WHEN IS IT TOO MUCH?

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WHEN IS IT TOO MUCH?

An examination of repetition effects on sales

Jacobien van Klinken

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When is it too much?

An examination of repetition effects on sales

Master Thesis Marketing Management and Marketing Management 20-06-2016

Author

Jacoba van Klinken (s2023121) Pop Dijkemaweg 72 9731 BG jacobienvanklinken@gmail.com +31627373679 First supervisor Dr. P. S. van Eck p.s.van.eck@rug.nl Second supervisor Dr. A. Minnema a.minnema@rug.nl University of Groningen

Faculty of Economics & Business Department of Marketing

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Summary

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Preface

Before I started the Master Marketing, I finished a bachelor’s degree in Psychology at the University of Groningen. Right from the start I was very interested in social psychology and therefore this became my specialization. I have always been interested in how to motivate, move and reach people, especially on a broader level. That is where Marketing came in, and before I knew it I was participating in this exciting Master thesis program. This is the last step in graduating from the Master Marketing Intelligence and Marketing Management. Almost half a year has passed since the first meeting with my supervisor and colleagues took place, and what an experience has it been. Investigating this topic has been a great opportunity for me to broaden my knowledge on how to optimize a campaign of which I hope to successfully launch someday. It has been exciting, though and educative – sometimes all at once. But now here I am, writing this preface as a final step, and I proudly present you my Master thesis: When is it too much? An examination of repetition effects on sales.

I would like to thank my first supervisor, dr. Peter van Eck, for all his effort and involvement, his input and willingness to share useful feedback, his open attitude and flexibility throughout the entire process. In addition, I am particularly grateful towards GfK for providing the dataset which has made this research possible.

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1. Introduction

Perhaps one of the things consumers value most about streaming services such as Netflix, is that they can (binge) watch whatever they want to, without being interrupted by ad blocks. A show broadcasted on national TV on the other hand, comes with a substantial amount of commercial breaks. In fact, in the Netherlands, television programs on commercial channels are interrupted on average every 20 minutes by an 8-minute block of advertising. That is, “any paid form of non-personal presentation and promotion of ideas, goods, or services by an identified sponsor” (Keller, 2013, p. 221). In addition to the fact that television commercial breaks are longer, the duration of a single advertisement is shorter, resulting in more ad exposures within a commercial break (Rotfeld, 2006). This advertising clutter has emerged in other channels such as radio, magazines and the latest evolved advertising platform, the internet, as well. Advertising spending has reached an amount of 564 million in the Netherlands alone (Nielsen, 2015). As a result, people are exposed to advertising stimuli 360 times a day according to Media Dynamics, INC. (Insights, 2014), which is not always fully appreciated by its audience. More specifically, consumers tend to have a negative attitude towards advertising in general (Ewing, 2013) and may perceive it as irritating (Ha & Mccann, 2008), intrusive (Lee, 2002) or even goal impeding (Cho & Cheon, 2004). In fact, consumers already showed ad avoiding behaviour in the 1980’s (Esslemont & McLeay, 1993). One might state that consumers feel forced to do so even more nowadays because of the ever increasing advertising clutter – to prevent being overwhelmed by advertising messages – which hampers reaching the target market effectively (Bellman, Rossiter, Schweda, & Varan, 2012; Kotler, 2003 as described in Laroche, Cleveland, & Maravelakis, 2006; Rumbo, 2002). In addition, perceived advertising clutter has found to be related to less favourable attitudes towards the ad itself and greater ad avoidance, although the effects differed per media channel (Elliott & Speck, 1998).

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7 Keller, 2003; Jeong et al., 2012; Kirmani, 1990; Miceli, Scopelliti, Raimondo, & Donato, 2014; Reinhard, Schindler, Raabe, Stahlberg, & Messner, 2014; Vakratsas & Ambler, 1999), which means that generally there is an optimal number of exposures of an advertisement. Much attention has been devoted to repetition effects, highlighting different aspects such as: humour used in the ad (Merluzzi & Johnson, 1985), degree of creativity (Lehnert, Till, & Carlson, 2013); comparing repetition effects of high-share versus low-share brands (Laroche et al., 2006), and brand logo’s (Miceli et al., 2014). However, little attention is given to the actual effect of repetition on business performance in terms of sales, for example, can additional exposures to advertising induce a decrease in sales after a certain point? A study which examines actual purchase behaviour is Danaher & Dagger (2013). They link media exposure in several types of channels to purchase intentions as well as actual purchase behaviour. However, their focus is not so much on repetition effects, but on advertising effectiveness in general. Thus, prior research with respect to repetition effects were most often hypothetical of nature. However, appraising advertising effects on sales in absolute terms as important is emphasized (Sethuraman, Tellis, & Briesch, 2011).

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8 This study aims to fill these two gaps. Firstly, this study will aim to fill the research gap between ad repetition effects and actual purchase behaviour. More specifically, the shape of the advertising response functions across channels will be investigated using real-life data of a retailer in The Netherlands, operating in the durables market. Actual sales will herein be the outcome measure. In addition, an explicit comparison of the advertising response functions across different channels will be made. In short, this study will address two questions: 1) what patterns do the advertising response

functions follow? and 2) how do the advertising response functions differ among channels?

This study has two major contributions. Firstly, new insights of relevance for both theoretical and managerial fields are generated, since existing theory is linked to real purchase data. On the one hand, it contributes to theory since it extends current literature and makes it more generalizable to real-life situations as behavioural evaluation is considered in terms of actual sales. On the other hand, consequences of frequency measures are of great relevance for practitioners since they are responsible for setting them. In addition, a clear understanding of the effects of repeated ad exposures might save organizations a lot of (unnecessary) costs. Besides merely overspending the marketing budget, the results might actually backfire. Secondly, this study contributes to the field of research regarding repetition effects, since to my knowledge, the current literature lacks extensive comparisons between different channel types. However, since communication options are ever increasing it is imperative to ‘mix and match’ all available options in order to set up an effective brand building campaign (Keller, 2013). Therefore, this research is based on an ad campaign distributed in the Netherlands across different channels such as folder, internet (banners, masthead), print, radio and TV. This creates an opportunity to investigate and compare repetition effects regarding a single ad across these channels. In other words, the effects of the specific characteristics of these channels on repetition effects with respect to purchase behaviour can be examined.

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2. Theoretical framework

2.1 Repetition effects

Perhaps one of the most used strategies in order to improve advertising performance is ad repetition within a given time interval. One of the reasons might be that ad repetition is associated with advertising effectiveness. First of all, repeated exposure positively influences recognition and recall (Jeong et al., 2012; Keller, 2013). In addition, for the justification of repetition measures usage, repeated exposure is thought to increase likeability towards the exposed object. This is also known as the mere exposure effect (Zajonc, 1968). The theory is a widely accepted and well-established phenomenon, and is still an important topic of research in more recent literature (for example: Hekkert, Thurgood, & Whitfield, 2013; Huang & Hsieh, 2013; Lindgaard, Fernandes, Dudek, & Brown, 2006). The theory entails that repeated exposures to a certain stimulus induces a change in attitude towards that stimulus, triggered by an increase in familiarity with that stimulus (Zajonc, 1968). Furthermore, novelty is associated with more negative states, such as uncertainty or conflict, which in turn increases the likelihood of negative affect. In addition, a recent study has shown that the mere exposure effect holds even without consciously being aware of perceiving the stimulus and that the effect is mainly driven by low-level processing (Huang & Hsieh, 2013), which has relevant implications for subliminal advertising.

