DEALING WITH THE COMPLEXITY OF MULTI-MEDIA ...

DEALING WITH THE COMPLEXITY OF MULTI-MEDIA INTERACTIONS: SYNERGY OR ANTAGONISM? Ceren Kolsarici, Queen’s University Demetrios Vakratsas, McGill University (Working Draft) Abstract Despite the highly touted potential for synergies in cross-media advertising, much has yet to be discovered about how the effects of multiple media combine to shape the sales response. Two challenges related to the investigation of media interaction effects are their complex nature and their specification in a sales response model. The authors adopt a flexible modeling approach, MARS (Multivariate Adaptive Regression Splines), which captures parsimoniously complex interaction effects and facilitates their measurement and interpretation. Analysis of multiple data sets on brand sales and media spending points to the following typology of media interaction effects: 1) synergistic (positive interactions), 2) antagonistic (negative interactions), and 3) asymmetric, where each medium does not contribute equally to the interaction. The findings show that 44% of media spend produces synergistic effects, whereas 21% produces antagonistic effects. Hence synergy is not the de facto outcome of cross-media advertising. Interestingly, lowbudget media play a key role in producing interaction effects.

Keywords: Integrated Marketing Communications; Cross-media advertising; Interaction response surfaces; Complexity; Statistical Learning.

The concept of synergy, according to which the combined effect of communication activities exceeds the sum of their individual effects, is a key tenet of Integrated Marketing Communications (IMC) and cross-media campaigns (Batra and Keller 2016; Naik and Raman 2003). The synergy hypothesis stems from the idea that “…integration involves unity and wholeness. Through this unity, synergy can be achieved.” (Duncan 2002, p.19). Hence, synergy represents a causal effect of media integration. In sales response models, synergy manifests itself through a positive interaction effect between individual media allocations, which is critical for budgeting decisions of firms engaging in cross-media campaigns (e.g. Naik and Peters 2009). However, since the seminal work of Naik and Raman (2003) relatively few studies have formally examined the effects of media interactions on market performance measures such as sales. This echoes the view of Assael (2011) that synergy research has not yet reached its potential. Hence, there is much to discover about the nature of the media interaction response surfaces. Investigation of potential synergies in cross-media campaigns presents researchers with two major challenges. First, cross-media effects are likely to exhibit complexity. Extant literature has consistently shown that response curves for single and aggregate media spending reflect complex phenomena such as thresholds, saturation, and supersaturation (e.g. Ackoff and Emshoff 1975; Dubé et al. 2005; Eastlack and Rao 1989; Eastlack and Rao 1986; Tellis 1988; Terui and Ban 2008; Vakratsas et al. 2004). Consequently, interaction response surfaces may exhibit similar complexity since phenomena related to media-specific response curves should also apply to interaction response surfaces. For example, if response to TV advertising alone is supersaturated (i.e. exhibits negative returns), due to over-exposure, then the combination of TV with other media at high allocation levels is also likely to cause supersaturation. This could lead to negative, instead of the expected positive, interaction effects. In other words, cross-media 1

campaigns may not always produce synergies, but instead result in antagonism1, synergy’s opposite. Taylor et al. (2013) provides evidence for antagonistic effects between TV and online advertising and attribute them to duplicate reach. An alternative explanation for antagonistic effects is rooted in the content of the messages communicated through different media and failure to achieve message consistency in a cross-media campaign. For example, Sridhar et al. (2016) find antagonistic effects between national and regional media advertising, possibly due to conflicting objectives: national advertising tends to be brand building but regional advertising is tactical. In the next section, we show, through a simple mathematical illustration, that antagonistic effects are actually inherent when response to aggregate spending is supersaturated. In addition to the possibility of synergistic or antagonistic effects, Assael (2011) suggests that interactions may also exhibit asymmetry. More specifically, he notes (Assael 2011, p. 10): “when synergy occurs between two media, the effects are not likely to be equal. One medium is likely to produce more positive effects than the other.” Consequently, the interaction between two media will not only depend on the total allocation to the media pair but also on which medium has a higher allocation share. The previous discussion suggests that cross-media campaigns can produce a range of effects, such as synergy, antagonism, and asymmetry, all of which may manifest on the same interaction response surface as distinct phenomena. For example, very low levels of allocation may produce zero interaction effects due to thresholds, medium level allocations may produce synergies, and high levels of allocation may produce antagonism due to supersaturation.

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Just as in the case of the term synergy, we borrow the terms antagonism and antagonistic effects from epidemiology (Porta 2008). Alternative terms used for antagonism include “negative synergy” (Enoch and Johnson 2010) and “antergy” (Ehrenberg-Bass 2012).

