimation. For defining the priors we used the means and standard deviations of all parameters. Obviously, this is not the most ideal situation. The consequences of this decision will be discussed in detail in chapter 5.

Coefficient Estimate 89% CI Rhat

Intercept 6.270 [ 6.177, 6.368] * 1.000

Base price -2.748 [-3.045, -2.437]* 0.999

Competitor base price -1.281 [-1.534, -1.029]* 0.999

Discounts main 2.049 [ 1.993, 2.103]* 1.000

Competitor discounts -0.393 [-0.465, -0.324]* 1.000

Affiliate impressions -0.118 [ 0.000, 0.000] 1.001

-0.001 [-0.001, -0.001]* 1.000 Display advertising impressions 0.932 [ 0.000, 0.000] 1.000

Other digital impressions 0.604 [ 0.548, 0.660]* 1.000

Number of cashbacks -0.002 [-0.003, 0.000] 1.000

Number of In-Store-Promotion days 0.613 [ 0.506, 0.725]* 0.999

LEAF_numstores 0.001 [ 0.001, 0.002]* 1.000

Presence of leaflets 0.832 [ 0.744, 0.908]* 1.000

9.638 [ 8.062, 11.075]* 0.999

-0.019 [-0.026, -0.012]* 1.000 Affiliate impressions x Competitor

traditional ad spend

1,07E-05 [ 0.000, 0.000] 1.001 Display advertising impressions x

-7,21E-04 [ 0.000, 0.000] 1.000 Other digital advertising impressions x

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28 Table 4.7 Output Bayesian Model with informative priors

The results from the model above are vastly different than the results of the model without priors. This could mean that the prior data offers a lot of extra information and thus alters the parameters. However, it is more likely that something has gone wrong. After running the model in the statistical software R several warnings were produced. Among these warnings were issues with the maximum tree depth and convergence of the Markov chains. According to the description of the ‘R_stan_arm’ package this means that we cannot analyze the results as they are unreliable. In chapter 5 we will discuss this detail in depth.

Coefficient Estimate 89% CI Rhat

Intercept 1.490e+05 [42811.100, 3.018e+05] * 34.896

Base price -0.114 [-0.229, 0.069] 1.66E+09

Competitor base price -0.028 [-0.307, 0.245] 3.62E+09

Discounts main 1.198 [-1.763, 1.714] 2.26E+08

Competitor discounts -0.662 [-1.824, 0.358] 4.67E+08

Affiliate impressions 0.465 [-1.323, 1.491] 5.27E+08

-0.686 [-4.602, 1.256] 9.83E+08

Display advertising impressions 0.002 [-0.016, 0.024] 5.484 Other digital impressions -10816.760 [-1.555e+05, 56035.641] 1.13E+08

Number of cashbacks 2.609 [-3.731, 4.373] 9.82E+08

Number of In-Store-Promotion days -2.498e+06 [-2.311e+07, 2.599e+07] 5.940

LEAF_numstores 755.875 [644.498, 856.937]* 2166.100

Presence of leaflets - 2.510 [-2.707, -2.385]* 83573.149

-0.319 [-3.937, 5.345] 2.08E+09

3.229 [2.170, 3.924]* 2.61E+08

-0.001 [-0.004, 0.004] 22,161

5.848e-07 [- 0.000, 0.000] 11,480 Other digital advertising impressions x

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29

4.3 Summary of results

In the table below we present the findings from all three models and whether they confirm our hypotheses or not. It becomes clear that indeed some effects are different between chains and that managers from different types of chains might draw different conclusions from these results.

4.4 Model Choice

Now that several models have been estimated and discussed we will choose a model that suits best in answering our research questions. For building our descriptive model we developed regression models based on two different estimation methods. Firstly, we estimated a model with Ordinary Least Squares estimation. This method resulted in three individual models for each type of retail channel. As mentioned before, OLS regressions require 6 assumptions to be met. From our tests it appeared that our model met most but not all assumptions. By transforming the data most of the assumptions have been met, except for the normality assumption. Due to technical issues we were not able to accommodate this problem. This problem will be discussed in the detail in the next chapter.