Although the effect holds across different types of stimuli, the mere exposure effect might not be as robust as advocated. For instance, a necessary condition for examining the effects of mere exposures is that the subject has had no prior exposure of the novel stimulus, or at least had not yet attached any specific response to it (Zajonc, 1968). Furthermore, in real-life settings, consumers are more often exposed to a bundle of stimuli, rather than one stimuli at the same time. This makes it difficult to determine the specific effects of mere exposure for complex, real-world stimuli (Hekkert et al., 2013), such as an advertising commercial – let alone the entire campaign. For instance, although the advertising might be new, consumers can already have attached a certain response to specific features used in that advertising, such as music, spokes persons or the brand itself.

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10 at first an increase in exposure leads to more favourable evaluations of the ad, but after a certain point additional exposures induce less favourable evaluations – is known as the two-factor theory (Berlyne, 1970; as described in Vakratas & Ambler, 1999). This theory entails that two psychological processes take place when consumers are exposed to repeated messages. The first is wear-in, in which habituation of a novel stimulus takes place, reducing uncertainty and other negative responses towards that stimulus. This in turn results in a more positive attitude. When the number of exposures go beyond a certain point the phenomenon of wear-out takes place. This is induced by tedium, resulting in a more negative attitude towards the message. In other words, boredom influences the linear exposure-affect curve (Bornstein, Kale, & Cornell, 1990). Using internal (“individual differences in boredom proneness”, p. 792) and external (“differences in stimulus complexity and interestingness”, p. 792) variables, they identified boredom as an inhibiting factor of the linear mere exposure effect. In addition, they found that stimulus complexity moderates the effect of boredom on mere exposure – “complex, interesting stimuli produce significantly stronger exposure effects than relatively simple, uninteresting stimuli” (p. 797). Similarly, a higher degree of creativity within an add seem to induce wear-in more quickly and inhibit wear-out (Lehnert et al., 2013).

An additional explanation for the inverted-U advertising-response function is related to the perceived credibility of the source (Campbell & Keller, 2003; Kirmani, 1990; Reinhard et al., 2014). More specifically, Campbell & Keller, (2003, p. 296), showed that participants tend to consider the persuasive, tactual character of the ad, the advertiser’s strategy and its (in)appropriateness more extensively when the number of exposure increased. They further added that the increase is greater for unfamiliar brands than familiar brands. Several studies have confirmed that ad repetition influences source credibility, and that too many exposures lead to a decrease of its credibility (Reinhard et al., 2014) and an increase in negative brand perceptions (Kirmani, 1990). As a result, in terms of persuasiveness, the advertisement might be less effective. In sum, it is evident that more exposure is not always better – in some cases it is even worse, when additional exposures induce negative feelings towards the ad. This can, in turn, flow over to the focal object of the advertisement. More specifically, ad attitudes are found to affect brand attitudes (Homer, 1990) which in turn can influence purchase intentions (Hwang, Yoon, & Park, 2011; Niazi, Ghani, & Aziz, 2012).

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11 too many exposures negatively affect the attitude towards the ad, this can lead to decreased effectiveness compared with low ad exposures. Therefore, it is expected that an increase in exposure to the advertisement leads to an increase in sales initially, but after a certain point an increase in exposure will lead to a decrease in sales. Stated differently, advertising exposure is expected to have as Leeflang, Wieringa, Bijmolt and Pauwels (2015, p. 38) state as “decreasing returns to scale” in every channel. As a result, the following hypotheses are proposed:

H1a: the print advertising response function has an inverted-U shape. H1b: the internet advertising response function has an inverted-U shape. H1c: the radio advertising response function has an inverted-U shape. H1d: the TV advertising response function has an inverted-U shape.

2.2 Type of channels

Different types of media channels obviously have different characteristics. For example, print ads such as a folder or an advertisement in newspapers or magazines are considered self-pacing, meaning that the consumer gets to decide whether or not to look at the ad and at what pace (Ha & Mccann, 2008; Keller, 2013, p. 226). Because of that, print ads can provide detailed information. However, print ads have a static nature and can be a passive medium. Internet advertising is considered to be a combination of both captive and self-pacing, with its dynamic environment that is characterized by interaction and high user control (Ha & Mccann, 2008). As the authors describe: ‘‘audiences become users of a

medium and process advertising messages to fulfil certain goals” (p. 573). Keller (2013, p. 237) states

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12 drawbacks. Since consumers use several media, sometimes even simultaneously, it is particularly interesting to investigate whether these specific characteristics might influence the effects of mere exposure. Again, the focus is on investigating whether repetition effects affect actual sales, rather than explaining mere exposure effects. Hence, in addition to H1, it is questioned whether the channel type in which the ad is presented affects the nonlinear curve, including print, internet, radio and TV.

However, it is rather difficult to come up with specific hypotheses, since current literature lacks extensive comparisons of one specific ad across channels. One might expect that channels that can make use of creative, dynamic, divergent and attention-getting elements within one ad, can postpone wear-out effects. For instance, Lehnert at al. (2013) found that within the domain of TV advertising, ads using more creativity are more liked and negatively influence wear-out effects (i.e. inhibit the wear-out, making the ad effective for a longer time). Bornstein et al. (1990) found a similar effect: stimuli with higher complexity and interestingness enhance positive effects of mere exposure. Since TV and internet have opportunities to implement such elements within the advertisement, including visuals and motion, one might suggest that these channels have a higher optimal number of exposures. In other words, it takes longer before the audience experiences boredom and the advertising response function would be less steep than for channels with a static nature such as print ads. Radio advertisement might then be somewhere in between, since it can make use of creative and interesting elements (such as imagery and sound) more than print ads but less then TV and internet advertising.

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13 in turn compare different channel types with respect to repetition effects. As theories outlined above oppose each other, no directive hypothesis will be formulated. Instead, the outcomes will be explored and discussed at the end of this paper. For now, the following hypothesis is proposed:

H2: the advertising response functions differ per channel.

Taken all proposed hypotheses together, the conceptual model is formalized as outlined in Figure 1 below.

Figure 1: Conceptual Model

3. Method

The dataset that will be used for this research was collected by GfK, a well-known market research institution. The data concerns a retailer in the Netherlands, with an excessive assortment of roughly __ individual articles. Its low pricing strategy and high service has turned in to a successful concept. The retailer is known for its attention-grabbing advertising, which can be characterized as loud, funny and to the point. The ad campaign of consideration was no different; a noisy environment with a lot of motion and changing imagines, implementation of humour, but still informative. This makes the dataset particularly useful for the current analysis - which is building a sales response model for the focal company by means of a regression, as will be elaborated upon in Section 3.2 below.

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14 While investigating the response functions of exposure to advertising on sales, the observations in which a purchase had been made at a competitor will not be taken into account. This decision has two reasons. Firstly, participants who have already bought a durable product, might already be less likely to make a purchase at all. Secondly, participants who buy durables at competitors might have a certain preference for a competitor, reducing the likelihood that the individual will make a purchase at the focal store. These two things might bias the results, since a potential decrease in sales would then not be due to effects incorporated in the model. Therefore, the sales response model will be estimated using only those observations in which a purchase at the focal company has been made (hereafter: purchase) and the observations in which no purchase was made. This means that the dataset is narrowed to 353,330 useful observations. A disadvantage is that this approach makes the dataset less representative for inhabitants of the Netherlands, since a substantial part of the Dutch market for these durables is not considered. As a consequence, the results should be interpreted with care with respect to generalizability. On the other hand, it might reveal the effects of the advertising campaign of the focal company on its sales better, which fits the purpose of this research.