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Capturing these phenomena in a model setting is challenging and requires a flexible, yet parsimonious approach due to the potentially high data requirements for estimation purposes. The second challenge relates to the specification of the interaction effect. Interactions in cross-media advertising campaigns represent causal effects (synergy, antagonism) and, as such, it is desirable to measure them directly through explicit specification of the interaction term and use of “natural” (untransformed) scales (Rothman 1974). The linear model of Naik and Raman (2003) provides an excellent example of direct measurement of the interaction effect using media spending variables in their natural (original) scale and specifying the interaction as a multiplicative term. The parameter of the linear interaction can then be readily interpreted as the synergy effect. By contrast, the multiplicative (“log-log”) model is an example of an implicit interaction specification, which uses a scale (log) transformation (e.g. Danaher and Dagger 2013). In its transformed scale, the model is additive and hence void of any interaction effects. Of course, interactions in the original scale (media spending) can be recovered, but they are difficult to measure and interpret since they involve multiple parameters and variables (e.g. Dhar and Weinberg 2015). Thus, direct measurement of the interaction effects is not possible. In addition, since the multiplicative model is inherently interactive it does not allow for testing the presence/absence of an interaction. Unfortunately, direct measurement of the interaction effect is frequently difficult to achieve parsimoniously with global parametric models. For example, modeling pairwise interaction effects of a campaign involving ten different media with a linear model requires 45 parameters just for the variables involving the interaction, which rapidly increases the computational burden and data requirements. This is the reason researchers resort to scale transformations such as the log-log with the aforementioned consequences regarding the 3

measurement and testing of the interaction effects. In addition, global parametric approaches cannot capture the multiplicity of interaction phenomena (synergy, antagonism, and asymmetry) on the same interaction surface. The discussion of the two major challenges suggests that a modeling approach to media interactions should be flexible, to accommodate complexity, but also intuitive enough to facilitate the measurement and interpretation of interaction effects. Such an objective is difficult to achieve parsimoniously within the context of global parametric modeling, a point that we will further elaborate in the methodology section. In this study, we seek to address these methodological challenges in order to obtain novel insights concerning interaction-related phenomena. Specifically, we use a time series extension of Multivariate Adaptive Regression Splines (MARS), a non-parametric approach rooted in statistical learning methodology (Friedman 1991), to examine the effects of media spending and their interactions on sales response. MARS builds up complexity parsimoniously by relying on expansions of simple (linear) basis functions while explicitly modeling interaction effects. We examine the effects of media interactions on brand sales across different product categories by analyzing spending data on all media tracked by a major provider (Kantar Media). We focus on media spending data since these are typically available to managers and inform their decisions on issues such as budget size and allocation (Fischer et al. 2011; Grabner and Moers 2015). Our choice of sales as the response measure is motivated by managerial decisionmaking practices as well as academic views that the promise of cross-media research will not be fulfilled until cross-media effectiveness can be linked to sales (e.g. Assael 2011). We do not form a priori expectations regarding the extent and nature of interaction effects for specific media-pairs. The reason is two-fold. First, given the potential for complex interaction 4

phenomena that may vary by medium and context (brand, message) it would be difficult to theorize about them. As Corning (1998, p.162) notes, complexity often implies that interaction effects “…are not easily predicted and may often be novel, unexpected, even surprising.” Second, very little theoretical ground has been laid on this issue. Rather, we offer explanations for the estimated interaction effects with an aim to lay the groundwork for fruitful future research including further theoretical development, which we discuss in the final section. We claim the following contributions. First, our study is the first to systematically examine interaction effects across different cross-media data sets. We also control for other critical marketing mix and exogenous variables such as price, promotions, competitor sales and seasonality. Second, we offer a flexible approach to modeling response curves and interaction surfaces by allowing them to be media-specific. Hence we extend previous approaches to modeling media-specific response curves (e.g. Eastlack and Rao 1986; Vakratsas and Ma 2005), by accounting for media-specific interaction surfaces. Third, we provide a typology of interaction effects which we catalogue according to our empirical findings. This categorization would be useful for managers who need to identify sources of advantage (synergy) but also “pain points” (antagonism) in their cross-media campaigns. Finally, by investigating the effects of cross-media synergies in complex settings our work addresses MSI’s top priority (MSI 2016). BACKGROUND AND CONCEPTUALIZATION We first provide a brief overview of the rationale for synergistic (antagonistic) effects, then we review the literature on the role of media interactions on performance measures, and finally we further elaborate on issues specific to the complexity in the media interaction effects.