Secondly, we created a model using the Bayesian approach. This type of model is able to incorporate prior data and use this information to create a more reliable model. In our case we did not possess over data from a previous studies that would suit our study. To accommodate for this we estimated two models. Firstly, a Naïve Bayesian model and secondly, to incorporate prior data, we used estimates from our own dataset. As has been discussed before, the model using our own priors came with several severe warnings. We have thus chosen to not incorporate this model in our selection.

Linear Regression Bayesian Regression

Hypothesis Technical superstores Hypermarkets Department stores Non-informative priors Informative priors

H1 Confirmed Confirmed Confirmed Confirmed No evidence

H1a Confirmed No evidence Confirmed Confirmed No evidence

H2 No evidence Confirmed No evidence Confirmed No evidence

H2a No evidence No evidence Reversed Confirmed Reversed

H2b No evidence No evidence No evidence Confirmed No evidence

H3 No evidence No evidence Confirmed No evidence No evidence

H4 Confirmed Confirmed Confirmed No evidence No evidence

H5 No evidence Confirmed Confirmed Confirmed No evidence

H5a Confirmed No evidence No evidence No evidence No evidence

H5b No evidence Confirmed Confirmed No evidence No evidence

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30 Often researchers are able to compare across models by judging the information criteria, like the Akaike Information Criterion (AIC) or the Constant AIC (CAIC). These criteria are very suitable for frequentist approach models. However, in our case, we also have a model that uses the Bayesian approach. It happens to be that for these type of models the AIC and CAIC are not possible to compute. Nevertheless, within the stan_arm package for R there is a possibility to calculate the LOO Information Criterion (LOOIC). This criterion aims to deliver the same interpretation as the AIC but made applicable for Bayesian models. Where the AIC does not take priors into account (being informative or non-informative), the LOOIC does. Even though they are not precisely the same criteria, we are able to compare the models by using these criteria as they both estimate the expect log predicted density. We will take a conservative stance though and also inspect other ways of picking the right model. Below we first present the AIC and LOOIC.

As with normal information criteria comparison we opt to choose the model with the lowest value. In our case this would be the model using the frequentist approach, i.e. the linear regression model. But as mentioned before, we will also look at other ways of assessing model choice. One of which is predictive validity. Even though our model was not built for making extensive predictions we can use its predictive validity to make an educated decision on what model to choose. As there is not one specific standard that measures predictive validity, we present below some of the most commonly used measures. Firstly, the Average Prediction Error (APE) is used to test if the model does not contain a bias in predicting the values. A score of 0, or close to it, is most ideal. That would mean that on average the predicted values are the same as the observed values (Leeflang et al., 2015). In our case the Linear Regression model scores better. Both values are negative, which indicates that the model underpredicts the actual values. We then also looked at the Average Squared Predictor Error (ASPE), which is the same as APE, but squared. Again, the value closest to zero would be most preferred, in our case the frequentist model is preferred.

We also checked if our models perform better than a naïve model. This can be easily determined by observing the Relative Absolute Error (RAE). This measure checks whether the proposed model is better than a naïve model that predicts the current value by the previous value (Leeflang et al., 2015). The model performs better when the RAE is lower than 1. In our case both our proposed models outperform the naïve model, albeit that the linear model significantly outperforms the Bayesian model. Additionally we also calculate Theil’s U. This metric has the same goal as the RAE as it measures whether the model

Information Criterion Linear Regression Bayesian Regression

AIC 170144.2 x

(36)

31 outperforms a naïve model. Same as with RAE this metric needs to be lower than 1. Again, for both our models we have a model that outperforms a naïve version, where our linear model is still the best.

From the foregoing paragraphs we can conclude that our linear model scores best on all criteria for deciding which model we will choose. Hence, why we pick this model as our final choice that is best suited for answering our main research question. We will use this model in delivering our managerial implications in chapter 5.2.

Predictive validity criterion Linear Regression Bayesian Regression

APE -0.1420814 -0.3769994

ASPE 14.4746 16.70181

RASPE 3.804551 4.086785

RAE 0.5913211 0.9240165

Competitor influence on marketing mix effectiveness