3.1 Data description

First of all, the dataset contains information about certain demographics. The overall average age of the dataset is ___. In the group of individuals who made a purchase the average age was ___ and those who did not purchase something at the focal company in the observational period had an average age of ___. In addition to age, the level of education was also measured. Thirteen different education forms are recorded, ranging from primary school to university degree (PhD). These were further divided into three categories: low, medium and high education. Lastly, the height of income of 82.8% of the subjects (17.2% decided not to reveal their income level) was explored which was measured in net monthly income. It was measured by means of an ordinal scale containing 20 different categories, starting with the category < €700. Every following category increased €200, making the second category €700-€900, the third €900-€1,100, and so forth. The scale continued up to the category of >€4,100. For comprehensiveness the results are combined in five categories (i.e. low: < €1,100; moderately low: €1,100-€1,900; moderate: €1,900-€2,700; moderately high: €2,700-€3,500; and high: > €3,500).

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15 these outliers were not exposed to any advertisement at all. However, it is reasonable to assume these do not stem from procedural errors, and hence it is decided not to adjust or exclude these observations, since they can contain valuable information with respect how the variable actually reacts. In addition, a logical inconsistency is found with respect to sales. Of all purchases that were made thirteen observations had a value of zero for sales. To adjust for this, the value is replaced by the weekly average of sales. In order to detect any seasonal influences sales are investigated over time. To get to a comprehensive overview, the weeks are aggregated into months. Sales peaks in terms of absolute value are detected in January, March and the highest one is in June. Although the total revenue increases substantially in the latter, the average price per purchase declines (see Figure 2). This can be due to tax refunds or holiday bonuses, that are usually distributed around this time of the year in The Netherlands.

Figure 2a: Total revenue in cents per month 2b: Average price per purchase in cents per month

Lastly, the dataset contains information regarding advertisement exposure. More specifically, contact chances with the ad per traditional media channel – that is folder, print, radio, TV; and actual contact with internet advertising – banner and mastheads are measured. This is done by two means. Firstly, exposure to traditional media channels (i.e. folder, print, radio and TV) are measured by means of the ‘Reach, Recency, Frequency method’. Subjects had to fill in a questionnaire regarding what they read, listen to or watch. In addition, they were asked how long ago it was that they were exposed to this material (for example, which TV channel, which magazines or newspaper, which radio program, et cetera) the last time and how often they consume this media usually. Based on this information contact chances are derived, also known as the “opportunity to see” or OTS measurement. Although it might be less accurate than actual exposures, it functions properly as a proxy for ad exposures.

Dec '10 Jan '11 Feb '11 Mar '11 Apr '11 May '11 Jun '11

Sales

Dec '10 Jan '11 Feb '11 Mar '11

Apr '11 May '11

Jun '11

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16 Therefore, these contact chances are interpreted as the frequency of actual exposures. Chances normally have the characteristic to not go beyond the interval of values between 0 and 1. However, in this case the contact chances of one week are added up and the sum of these can be higher than 1. For example, the print advertisement was distributed within several newspapers and journals. If a customer would read more than one of these, the separate chances are still between 0-1, but added up they can exceed the value of 1. It should be noted, that a folder was distributed once a week. Hence, the contact chance of the variable folder will not exceed the value of 1. Secondly, exposure to internet advertisement was done by means of passive measurement. That is, internet behaviour was tracked by using cookies (Consumentenbond, n.d.). A cookie is a small text file which is stored on the hard drive of the user’s computer, the moment a certain web page is visited and contains information regarding internet behaviour. This makes it possible to see which websites are visited by the subjects and therefore which advertisements they have been exposed to. Thus, without using questionnaires the actual contacts with the internet advertisements are determined with accuracy. Taken altogether, this makes the dataset particularly useful since it links individual-level ad exposure across several media channels with the purchase behaviour of these same individuals. In other words, repetition effects on sales can be investigated per channel at an individual level. In order to detect any effect, the variables should contain some variation, which is examined next (see Figure 3).

Figure 3: Boxplots per channel

As can be seen, variation is for all variables relatively low, indicated by the small surfaces (Q1-Q3) within the boxplots. However, variation within the variables does differ across channels. Variation is greatest within TV (σ2 =__), followed by print (σ2 =__) and radio (σ2 =__). Folder has a variance of

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17 value of folder cannot exceed one, which explains the lower variance. Variation is particularly low in the internet variables: for banner, σ2=__ and for masthead, σ2=__. This might form difficulties to examine the effect of internet advertising exposure on sales. In addition, for every channel except folder there are quite some outliers detected. Assuming that these do not stem from procedural errors, the observations are kept in the analysis in order to maintain the variation within these variables.

To check for potential seasonalities, Figure 4 on the next page shows an overview of the mean exposures across channels over time. The average number of exposures fluctuate over time. Overall, the exposure to an ad of the focal company is highest for TV (𝑥̅ =__), followed by print (𝑥̅ =__). Both show a steep decrease in February, whereas radio has its highest peak there. Exposures to radio advertisements are particularly low in December, but relatively stable across the other months. The overall mean is __, which is a relatively low compared to the other traditional media channels, TV and print. Exposure is lowest for internet advertisements; both the average values of masthead and banner does not exceed the value of __. As well as for the internet variables, the exposures to folder is remarkably stable (𝑥̅ =__), which might be due to the fact that a folder was only distributed once a week, whereas opportunities to see or hear the other channels can differ. Noteworthy is that the patterns in Figure 4 show an opposite evolvement than the pattern of sales over time (Figure 2a). More specifically, whereas sales show a substantial increase in the month June, exposures to advertisement decrease heavily. In fact, for every observation the contact chances of any channel has the value of zero, except for the channel folder, which continues to have an average value of __ in June. This might not be what one would expect, but it might be that the campaign has actually ended at the end of May – with the exception of folder – but due to lagged effects the sales might have increased.

Figure 4: Average contact chances over time

December January February March April May June

Average number of exposure

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3.2 Model development

To investigate the effects of exposure on sales, a sales response model will be built by means of a regression. Sales can be measured either in absolute terms (i.e. euro’s spent) or purchase chances. Here, the outcome measure will be addressed in terms of value (i.e. the total expenditures in the observation period). In order to validate the model after estimation a hold-out sample will be created. A random variable will divide the dataset in such a way that 10,1% of the remaining observations will not be taken into the estimation process. This 10%-sample will be used for quantifying the predictive validity of the estimated model, leaving 317,778 observations for the estimation process.

Examining whether the relationship between sales and advertising exposure has an inverted-U shape (H1), the sales response model will be analysed. This response model will be expressed in two functional forms. Sales will first be expressed in a linear additive form and secondly, as an additional analysis, the model will be computed using a multiplicative functional form. Computing the same model in different functional forms creates opportunities of gaining extra insights and to get a great overview of the data and the response function. In order to investigate whether the response curve will change when the customer is exposed to the ad in a different channel (H2), the effect of each channel needs to be examined separately. The parameters corresponding with exposure in the different channels will therefore be compared with each other and tested for significance, using a z-test (also used in the dissertation of Hans Risselada, 2012, p. 54) with the following formula:

Z=

𝛽𝑖−𝛽𝑗

√ 𝑆𝐸𝛽_𝑖2+𝑆𝐸𝛽_𝑗2−2𝐶𝑜𝑣 (𝛽_𝑖,𝛽_𝑗)

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19 (banner and masthead) do not differ too much in nature and can be integrated into one variable as well which is named internet. Hence, these four variables are combined into two new ones, also with an eye on the relatively low variation within these variables (Figure 3). The new correlations are shown in Table 1. The correlation between TV and the new print variable is relatively high compared to the rest, which should be taken into account during the analysis. If it does not disturb the results, then it can be assumed that exposures across channels are independent, regarding that all other independent variables do not correlate strongly. In the following sections it will be described how the sales response model will be obtained. Firstly, the linear additive model will be discussed followed by the multiplicative form.