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Rationale for Synergistic (Antagonistic) Effects Media complementarity and source magnification have both been suggested as potential rationales for media synergy in the literature (e.g. Chang and Thorson 2004; Dijkstra et al. 2005). Media complementarity is based on the idea that the combination of multiple media with different modalities and audience control (pacing) will leverage the strengths of each medium while minimizing their weaknesses (Dijkstra et al. 2005). Modality refers to the mode of presentation or format of a medium (e.g. verbal vs. visual). Control refers to the ability afforded by a medium to the audience to manage exposure of the message through pacing (e.g. print is self-paced whereas TV is externally paced). Hence, messages communicated through multiple media will be more effective due to the synergies built among them by leveraging their strengths in an integrated campaign. With respect to modality this is similar to the idea based on encoding variability that different presentation modes can facilitate learning (e.g. Edell and Keller 1989). Chang and Thorson (2004) suggest that communication through multiple media, representing multiple message sources, can evoke more cognitive responses than single media repetition by probing higher processing (Harkins and Petty 1981). Message complementarity is critical for the multiple source effect, since different supporting arguments can enhance cognitive activity when presented through multiple media sources (Batra and Keller 2016; Harkins and Petty 1981). However, multiple presentation modes can also cause a distraction and interfere with learning particularly if there is no commonality or coordination of the message across media. For example, a tactical promotional message in a local medium may be perceived as contradictory (antagonistic) to a brand-building message in a national medium (Sridhar et al. 2016). Consequently, perceived message inconsistency across media may result in antagonistic effects. The multiple source perspective also allows for the possibility for antagonistic effects, if the 6

arguments presented through multiple media are weak (Harkins and Petty 1981; Moore and Reardon 1987). Finally, audience duplication in a multi-media campaign may cause increased repetition hence cancelling out media synergies and producing an antagonistic effect instead (Taylor et al. 2013). In sum, previous literature suggests that although varied modality, control, and sources in a multi-media campaign could create a synergistic effect, they may also produce antagonistic effects if the message and its communication are not consistent, the arguments presented are weak and the repetition is high. Media Interaction Effects on Sales We restrict our attention to studies concerned with interaction effects on market performance measures such as sales. As pointed out earlier, the relevant literature is rather scant and typically focuses on: 1) interactions involving a specific media pair (e.g. TV-magazines), and 2) optimal allocation implications of interactions. Research involving a limited number of media has provided evidence for synergies (positive interactions) between TV and print (Naik and Raman 2003), TV and direct mail (Stafford et al. 2003), as well as radio and newspaper advertising (Jagpal 1981). More recently, researchers have focused on the role of online media in synergies with mixed results. Havlena, Cardarelli and Montigny (2007), Naik and Peters (2009) and Kumar, Choi and Greene (2017) provide evidence for online-offline synergies. On the other hand, Taylor et al. (2013) find evidence for antagonistic effects between TV and Internet, attributed to duplicate reach (i.e. the two media reaching mostly the same viewers multiple times) which leads to interaction supersaturation. The impact of media interactions on budget allocation has been studied by Naik and Raman (Naik and Raman 2003) and Naik and Peters (2009). Naik and Raman (2003) show that 7

in the presence of media synergies managers should decrease (increase) the proportion of media budget allocated to the more (less) effective communications strategy. This finding, also supported by Naik and Peters (2009) in the context of online-offline media interactions, highlights the significance of considering media with a smaller contribution, a suggestion also made by Eastlack and Rao (1989) who emphasized the need to account for media-specific response functions. Naik and Peters (2009) also distinguish between “across” (offline-online) and “within” (offline) media synergies. Complexity of Media Interactions Although synergy is the desired outcome of a cross-media campaign, we have already discussed evidence that points to antagonistic effects (Sridhar et al. 2016; Taylor et al. 2013). The possibility of antagonistic effects can in fact be illustrated mathematically by assuming a quadratic sales response function for total (aggregate) media spending, which accounts for supersaturation effects (e.g. Nguyen 1985; Tellis 1988; Tull et al. 1986). More specifically, omitting the time subscript,𝑡, for simplicity, the sales response function has the following form: 𝑆 = 𝛼 + 𝛽𝑋 − 𝛾𝑋 2

(1)

where 𝑆 represents sales and 𝑋 total media spend with >0. If we assume that total media expenditure is allocated to two media, such as TV (𝑋1) and magazines (𝑋2 ), then the sales response function can be expanded as follows: 𝑆 = 𝛼 + 𝛽(𝑋1 + 𝑋2 ) − 𝛾(𝑋1 + 𝑋2 )2 & = 𝛼 + 𝛽𝑋1 − 𝛾𝑋12 + 𝛽𝑋2 − 𝛾𝑋22 − 2𝛾𝑋1 𝑋2 where the last term in the last equation represents an antagonistic effect. In other words, antagonism is inherent in an aggregate spending response model with supersaturation. The expression also suggests that aggregate spending supersaturation is partly driven by this

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(2)

antagonistic effect, as well as individual media supersaturation, consistent with the findings of Taylor et al. (2013). Of course, this mathematical illustration is a stylized example based on a “top-down” modeling approach that starts with the response to aggregate media spending for the specific case of supersaturation. In such an approach, the specification of media interactions is dictated by the response to aggregate media allocation. If one were to choose a more granular “bottom-up” modeling approach that starts from response to individual media allocations, which is our objective in this paper, there are additional possibilities for the shape of the interaction response surface. For example, similarly to media-specific response curves, interactions may also exhibit threshold and saturation effects. This implies that for low allocation levels to a media pair their interaction can be non-significant, positive for medium levels (synergistic effects), and negative for high levels (antagonistic effects). The presence of all these effects may shape a complex response surface landscape that can only be captured by a flexible modeling approach. Another possible phenomenon related to media interactions is asymmetry or direction of the interaction (Assael 2011). Prompted by the findings of Pilotta and Schultz (2005), Assael (2011) posits that one medium may be more “dominant” in the interaction, and “lift” the “weaker” medium whereas the opposite may not be true. For example, a TV ad may lift the effect of an Internet display ad because of its modality (Dijkstra et al. 2005) but the Internet ad may not have the same effect on TV. Alternatively, if the Internet display ad convey novel information it may lift the TV ad effectiveness through their interaction. The standard linear model specification with multiplicative interaction terms does not allow for such an asymmetry. Finally, a medium’s effect on sales response may manifest only through interactions. In other words, certain media have a supporting, or ancillary, role and generate response only in 9

combination with another medium without a direct (main) effect. In the case of synergy, Raman and Naik (2004) have used the term “catalytic” to describe such effects. This also highlights the importance of including interactions in cross-media response models since their omission could lead to significant bias. METHODOLOGY The discussion and illustrations of the previous section establish that a methodological approach should combine a) modeling flexibility to capture the complexity of response curves and interaction surfaces, and b) direct measurement of the interaction effects through explicit specification and use of untransformed scales to facilitate interpretability. This should be achieved parsimoniously since accounting for interaction effects increases considerably the number of required terms, and model parameters should be expended prudently. A global parametric approach is unlikely to satisfy the above criteria since it lacks flexibility (Friedman 1991) and parsimony. For example, using a flexible multi-functional global parametric response model (e.g. Pantelidaki and Bunn 2005) requires testing of different combinations of marginal response functions for each medium or media pair. In addition, for response to certain media and interaction pairs, there are no generally accepted functional forms and hence no a priori theorygrounded specification. Other statistical learning methodologies, such as Artificial Neural Networks (ANN), are flexible but lack ease of interpretation. In order to satisfy the above criteria and to account for the temporal nature of the advertising sales relationship, we use Time-Series Multivariate Adaptive Regression Splines (TS-MARS) 2, due to Lewis and Stevens (1991), to model interaction response surfaces. In this section, we introduce MARS, as originally developed by Friedman (1991) and then discuss the

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We thank an anonymous reviewer for this suggestion.

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time-series extension in the context of our study. MARS is a non-parametric methodology that builds up complexity parsimoniously (at a low computational cost) while maintaining accuracy (De Veaux and Ungar 1994). It does so by relying on the principle of recursive partitioning where the response function is estimated by optimally dividing the domain of each predictor variable (spending per medium). The resulting response is an expansion in a set of piecewise linear functions that are non-zero over only a limited range of the predictor variable. Figure 1 illustrates the form of such a function with reflected pairs (𝑥 − 0.5)+ and (0.5 − 𝑥)+ where the subscript “+” refers to the positive part of the function (𝑖. 𝑒. (𝑥 − 𝑘)+ = 𝑚𝑎𝑥(𝑥 − 𝑘, 0)). - - Figure 1 about here - In Figure 1, the solid and the dashed lines represent the two reflected pairs in the shape of hinge functions, which are also referred to as MARS basis functions. The constant in each basis function is called the knot and locates its turning point. In this illustration, the knot location for both functions is the same at k=0.5. As demonstrated in Figure 1, a key advantage of using piecewise linear basis functions is that they operate locally since they are zero over part of their range. This also means that when they are multiplied with other functions of similar structure to produce interaction effects, the result is non-zero over a limited region of the interaction surface. Figure 2 depicts a function, ℎ(𝑋1 , 𝑋2 ) = (𝑋1 − 𝑘1 )+ ∙ (𝑘2 − 𝑋2 )+, resulting from the product of MARS basis functions. The expansion of such basis functions and their products can achieve the desired complexity in response curves and surfaces. Consequently, the response surface is built up parsimoniously using non-zero components locally (Hastie et al. 2001). Use of higher order basis functions would lead to non-zero products everywhere and result in loss of parsimony. Hence, by using linear basis functions we trade off smoothness for parsimony. 11

- - Figure 2 about here - The MARS representation can take on the following form: 𝑁𝑚 𝑓̂(𝑋) = 𝛽0 + ∑𝑀 𝑚=1 𝛽𝑚 ∏𝑛𝑚 =1[𝑠𝑛𝑚 (𝑋𝑝𝑛𝑚 − 𝑘𝑛𝑚 )]+