Folder Banner Masthead Print Radio TV Printnew Internet

Folder 1 Banner .001 1 Masthead .006** .006** 1 Print .102** .009** .019** 1 Radio .053** -.001 .004* .013** 1 TV .104** .008* .053** .228** .029** 1 Printnew .020** .237** 1 Internet -.001 .008* .009** 1

** Correlation is significant at the .01 level (2-tailed) * Correlation is significant at the .05 level (2-tailed) Table 1: Correlation matrix

3.2.1 Linear additive model

In the linear additive model, the absolute change in sales is proportional to the absolute changes in the independent variables, all added together (i.e. the βi’s). The linear additive form has the advantage that

it is the simplest functional form that enables to investigate a relationship, such as between sales and advertising exposure. On the other hand, this also means that interaction effects between the independent variables are assumed not to be present. The regression will be estimated by means of Ordinary Least Squares (OLS) and can be used for (dis)confirming the proposed hypotheses. This entails that a regression line will be generated in such a way that it minimizes the sum of the squares of the vertical distances, i.e. the residuals, of the observed sales values from the predicted sales values (Moore, McCabe & Craig, 2009a, p. 610). More specifically:

𝜀_𝑡 = 𝑆𝑎𝑙𝑒𝑠_{𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑟𝑑}− 𝑆𝑎𝑙𝑒𝑠_{𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑}= 𝜀_𝑡= 𝑆𝑎𝑙𝑒𝑠_𝑜𝑏𝑠 − (𝛽₀− 𝛽₁𝑋₁− ⋯ − 𝛽_𝑖𝑋_𝑖).

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20 ∑ 𝑆𝑎𝑙𝑒𝑠_𝑜𝑏𝑠 − (𝛽₀− 𝛽₁𝑋₁− ⋯ − 𝛽_𝑖𝑋_𝑖)2 𝑇 𝑡=1 = ∑(𝜀_𝑡)2 𝑇 𝑡=1

Since sales is, in this paper, expressed as a function of advertising exposure, exposures per channel (print, internet, radio and TV) serve as independent variables to the model. In order to investigate whether there is an optimal number of exposures, the quadratic effects of each of these channels will be added into the model, resulting in four additional parameters to estimate:

𝑆𝑡= 𝛽0+ 𝛽1𝑃𝑡+ 𝛽2𝑃𝑡2+ 𝛽3𝐼𝑡+ 𝛽4𝐼𝑡2 + 𝛽5𝑅𝑡+ 𝛽6𝑅𝑡2+ 𝛽7𝑇𝑉𝑡+ 𝛽8𝑇𝑉𝑡2

Although the model is not linear in its variables after the inclusion of the quadratic terms, the model is linear in its parameters. Hence, it is considered to be a linear additive model.

In addition, marketing and its effects, are dynamic in essence (Leeflang et al., 2015, p. 50) and that should be accounted in the model. In this case it means that the advertising campaign is most likely not solely effective in period t (i.e. at the moment of exposure), but its effect may endure throughout future periods. For instance, Macé & Neslin (2004) estimated 39,441 pre- and post-promotion dip elasticities, providing substantial evidence for dynamic advertising effects. This will be incorporated by means of a “stock” variable, which contains the dynamic effects of advertising. The procedure on how this variable is derived is described in detail in Appendix 1. It should be noted that while creating this lagged variable, missing values come into existence. More specifically, since the dataset contains time series data, every first observation of a household becomes useless since it is impossible to generate a lagged value for this observation. Therefore, these observations are excluded from further analysis, inducing a loss in degrees of freedom. Fortunately, the dataset contains enough observations so that 0this is not problematic. The partial adjustment linear additive model then is:

𝑆_𝑡 = 𝛽₀+ 𝛽₁𝑃_𝑡+ 𝛽₂𝑃_𝑡2_{+ 𝛽}

3𝐼𝑡+ 𝛽4𝐼𝑡2+ 𝛽5𝑅𝑡+ 𝛽6𝑅𝑡2+ 𝛽7𝑇𝑉𝑡+ 𝛽8𝑇𝑉𝑡2+ 𝜆𝑆𝑡−1

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21 continuous variable in the model. Secondly, the level of education of the subject might also influence the way messages are processed, because a higher educated person might have developed different cognitive structures than a lower educated individual, resulting in higher cognitive performances (Le Carret et al., 2003). In addition, higher educated people in general have a higher perceptual processing speed than lower educated people (Wilms & Nielsen, 2014). Taking that together, the level of education might influence the way advertisements are perceived. Education will be added as a dummy variable in the model, with three levels as described earlier (i.e. low, medium, high, where the first functions as the reference level). Hence, two dummy variables will be created and added to the model. In addition, the net income per month determines the purchasing power of the customer, which needs to be accounted for. Although the variable income is measured in categories, it will be added as a continuous variable to the model, since there are sufficient categories (i.e. 20) to treat it as continuous. Taken all together, the end model is obtained as:

𝑆_𝑡 = 𝛽₀+ 𝛽₁𝑃_𝑡+ 𝛽₂𝑃_𝑡2+ 𝛽₃𝐼_𝑡+ 𝛽₄𝐼_𝑡2+ 𝛽₅𝑅_𝑡+ 𝛽₆𝑅_𝑡2+ 𝛽₇𝑇𝑉_𝑡+ 𝛽₈𝑇𝑉_𝑡2+ 𝜆𝑆_𝑡−1+ 𝛽₉𝐴_𝑖 + 𝛽₁₀𝐸𝐻_𝑖+ 𝛽₁₁𝐸𝑀_𝑖 + 𝛽₁₂𝐼𝑛_𝑖 +ℰ𝑡,

where St = sales at time t; β0 = constant;

βi = corresponding parameters;

Pt = exposure to print ad at time t;

It = exposure to internet ad at time t;

Rt = exposure to radio ad at time t;

TVt = exposure to TV ad at time t;

X2 = quadratic term of the above variables; λ = retention rate;

St-1 = lagged sales;

Ai = age of customer i;

EHi = dummy variable indicating high level of education of customer i;

EMi = dummy variable indicating medium of education of customer i;

(low level of education serves as reference level) Ini = income of customer i;

ℰ𝑡 = error term.

3.2.2 Multiplicative model

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22 priority, this creates the opportunity to account for potential synergy effects, which can play an important role in determining the relationship, and hence, should be taken into account. Another advantage is that the coefficients can be interpreted as elasticities. Say that sales can be expressed in the formula below:

𝑆_𝑡= 𝛽₀𝑃_𝑡𝛽1_𝛽

2 𝐷𝑡_𝜀

𝑡,

where an elasticity is written as: ƞ

=

𝜕𝑆𝑡 𝜕𝑃_𝑡

×

𝑃_𝑡 𝑆_𝑡

,

then: ƞ = (𝛽0𝛽1𝑃𝑡 𝛽1−1_𝛽 2 𝐷𝑡_𝜀 𝑡)× 𝑃𝑡 𝛽₀𝑃_𝑡𝛽1𝛽₂𝐷𝑡𝜀_𝑡

=

𝛽0𝛽1𝑃𝑡𝛽1𝛽2𝐷𝑡𝜀𝑡 𝛽₀𝑃_𝑡𝛽1𝛽₂𝐷𝑡𝜀_𝑡

=

β

1

.