(3)

where 𝛽0 is the intercept, M is the number of terms in the model, 𝑋𝑝 is the 𝑝𝑡ℎ predictor variable (i.e. 𝑝 = 1,2, … , 𝑃), 𝑘𝑛𝑚 is the knot point, 𝑠𝑛𝑚 takes on values  1 to indicate the orientation (right or left) of the associated reflected pair and 𝑁𝑚 is the number of splits that give rise to term m. Since we focus our attention on main effects and two-way (pairwise) interactions we set max(𝑁𝑚 ) = 2, such that when 𝑁𝑚 = 1, the 𝑚𝑡ℎ term consists of a single basis function (i.e. univariate) and when 𝑁𝑚 = 2, it is formed as a product of two basis functions (i.e. bivariate). Equation (3) represents the general formulation of an estimated MARS model where 𝑋 on the left hand side is the (𝑃𝑥1) vector of predictor variables and the right hand side contains the 𝑋𝑝 ’s that survive shrinkage. We discuss model pruning in MARS and construction of the specification in Equation (3) in detail in the next subsection. The above expansion can produce flexible response curves and surfaces due to the piecewise nature of the basis functions and the presence of knots that can create turning points and break down the interaction response surface into regions characterized by distinct phenomena such as synergy, antagonism, and asymmetry. We can illustrate the ability of MARS to model asymmetric interactions as follows. Let’s assume the product of two basis functions as shown in (4) represents the interaction term for two media over a region of the response surface: 𝛽(𝑋1 − 𝑘1 )+ (𝑋2 −𝑘2 )+

(4)

with 𝑘1 > 𝑘2 > 0 representing the two knot locations,𝑋1, 𝑋2 representing spending for medium 1 and 2 respectively, and 𝛽 > 0 (to ensure positive interaction obtained via the cross-partial 12

derivative). To demonstrate the asymmetry in interaction, we compare the interaction contributions of symmetric media allocation pairs to the sales lift. More specifically, we assume that  advertising dollars are allocated to the pair of media and the allocation is split first as (𝑋1 = 𝑝𝛼, 𝑋2 = (1 − 𝑝)𝛼) and then as (𝑋1 = (1 − 𝑝)𝛼, 𝑋2 = 𝑝𝛼) with 1>p> 0.5 and 𝑝𝛼 > (1 − 𝑝)𝛼 > 𝑘1 > 𝑘2 > 0. The previous assumptions ensure that the basis functions will be nonzero and one allocation amount (𝑝𝛼) will be larger than the other. If p=0.5 then the allocations are split equally between the media and the case is trivial (symmetric effects). Then the corresponding interaction terms become: 𝐼(𝑝𝛼, (1 − 𝑝)𝛼) = 𝛽(𝑝𝛼 − 𝑘1 )((1 − 𝑝)𝛼−𝑘2 ) and, 𝐼((1 − 𝑝)𝛼, 𝑝𝛼) = 𝛽((1 − 𝑝)𝛼 − 𝑘1 )(𝑝𝛼 − 𝑘2 ) It can be easily deduced that 𝐼(𝑝𝛼, (1 − 𝑝)𝛼) > 𝐼((1 − 𝑝)𝛼, 𝑝𝛼), hence the incremental allocation of the larger amount 𝑝𝛼 results in a greater contribution to the interaction term for medium 1 compared to medium 2. From this perspective, medium 1 is the “dominant” medium. We fully illustrate asymmetric effects in the empirical analysis. This ability of the MARS specification to capture asymmetric effects is due to the flexibility produced by the expansion of products of basis functions as illustrated above. In addition, one can recast the MARS expansion into an intuitively appealing ANOVA decomposition: 𝑓̂(𝑋) = 𝛽0 + ∑𝑁𝑚=1 𝑓𝑖 (𝑋𝑖 ) + ∑𝑁𝑚=2 𝑓𝑖,𝑗 (𝑋𝑖 , 𝑋𝑗 )

(𝑖, 𝑗) ∈ {1, … , 𝑃}

(5)

The right hand side of equation (5) consists of the intercept, the sum of all basis functions that involve a single variable (main effects), 𝑓𝑖 (𝑋𝑖 ), and the sum of all basis functions that involve two variables (interaction effects), 𝑓𝑖,𝑗 (𝑋𝑖 , 𝑋𝑗 ), respectively. The ANOVA 13

decomposition provides an intuitive illustration of the ability of MARS to explicitly specify interaction effects, as well as its reliance on the simple arithmetic concepts of addition (for univariate or main effects) and multiplication (for interaction effects) to synthesize complex response curves and surfaces. While the proposed estimation method possesses characteristics that make it a good candidate for investigating complex media interactions, it is important to note its limitations. First, as noted above, MARS achieves parsimony through the piecewise linear structure of the basis functions and their local operation, but it does so at the cost of the smoothness of the response function. In other words, while MARS models often have low variance, they are not as flexible when compared to their popular counterparts such as generalized additive models and recursive partitioning. Second, MARS can suffer from low efficiency, particularly with higher order models and small sample sizes. Since we focus on MARS models with two-way interactions and work with moderate to large size data sets, estimation speed is not an important concern. Finally, MARS is developed to handle cross-sectional rather than time-series data. We address this issue by employing TS-MARS, a time-series extension of the original MARS specification. In the following, we discuss the MARS algorithm in details and introduce TSMARS as an extension. The TS-MARS Algorithm Given the temporal aspect of the advertising sales relationship, we model media response functions using the time-series extension of Multivariate Adaptive Regression Splines (TSMARS), due to Lewis and Stevens (1991). TS-MARS allows for nonlinear threshold modeling of time series data using an autoregressive structure. For example, Equation (6) depicts an AR(1)

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model of sales (𝑆) where, 𝜆 is the carryover effect, 𝑙𝑚 (𝑋) is a basis function in Λ or a product of two such functions, 𝑀 is the total number of terms in the model and the error term 𝜀𝑡 ~𝑁(0, 𝜎 2 ). 𝑆𝑡 = 𝛽0 + 𝜆𝑆𝑡−1 + ∑𝑀 𝑚=1 𝛽𝑚 𝑙𝑚 (𝑋) + 𝜀𝑡

(6)

Since basis functions are the fundamental building blocks of any MARS model, they deserve further elaboration. In short, basis functions are piecewise linear functions in the form of reflected pairs (i.e. (𝑥 − 𝑘)+ and (𝑘 − 𝑥)+ ) created for each predictor 𝑋𝑝 with the knot B

corresponding to an observed value of that predictor. MARS first creates a universal set, Λ, of reflective pairs for each input,𝑋𝑝 , with knots at each observed value, 𝑥𝑡𝑝 . If all inputs are distinct, Λ includes 2𝑇𝑃 candidate functions as potential additions to the MARS model, where 𝑃 is the number of variables and 𝑇 is the number of observations for each variable. Λ = {(𝑋𝑝 − 𝑘)+ , (𝑘 − 𝑋𝑝 )+ }𝑘∈{𝑥1𝑝 ,𝑥2𝑝,…,𝑥𝑇𝑝 ,}

(7)

𝑝=1,2,…,𝑃

The MARS algorithm works similarly to a forward stepwise linear regression, followed by backward elimination to control for over-fitting. However, unlike a regular regression where the original variables enter progressively into the model, MARS builds the model using the basis functions and their interactions. MARS picks the interactions that improve fit in the forward selection process and removes the terms that will lead to a smaller increase in the model error, during the backward elimination. In a way, the forward selection process intentionally creates an over-fit model that explains the data really well but will not generalize satisfactorily to new data. The backward elimination prunes the model by removing ineffective basis functions, one by one, to improve generalizability. Accordingly, the TS-MARS model in Equation (6) is built from the bottom up by starting with a constant function, l0 ( X )  1 . At each stage, we consider the products of terms already in 15

the model, 𝑙𝑚 (𝑋), with each of the reflected pairs in the universal set, Λ, as candidates for entry. We add the term that results in the largest decrease in training error. The term included into the MARS model at each iteration of the forward selection phase has the following general form: 𝛽̂𝑀+1 𝑙𝑚 (𝑋)(𝑋𝑝 − 𝑘)+ + 𝛽̂𝑀+2 𝑙𝑚 (𝑋)(𝑘−𝑋𝑝 )+

(8)

The coefficients ˆ M 1 and ˆ M  2 , are estimated by least squares together with the remaining M+1 coefficients in the model, including the intercept. Following the forward selection procedure, a backward pruning process is applied where the basis functions that contribute least to model fit are progressively removed until the best submodel is reached. As training error, we use the generalized cross-validation (GCV), which is a lack-of-fit measure that determines the knot locations and the optimal number of basis functions 𝛾 in the final TS-MARS model: 1

𝐺𝐶𝑉 = ∑𝑁 𝑖=1 𝑁

(𝑆𝑖 −𝑆̂𝑖 )2 (1−

𝐶(𝛾) 2 ) 𝑁

(9)

The numerator in Equation (9) is the average squared-error while the denominator is a penalty function accounting for the increased variance associated with higher model complexity. C(𝛾) 3 represents the effective number of parameters which, in addition to the number of terms in the model, include the number of parameters used to determine optimal knot positions. The way it is formulated, GCV is a form of regularization that trades the goodness of fit with model complexity. For further details on the TS-MARS algorithm, the interested reader may refer to Lewis and Stevens (1991) and the original article (Friedman 1991).