In addition, a multiplicative model is considered to be nonlinear in nature, but it can be linearized by taking the natural logarithm (i.e. log-log model). The channel variables with respect to exposures serve here as the independent variables. To avoid that the whole equation would become zero and hence St – which is possible since contact chances can take on values of zero – a value of one

will be added to every variable containing contact chances. The same holds for the dummy variables of education, these cannot simply be added as a continuous variable to a multiplicative model. Adding a dummy variable as such (i.e. the variable in the base number and the regression coefficient in the exponent) can result in the whole equation being zero, since dummy’s take on values of zero or one. Therefore, these dummy variables need to be ‘flipped around’, meaning that the variable is in the exponent and the regression coefficient in the base number. Since the models merely differ in functional form (i.e. the same variables will be taken into the model), the evolution of the multiplicative model will not be discussed in further detail. Important to note here is that, St should be added with a

value of one for the same reason described above. Using the same structure, but different assumptions, the partial adjustment model results in the following multiplicative model:

𝑆_𝑡= 𝛽₀⦗∏ 𝑃_𝑡𝛽1_𝑃 𝑡 2𝛽2_𝐼 𝑡 𝛽3_𝐼 𝑡 2𝛽4_𝑅 𝑡 𝛽5_𝑅 𝑡2𝛽6 𝑇𝑉𝑡 𝛽7_𝑇𝑉 𝑡 2𝛽8_S t−1 λ _⦘𝐴 𝑖 𝛽9_𝛽 10𝐸𝐻𝑖𝛽11 𝐸𝑀𝑖_𝐼𝑛 𝑖 𝛽12 ℰ𝑡 𝐼 𝑖=1

As mentioned before, the model is nonlinear in parameters and hence, needs to be linearized. This can be done by taking the logarithm, which results in the following:

ln𝑆𝑡 = ln𝛽0+ 𝛽1ln𝑃𝑡+ 𝛽2ln𝑃𝑡2+ 𝛽3ln𝐼𝑡+ 𝛽4ln𝐼𝑡2 + 𝛽5ln𝑅𝑡+ 𝛽6ln𝑅𝑡2+ 𝛽7ln𝑇𝑉𝑡+ 𝛽8ln𝑇𝑉𝑡2

+ 𝜆ln𝑆_𝑡−1+ 𝛽₉ln𝐴_𝑖 + 𝐸𝐻_𝑖ln𝛽₁₀+ 𝐸𝑀_𝑖ln𝛽₁₁+ 𝛽₁₂ln𝐼𝑛_𝑖 + lnℰ𝑡

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23

4. Results

In order to investigate whether there is an inverted-U shape in the relation between sales and advertising exposure (H1), and whether the relationship shape differs per channel (H2); two regression analyses are done. However, in order to estimate the parameters with OLS, several assumptions are made concerning different elements of the model (Leeflang et al., 2015, p. 122). Four of these are assumptions regarding the residuals, and there is one additional assumption with respect to the independent variables. Before going into further details regarding the results, tests will be done whether these assumptions are satisfying, which is discussed in the following sections. Again, the linear additive model will firstly be checked, followed by the multiplicative model. The final results of both models are presented in Section 4.3 and 4.4. The overall conclusions with respect to the hypotheses can be found in Table 4 at the end of this section.

4.1 Assumptions linear additive model

To test the assumptions, residuals are necessary. Therefore, an initial regression analysis was conducted on the end model presented in Section 3.2.1. The R2 amounts to .000. The overall model, however, is significant (F=6.733, p=.000) and most of the relevant variables seem to have significant effects on sales (see Table 2, page 28).

4.1.1 Nonzero expectation

The first assumption is regarding to the unbiasedness of the estimated parameters, of which violation is the most serious one according to Leeflang et al. (2015, p. 124). Unbiasedness is only possible when the model is correctly specified with respect to completeness, meaning that all relevant predictors are taken into the model (and irrelevant ones are excluded) and an appropriate functional form is implemented. Unbiasedness plays an important role in whether (omitted) predictor variables correlate with each other, both positively and negatively. In short, this assumption is expressed as:

𝐸(𝜀_𝑡) = 0,

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24 𝑆_𝑡 = 𝛽₀+ 𝛽₁𝑃_𝑡+ 𝛽₂𝑃_𝑡2_{+ 𝛽}

3𝐼𝑡+ 𝛽4𝐼𝑡2+ 𝛽5𝑅𝑡+ 𝛽6𝑅𝑡2+ 𝛽7𝑇𝑉𝑡+ 𝛽8𝑇𝑉𝑡2+ 𝜆𝑆𝑡−1+ 𝛽9𝐴𝑖

+ 𝛽₁₀𝐸𝐻_𝑖+ 𝛽₁₁𝐸𝑀_𝑖 + 𝛽₁₂𝐼𝑛_𝑖 + 𝛽₁₃Ŝ2_{+ 𝛽}

14Ŝ3+ℰ𝑡,

where Ŝ2 _{and Ŝ}3_{= predicted sales to the power of 2 and 3. The test showed the regression that the}

coefficient for Ŝ2 is significant (β=-.001, p=.038) but not for Ŝ3 (β=.000, p=.215). Hence, it can already be concluded that the first assumption is not violated. To formally test whether the R2 of this new model, or unrestricted model, significantly differs from the old model, or restricted model, an F-test can be conducted based on the incremental R2. However, in this case the R2 of both models amounts to zero, confirming that the extended model does not significantly differ, and hence, the assumption of nonzero expectation is not violated.

4.1.2 Non-correlated disturbances

The second assumption concerning residuals only plays a role in time-series data, which is the case here. The assumption is that covariances between residuals at different points in time is zero and is formulated as:

𝐶𝑜𝑣(𝜀_𝑡, 𝜀_𝑡′_{) = 0,} _{𝑡 ≠ 𝑡,}

If the assumption is violated, one can speak of autocorrelation which implies that the residuals are related to the residuals of the previous period. In other words, the value of a residual can to a certain extent ‘predict’ the value of the next residual, which similarly as violation of the second assumption, lowers the efficiency of the OLS-estimation (Leeflang et al., 2015, p. 129). This would imply that there is a pattern present in the disturbance terms, while there should be no pattern present in the residuals. In fact, no information should be captured within the residuals, but all of it should be explained by the predictors. Stated differently, if there is autocorrelation, then some or even all covariances between residuals at different points in time will be higher than zero. If the residuals are autocorrelated, then the disturbance term is:

𝑢_𝑡 = 𝜌𝑢_𝑡−1+ 𝜀_𝑡, ⎸𝜌⎹ < 1, where ut = disturbance term;

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25 On the right a visual representation is

provided, in which the residuals are plotted against time (Figure 5). At first sight, it looks to some extent that negative autocorrelation might exist here: the observations tend to have positive value, followed by negative ones, and vice versa. The correlation coefficient between the residuals and the lagged residuals was generated to further examine potential autocorrelation. The

correlation was found to be non-significant (r=-.003, p=.086). To formally test whether residuals are autocorrelated, the Durbin-Watson (1950, 1951, as described in Leeflang et al., 2015, 130) was computed, which is the most well-known test statistic to detect (first-order) autocorrelation. The Durbin-Watson test statistic is based on the variance of the difference between two successive error terms, which leads to the following formula:

𝐷𝑊 =∑ (𝜀𝑡− 𝜀𝑡−1) 2 𝑇 𝑡=2 ∑𝑇 𝜀_𝑡2 𝑡=1 , 0 ≤ 𝐷𝑊 ≤ 4

The Durbin-Watson test revealed a value of 2.004, where the ideal value of the Durbin-Watson is 2, which would mean that the residuals are not autocorrelated. To significantly test this value, there are lower and upper bounds formulated at various significance levels (dL and dU). This can be graphically

shown as follows:

Figure 6: D.W. Table

The inconclusive regions are indicated by the question mark above it, which are between dL and dU;

4-dU and 4-dL. If negative autocorrelation would indeed be the case here, the Durban-Watson value

should therefore lie between 4-dL and 4. The upper and lower bounds are derived from the

Durbin-Watson table (“Critical Values for the Durbin-Durbin-Watson Test: 5% Significance Level,” n.d.), for T=2000 (number of observations; which is the maximum in the table) and K=14 (the number of parameters, including the intercept). The corresponding values are: dL=1.913 and dU=1.940; and 4-dU=2.06 and

4-dL=2.087. The Durban-Watson value (2.004) lies between dU and 4-dU, meaning that there is no

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26 autocorrelation present within the residuals. Hence, it is safe to conclude that the second assumption is not violated.

4.1.3 Homoscedasticity

The third assumption regarding the error term is that the residuals are homoscedastic, which entails they assumed to have the same variance across every observation, both cross-sectional and across time:

𝑉𝑎𝑟(𝜀_𝑡) = 𝜎2_.

If the residuals are found to be heteroscedastic (i.e. if the assumption is violated), the estimator of the regression coefficients remain unbiased (Hayes & Cai, 2007). However, the variances of the parameter estimates can be biased, which consequently can result in significance tests being liberal or conservative. Stated differently, the OLS parameters would be reduced in efficiency (Leeflang et al., 2015, p. 126). Heteroscedasticity seem to occur mainly in cross-sectional data. Although the current dataset is time serial in nature, it is more or less approached as a cross-sectional data. Therefore, there should be tested for potential heteroscedasticity. To formally test this, the Breusch-Pagan test for heteroscedasticity is conducted (Breusch & Pagan 1979, as described in Leeflang et al., 2015, p. 128). In this test, the squared residuals are regressed as a function of all the independent variables in the model. Hence:

𝜀_𝑡2 = 𝛿₀+ 𝛿₁𝑃_𝑡+ 𝛿₂𝑃_𝑡2 + 𝛿₃𝐼_𝑡+ 𝛿₄𝐼_𝑡2+ 𝛿₅𝑅_𝑡+ 𝛿₆𝑅_𝑡2+ 𝛿₇𝑇𝑉_𝑡+ 𝛿₈𝑇𝑉_𝑡2+ 𝛿𝑆_𝑡−1+ 𝛿₉𝐴_𝑖 + 𝛿10𝐸𝐻𝑖+ 𝛿11𝐸𝑀𝑖 + 𝛿12𝐼𝑛𝑖 + 𝑢𝑡,

and the null hypothesis (the error term is homoscedastic, i.e.: H0: 𝛿1 = 𝛿2 = … = 𝛿12 = 0) is tested with

the formula below:

F = 𝑅 𝜀𝑡2 2 _{/ 𝐾} (1−𝑅 𝜀𝑡2 2 _{)/ (𝑇−𝐾−1)}

,

where K is the number of estimated parameters and T is the number of observations. Running the regression showed a non-significant F-value (F=1.034, p=.415). Hence, it can be concluded that the third assumption regarding homoscedasticity is not violated.

4.1.4 Normality

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27 are based on the normal distribution. Hence, the fourth assumption is that the residuals are normally distributed. The Kolmogorov-Smirnov test, which is a well-known statistical test for testing normality, amounts to .497 with a p-value of .000. Hence, it can be concluded that the fourth assumption is violated. Therefore, the estimated p-values regarding the estimated parameters cannot be trusted. One explanation might be that there are outliers present within the residuals. In an attempt to tackle this, a dummy variable for the seven most extreme outliers is generated. These dummies indicate the case number of the corresponding extreme value, which consequently sets the residual equal to zero. In other words, the dummy variables correct the outliers within the residuals in the linear regression analysis, which leaded to the following model (the subscriptions are the corresponding case numbers):

𝑆_𝑡 = 𝛽₀+ 𝛽₁𝑃_𝑡+ 𝛽₂𝑃_𝑡2+ 𝛽₃𝐼_𝑡+ 𝛽₄𝐼_𝑡2+ 𝛽₅𝑅_𝑡+ 𝛽₆𝑅_𝑡2+ 𝛽₇𝑇𝑉_𝑡+ 𝛽₈𝑇𝑉_𝑡2+ 𝜆𝑆_𝑡−1+ 𝛽₉𝐴_𝑖 + 𝛽₁₀𝐸𝐻_𝑖 + 𝛽₁₁𝐸𝑀_𝑖 + 𝛽₁₂𝐼𝑛_𝑖 + 𝛽₆₀₁₄₆+ 𝛽₃₄₄₉₄₂+ 𝛽₃₄₃₆₅₃+ 𝛽₃₀₈₈₄₈+ 𝛽₆₁₃₅₅ + 𝛽₃₀₆₉₀₉+ 𝛽₆₈₉₀₂+ ℰ𝑡,

As a first, it increased the adjusted R2 substantially: initially R2adj was .000, whereas after the inclusion

of the indicator dummies R2adj amounts to .305. Furthermore, the F-value amounts to 6733.389

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28 Bootstrap*

95% confidence interval

Model β Std. Error Sig. Sig. Lower upper

Constant 183.783 41.400 .000 .072 -191.108 282.163 Print .681 6.348 .915 .932 -10.896 12.162 Print2 _-.046 _.472 _.922 _.918 _-1.042 _.996 Internet 63.308 26.402 .016 .342 -7.131 434.924 Internet2 _-.259 _.119 _.030 _.374 _-6.689 _.042 Radio 29.267 9.266 .002 .308 5.408 60.169 Radio2 -1.486 .529 .005 .036 -3.058 -.284 TV -7.370 3.689 .046 .037 -15.293 -1.231 TV2 .325 .190 .087 .180 -.053 .947 Lagged Sales .008 .002 .000 .056 .002 .018 Age -2.725 .466 .000 .001 -3.638 -1.910 Educationmedium 4.600 16.106 .775 .753 -26.023 35.271 Educationhigh 13.249 16.059 .409 .375 -15.123 41.769 Income .167 .187 .373 .361 -.161 .572 *Based on 1000 samples

Table 2: Results regression linear model

4.1.5 Linearly independent predictor variables

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29 𝑉𝐼𝐹_𝑖 = 1

1 − 𝑅_𝑖2,

There are some alarmingly high VIF-values. These concern, however, only the advertising exposure variables and their quadratic effects (for print and print2 VIF>9, for internet and internet2 VIF>5, for radio and radio2 VIF>7, for TV and TV2 VIF<5). For all the other independent variables in the model the VIF varies between 1.000 and 1.504, which is an acceptable value. In essence, VIF’s of an independent variable are based on the relation of that variable with all other explanatory variables in the analysis. To detect which relations among the independent variables cause multicollinearity, a correlation matrix is computed. There are no large (>.6) correlations detected between any of the predictor variables, except for the correlations between the linear effects and the quadratic effect of the advertising variables (r(print,print2)=.942 r(internet,internet2)=.911 r(radio,radio2)=.933,

r(TV,TV2)=.878; p<.01). This means that the high VIF-values are caused by these correlations. It makes sense that these variables correlate, since every X2-term is a transformation of the original

variable. However, they are not linearly dependent on each other since the transformation is not a linear, but a quadratic one of the original variable. Therefore, in this case these high values can be neglected and it is safe to assume that assumption of linearly independent predictors is not violated, although the VIF-values are beyond the criterion of 5.

In sum, one of the five assumptions regarding linear regression is violated. This concerns the normality assumption, which means that the residuals do not follow a normal distribution. The estimates themselves are not affected by this violation, but the estimated p-values might not be as trustworthy as desired – which is to some extend supported by the Bootstrap analysis. Hence, the model proposed in Section 4.1.5 which is used to analyse both the proposed hypotheses, must be interpreted with appropriate cautiousness. Its results are presented in Section 4.3 and Section 4.4. Next, the multiplicative model is examined with respect to its appropriateness. Since this model is linearized by taking the logarithm and therefore estimated using OLS, the same assumptions as discussed throughout Section 4.1.1 – 4.1.5 hold for the multiplicative model. These will be examined firstly before analysing the results. As these assumptions are extensively discussed in the previous sections, the next section will address them briefly to see whether it makes sense to use the multiplicative model as a supportive analysis.