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Simulation studies have shown that selecting an additional knot in a piecewise linear regression is equivalent to introducing 3 additional parameters. Hence, 𝐶(𝛾) = 𝑟 + 𝑐𝐾, where r is the number of terms, K is the number of knots selected in the forward process, and c is the penalty term which is commonly between 2 and 3. (Hastie, Tibshirani and Friedman 2001).

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EMPIRICAL APPLICATION Data In the interest of providing a broad examination of media interactions, we use data sets from durable (hybrid cars) and non-durable (packaged) goods (yogurt and beer) categories in the US market. We use aggregate market level data, which is the principal data source in many industries and the basis for media allocation and scheduling decisions. Since data are available monthly for durables and weekly for packaged goods, we are also able to estimate cross-media response for different levels of data frequency. In the hybrid subcategory, we focus on monthly data for the top two car models, namely Toyota Prius and Honda Civic. For the consumer packaged goods, we employ weekly data for Danone and Yoplait for yogurt, and Budlight, Budweiser, Coors Light and Miller Lite for beer. Similar to the automobile brands, these are the highest selling and most frequently advertised brands in their corresponding categories accounting for 60% and 40% of the yogurt and beer category sales respectively. The source for sales data is JD Power and Associates (JDPA) for hybrid cars and IRI for the packaged goods brands; Kantar media is the source for media spending data. The advertising data represent monthly (durables) or weekly (non-durables) spending broken down by seven media (i.e. National TV, Regional TV, Magazine, Internet, Outdoor, Newspaper, Radio). Following Sridhar et al. (2016) we group television advertising into national (i.e. cable TV and network TV) and regional (i.e. syndicated TV and spot TV) spending. In our empirical application, brands utilize 5 to 7 media during the observation period providing a rich context for the investigation of complex cross-media effects. We use several control variables such as price, promotions, coupons, competitor sales, government incentives (for the hybrid category), seasonality, and pulsing dummies for each 17

media to capture the cross-media advertising-sales relationship more accurately. The IRI data includes weekly store level sales, promotions and price for each SKU between 2001 and 2011. We aggregated the packaged goods data from i) SKU to brand level, ii) weekly to monthly level, and iii) store to market level as follows. First, the sales, price, coupon and promotions data are aggregated from SKUs to brand, and store to market level. In the aggregation process, we standardize the variables where possible (e.g. price per ounce) and average across SKUs weighted by the store-level SKU sales. We use a similar procedure to get the mean price promotion and mean coupon probability for each brand at the market level. Second, we aggregate these brand and market-level weekly variables to monthly level by taking into account the start and end dates of the observed weeks. In cases where a week spans over two consecutive months, the aggregation is carried out by taking the weighted average of variables with the number of days/week in each month assuming uniform distribution across the days of the week. Third, we drop feature and/or display variables due to high correlation of their frequency with price promotions. Finally, we adjust prices for inflation by dividing them by the consumer price index of each month for the respective product category according to the US Bureau of Labor Statistics. Summary statistics for the data are presented in Table 1. - - Table 1 about here - A closer examination of Table 1 suggests that TV (national and regional) and magazines are “high budget” media, to which the overwhelming majority of the advertising budget is allocated, whereas newspapers, internet, outdoor, and radio are “low budget” media. This distinction will prove to be meaningful in our discussion of the findings.

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Model Specification and Estimation We employ the following semiparametric specification of the TS-MARS model: 2 𝑆̂𝑡 = 𝛽0 + 𝜆𝑆𝑡−1 + ∑𝐿𝑙=1 𝛼𝑙 𝑔(𝑍𝑙𝑡 ) + ∑𝑀 𝑚=1 𝛽𝑚 ∏𝑛𝑚 =1[𝑠𝑝(𝑛𝑚 )𝑡 (𝐴𝑝(𝑛𝑚 )𝑡 − 𝑘𝑝(𝑛𝑚 ) )] + 𝜀𝑖 (10) +

where St denotes the unit sales at time 𝑡, 𝑡 = 1,2, … 𝑇; 𝜆 measures the sales carryover, 𝐴𝑝𝑡 , is the advertising spending for medium 𝑝,𝑝 ∈ {1,2, … , 𝑃}; 𝑍𝑙𝑡 is the control variable 𝑙 at time 𝑡. In Bi