4.2 Assumptions multiplicative model

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30 ln𝑆_𝑡 = ln𝛽₀+ 𝛽₁ln𝑃_𝑡+ 𝛽₂ln𝑃_𝑡2_{+ 𝛽}

3ln𝐼𝑡+ 𝛽4ln𝐼𝑡2 + 𝛽5ln𝑅𝑡+ 𝛽6ln𝑅𝑡2+ 𝛽7ln𝑇𝑉𝑡+ 𝛽8ln𝑇𝑉𝑡2

+ 𝜆ln𝑆_𝑡−1+ 𝛽₉ln𝐴_𝑖 + 𝐸𝐻_𝑖ln𝛽₁₀+ 𝐸𝑀_𝑖ln𝛽₁₁+ 𝛽₁₂ln𝐼𝑛_𝑖 + lnℰ_𝑡

This model is used to test the assumptions that concur with OLS regression. The initial analysis of the multiplicative model showed the following results. The R2 amounts to .001, and the overall model is significant (F=17.829, p=.000). Table 3 on page 35 gives an overview of the estimated parameters and their initial significance. At first sight, print, internet, radio and TV seem to affect sales. However, to be able to interpret these results (i.e. whether OLS is the appropriate method to do investigate this data with this model), assumptions must be tested for violation. As mentioned before, the assumptions are: 1. E(εt) = 0 for all t; 2. Cov(εt, εt’) = 0 for t ≠ t’; 3. Var(εt) = σ2 for al t; 4. εt is normally distributed and

5. the vectors in independent variables are linearly independent, which are discussed next.

4.2.1 Nonzero expectation

To test the first assumption, the model is again extended with the predicted values of sales to the powers 2 and 3 (Ŝ2 and Ŝ3) in order to conduct Ramsey’s RESET-test. After linearization, this resulted in the following model:

ln𝑆𝑡 = ln𝛽0+ 𝛽1ln𝑃𝑡+ 𝛽2ln𝑃𝑡2+ 𝛽3ln𝐼𝑡+ 𝛽4ln𝐼𝑡2 + 𝛽5ln𝑅𝑡+ 𝛽6ln𝑅𝑡2+ 𝛽7ln𝑇𝑉𝑡+ 𝛽8ln𝑇𝑉𝑡2

+ 𝜆ln𝑆_𝑡−1+ 𝛽₉ln𝐴_𝑖 + 𝐸𝐻_𝑖ln𝛽₁₀+ 𝐸𝑀_𝑖ln𝛽₁₁+ 𝛽₁₂ln𝐼𝑛_𝑖 + 𝛽₁₃lnŜ2_{+ β} 14𝑙𝑛Ŝ3

+ lnℰ_𝑡

Whereas the corresponding estimated parameter for Ŝ2 was significant (β13=-3.172, p=.022), the

parameter for Ŝ3 was not (β14=1.095, p=.208). Since the R2 for this model is exactly .001 as well, there

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31

4.2.2 Non-correlated disturbances

Regarding the second assumption, the residuals are plotted against time (months) and can be seen in Figure 7. The figure shows a similar pattern as Figure 5, which slightly looked like an indication of negative autocorrelation. To examine this, a correlation coefficient between the residuals and the lagged residuals was computed. Although the correlation was relatively small, it was significant (r=.007, p=.000). To formally test whether autocorrelation is present, the Durban-Watson was computed, using the formula described

in Section 4.1.2. The estimated test statistic was 1.984 and the corresponding lower (dL) and upper

(dU) bounds were, (at a significance

level of 5%, T=2000 and K=14, the same as for the linear model), dL=1.913

and dU=1.940; and and 4-dU=2.06 and

4-dL=2.087. Hence, there is no

autocorrelation present in the data. In sum, it can be said that: Cov(εt, εt’) = 0

for t ≠ t’ and the assumption is not violated.

4.2.3 Homoscedasticity

Thirdly, with respect to the assumption of homoscedasticity, the Breusch-Pagan test for heteroscedasticity was conducted, which lead to the following model:

𝑙𝑛𝜀𝑡2 = 𝑙𝑛𝛿0+ 𝑙𝑛𝛿1𝑃𝑡+ 𝑙𝑛𝛿2𝑃𝑡2+ 𝑙𝑛𝛿3𝐼𝑡+ 𝑙𝑛𝛿4𝐼𝑡2+ 𝑙𝑛𝛿5𝑅𝑡+ 𝑙𝑛𝛿6𝑅𝑡2+ 𝑙𝑛𝛿7𝑇𝑉𝑡+ 𝑙𝑛𝛿8𝑇𝑉𝑡2

+ 𝑙𝑛𝛿𝑆_𝑡−1+ 𝑙𝑛𝛿₉𝐴_𝑖+ 𝐸𝐻_𝑖𝑙𝑛𝛿₁₀+ 𝐸𝑀_𝑖𝑙𝑛𝛿₁₁+ 𝑙𝑛𝛿₁₂𝐼𝑛_𝑖+ 𝑢_𝑡.

Running the regression showed a significant F-value (F=17.670, p=.000), and most predictor variables showed a strong significant effect in explaining the squared residuals. More specifically, for the variables lnprint, lnprint2, lnSt-1 and age a p-value of .000 was found. Furthermore, lninternet (p=.004),

lnradio (p=.010), lnTV (p=.004), lnTV2 (p=.026), and lnincome (p=.002) seemed to have a significant effect. No significant effect was found for lninternet2 (p=.168), lnradio2 (p=.066), and both the education dummies EM (p=.590) and EH (p=.682). This implies that the assumption of homoscedasticity is violated and therefore not all disturbance terms have equal variances. Consequently, parameters estimates as given in Table 3 may be inefficient, meaning that the variances

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32 of effects are biased (Leeflang et al., 2015, p. 126). Regarding the fact that heteroscedasticity was not found to be present in the estimation of the linear model, it might be that the log-transformation induced greater variability across residuals. Leeflang et al., (2015, p. 126) state that the true source of heteroscedasticity is usually hard to retrieve, which is in some way confirmed by the finding that most predictor variables seem to induce heteroscedasticity. However, after a visual examination of the residuals, it seemed that the variances of the residuals differ greatly when the residuals were divided by a variable that indicated whether a purchase was made (see Figure 8). This was confirmed by the homogeneity of variance test, Levene’s test statistic amounted to 478249.964 (p=.000).

Figure 8: Variance residuals in none purchase situations versus purchase situations

In an attempt to remedy this, a Generalized Least Squares method (GLS) was implemented (Leeflang et al., 2015, p. 177,178). The general idea of GLS is that it takes out the patterns of the residuals, which are assumed not to be present whilst conducting OLS. Hence, GLS is in essence OLS applied to a transformed model. In this case, to take out the pattern of the residuals in order to equalize the variances across observations, the following was done:

𝑆𝑎𝑙𝑒𝑠_𝑡∗ = 𝑆𝑎𝑙𝑒𝑠𝑡 𝜎1 𝑎𝑛𝑑 𝑋𝑖𝑡 = 𝑋_𝑖𝑡 𝜎1 (𝑖 = 1, … , 𝐼) 𝑓𝑜𝑟 𝑡 = 1, … , 𝑇∗, 𝑆𝑎𝑙𝑒𝑠_𝑡∗ = 𝑆𝑎𝑙𝑒𝑠𝑡 𝜎2 𝑎𝑛𝑑 𝑋𝑖𝑡 = 𝑋_𝑖𝑡 𝜎2 (𝑖 = 1, … , 𝐼) 𝑓𝑜𝑟 𝑡 = 1, … , 𝑇,

where σ1 is the standard deviation of the residuals in case of non-purchase (0.017) and σ2 is the standard

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33 (2007) state that these GLS estimates may still be inaccurate if the weights chosen do not correspond correctly to the form of heteroscedasticity, which might be the case here.

Fortunately, the authors provide an appropriate alternative: a heteroscedasticity-robust inference by means of a heteroscedasticity-consistent standard error (HCSE) estimator. Herein, the regression model is estimated using OLS – in this case, that means going back to the initial, non-transformed variables – but the standard errors are estimated with an alternative method that does not make the assumption of homoscedasticity. Stated differently, the standard errors are adjusted for the heteroscedasticity that is present in the data, resulting in more robust estimates of these standard errors. Going into details and explaining the procedure step by step goes beyond the goal of this paper, but Hayes and Cai (2007) give a clear description of why this is an appropriate method to conduct, and the steps that need to be taken. They provide a set of macros (for SPSS and SAS) so that the HCSE estimators for OLS linear regression models can be implemented, which can be found in Appendix 2. The estimates of the HCSE’s and its influences on the initial significance tests can be found in Table 3 in Section 4.2.4. Since the regression coefficients estimates themselves are not biased by potential heteroscedasticity, they are not affected by the heteroscedasticity-consistent inference.

When the standard errors (SE) of the initial analyses are compared with the HCSE-estimates, it can be detected that the heteroscedasticity present in the data biased the variances of some parameters downwards. This was the case for lnInternet, lnInternet2, lnRadio and lnRadio2. Consequently, the corresponding p-values of the significance tests are affected. Where lnInternet and lnInternet2 initially showed p-values of .003 and .156, respectively, the HCSE-estimation showed p-values of .141 and .343. Although the ultimate conclusion for the quadratic effect of internet would not change (since p>.10 in both cases), it would for the linear effect of internet. More specifically, after conducting HCSE-estimation internet does not seem to affect sales, neither quadratic or linearly. The corresponding p-value of the linear effect of radio changed from .013 to .041; the quadratic effect of radio changed from being marginally significant (p=.080) to insignificant (p=.144). In addition, in the initial analysis the variances of the parameter estimates corresponding with lnTV and lnTV2_were

apparently somewhat upwards biased. This is indicated by smaller corresponding p-values in the HCSE-estimation procedure: for lnTV it changed from .004 to .003 and for lnTV2_{from .025 to .019.}

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4.2.4 Normality

Since heteroscedasticity can have an impact on the normality of the residuals (Leeflang et al., 2015, p.133), chances exist the residuals are not normally distributed. The Kolmogorov-Smirnov test confirms this by revealing a significant test statistic that amounts to .493 (p=.000). In addition to heteroscedasticity, the presence of outliers in the residuals can also influence the normality of the residuals (Leeflang et al., 2015, p. 135). After a closer examination of the residuals, several outliers can be detected. To see whether these observations might disturb the normal distribution, the model is extended with seven indicator dummy variables the same way as in Section 4.1.4. Inclusion of these indicator dummies did slightly improve the R2 of the overall model. Initially R2 amounted to .001;

R2=.011 and R2adj=.010 of the extended model (F=163.963, p=.000). However, problems with

non-normality of the residuals were not solved by the inclusion of these indicator dummies. The Kolmogorov-Smirnov remains significant (test statistic = .494, p=.000). It should be concluded that the assumption of normally distributed error terms is violated. Therefore, a Bootstrap based on 999 samples was conducted, which makes the corresponding p-values of the significance tests more trustworthy as explained earlier. The results are also presented in Table 3 on the next page, together with the HCSE-estimates. The parameter estimates themselves are not affected by the Bootstrap analysis. The Bootstrap confirms the results of the HCSE-estimation procedure.

4.2.5 Linearly independent predictor variables

Similar in case of the linear model (Section 4.1.5), there are substantially high VIF-values for all the advertising exposure variables (for lnprint and lnprint2 VIF>10, for lninternet and lninternet2 VIF>6, for lnradio and lnradio2 VIF>12, for lnTV and lnTV2 VIF>11). For all the other variables the VIF-values vary from 1.001 to 1.531. After closer examination of the correlation matrix, it turned out that there are only large (>.6) correlations between the linear and quadratic function of the variables (r(lnprint,lnprint2_{)=.950 r(lninternet,lninternet}2_{)=.925 r(lnradio,lnradio}2_{)=.957, r(lnTV,lnTV}2_)=.953;

p<.01). In essence, since the quadratic terms are not linear functions of the original variables, the

assumption that the predictor variables are linearly independent is not violated. This means that the high VIF-values can be ignored.

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35 Bootstrap** HCSE Sig. 95% confidence interval

Model β SE Sig. SE Sig. Lower Upper

lnConstant .155 .015 .000 .016 .000 .001 .123 .185 lnPrint .028 .005 .000 .005 .000 .001 .018 .037 lnPrint2 -.012 .002 .000 .002 .000 .001 -.017 -.008 lnInternet .228 .076 .003 .154 .141 .122 -.031 .576 lnInternet2 -.035 .024 .156 .037 .343 .348 -.122 .069 lnRadio .022 .009 .013 .101 .041 .036 .001 .043 lnRadio2 -.007 .004 .080 .005 .144 .158 -.016 .002 lnTV -.013 .004 .004 .004 .003 .004 -.021 -.004 lnTV2 .004 .002 .025 .002 .019 .032 .001 .008 lnLagged Sales 2.189*10-6 _.000 _.000 _.000 _.013 _.001 _.014 _.034 lnAge -.033 .004 .000 .004 .000 .001 -.041 -.025 Educationmedium* -.001 (βEM=.999) .003 .595 .003 .584 .595 -.007 .004 Educationhigh* .001 (βEH=1.001) .003 .684 .003 .680 .685 -.005 .007 lnIncome .003 .001 .003 .001 .003 .006 .001 .006

*Variables are ‘flipped around’, then βi = elnβi

**Based on 999 samples

Table 3: Results regressions multiplicative model

4.3 Inverted-U hypothesis 4.3.1 Findings linear model

In order to investigate what patterns the advertising response functions follow, the following model was proposed:

𝑆𝑡 = 𝛽0+ 𝛽1𝑃𝑡+ 𝛽2𝑃𝑡2+ 𝛽3𝐼𝑡+ 𝛽4𝐼𝑡2+ 𝛽5𝑅𝑡+ 𝛽6𝑅𝑡2+ 𝛽7𝑇𝑉𝑡+ 𝛽8𝑇𝑉𝑡2+ 𝜆𝑆𝑡−1+ 𝛽9𝐴𝑖

+ 𝛽10𝐸𝐻𝑖+ 𝛽11𝐸𝑀𝑖 + 𝛽12𝐼𝑛𝑖 +ℰ𝑡,

The overall model was strongly significant (F=6.733, p=.000), with a R2 and R2adj that both amounted

to .000. The explaining power of the model substantially increased after the inclusion of the indicator variables for the outliers of the residuals (F=6733.389, p=.000; with a R2adj of .305. These dummy

variables set the corresponding residuals at zero, meaning that the predicted value of these observations perfectly fit within the regression line, inducing an increase in R2adj. However, the overall fitness of

WHEN IS IT TOO MUCH?

WHEN IS IT TOO MUCH?

An examination of repetition effects on sales

When is it too much?

An examination of repetition effects on sales

Summary

Preface

Table of Contents

1. Introduction

2. Theoretical framework

3. Method

Average number of exposure

Z=

=

×

,

=

=

β

.

4. Results

,