addition to marketing mix (i.e. inflation-adjusted price, coupons, promotional in form of price discounts for CPG and government incentives for hybrid brands) and other exogenous variables such as competitor sales and seasonality, the matrix 𝑍 also includes a pulsing dummy for each medium to control for advertising schedule (on/off) effects. The function 𝑔() takes the logarithmic form for all but the dummy variables which enter the model linearly. 𝑀 is the number of terms in the final model; 𝑘𝑛𝑚 is the knot (i.e. turning point) corresponding to the term, 𝑛𝑚 . The right-most term in the equation corresponds to the basis functions representing main effects (i.e. 𝑛𝑚 = 1) followed by the interaction terms (𝑛𝑚 =2) involving that basis function. 𝛽0 is the coefficient of the constant basis function (intercept) and the sum is over the basis functions retained after the backward elimination process. The term 𝑠𝑝(𝑛𝑚 )𝑡 takes on values  1 to indicate the orientation (right or left) of the associated reflected pair. RESULTS Our findings are summarized in Tables 2-4 and illustrated through the case of Yoplait which exemplifies the phenomena captured by our analysis in Figure 3. Before we begin the discussion of interaction response surfaces, it is worth elaborating on how media spending as well as control variables are retained in the model. The relative importance of the media variables in terms of their sales contribution is presented in Table 2. We operationalize variable importance as a measure of the effect of a 19

change in a focal media variable on brand sales. To obtain the rankings, we calculate the increase in the lack-of-fit measure, GCV, at each step of the backward elimination process compared to the previous step. We then sum these increases in GCV for each variable over all pruning steps that include the variable. Media which cause larger net increases in the GCV when eliminated from the MARS specification are considered more important (Friedman 1991) and ranked higher in Table 2. The last column lists the control variables that survived shrinkage; however, the control variables are excluded from the rankings to maintain focus on the media variables. In line with expectations, high-budget media such as national TV for most brands, and magazines and regional TV for the automobile brands are important drivers of sales. More interestingly, low-budget media such as internet and outdoor carry a high ranking in terms of variable importance for various brands in all three categories. In most of these cases, such media do not have a direct (main) effect on sales and are featured in the final MARS model through interaction effects only, hence serving at an ancillary capacity (Raman and Naik 2004). In other words, the lack of main effect response to a medium, such as Internet advertising for Miller Lite and Yoplait or outdoor advertising for Budweiser, does not necessarily imply that they cannot play a key role in the overall response. On the contrary, these media can play a significant role in terms of driving sales due to the strong interaction effects they produce with other media and make the case for catalytic effects. We note such media with an asterisk in subsequent Tables. - - Table 2 about here - Interaction Response Surfaces Table 3 provides detailed breakdowns of all estimated pairwise interactions for the six brands analyzed. We use basis functions and knots in the final MARS model to break down the 3-dimensional interaction response surface on a (2-dimensional) plane into regions of positive 20

(synergy), negative (antagonism), or zero effects. Then, for each media pair, we calculate the percentage of joint spending which results in synergistic or antagonistic regions over the entire surface plane and report it in the Table. The interaction response surface can then be synthesized by combining the effects corresponding to the distinct spending regions defined by the estimated MARS knots. This is illustrated in Figure 3 for the case of Yoplait, where the x- and y-axes denote spending for each medium involved in the interaction, and the z-axis represents the incremental impact on sales assuming the remaining variables are at their median level. A closer examination of the Table suggests that antagonistic effects can cover as much as 75% of the interaction surface, in terms of the joint spending, for some pairwise interactions. In addition, interactions are rarely nonzero everywhere lending validity to our claim regarding the multiplicity of the interaction-related phenomena and the use of hinge functions to capture them. Zero interactions could be due to the existence of threshold effects for low levels of spending, or saturation for high levels of spending on the media involved in the interaction. This validates our argument that thresholds and saturation manifest not only on media-specific response curves but also on interaction response surfaces. Finally, antagonistic effects often occur at lower spending levels for at least one of the media involved in the interaction. The previous observations are indicative of the complexity of interaction effects and will be further discussed through the illustration of the Yoplait case (Figure 3), and the summary of our findings. - - Table 3 about here - - - Figure 3 about here - Illustration: Regional TV-Internet interaction for Yoplait. The regional TV (RTV)-internet interaction surface for Yoplait typifies the findings of Table 3 since it is composed of regions reflecting antagonistic, synergistic, and asymmetric effects. Thus, it provides a good basis for discussion as well as an opportunity to illustrate the measurement of 21

interaction effects using the knots of the basis functions. Specifically, the basis function expansion for this interaction has the following form: 𝑆̇ = −.034(𝑅𝑇𝑉 − 700)+ ∗ (126 − 𝐼𝑛𝑡𝑒𝑟𝑛𝑒𝑡)+ − .010 ∗ (𝑅𝑇𝑉 − 700)+ ∗ (𝐼𝑛𝑡𝑒𝑟𝑛𝑒𝑡 − 126)+ (11)

The above expansion suggests that regional TV has a turning point (knot) at 700 and Internet has turning point (knot) at 126 (note that media variables are in $1000s). Consequently, this splits the interaction surface into four regions: two regions of zero interactions and two regions of nonzero interactions, one corresponding to positive (synergistic) effects and one corresponding to negative (antagonistic) effects. We show the corresponding tree structure of this interaction in Figure 4 to illustrate the recursive partitioning nature of the algorithm. The sign of the interaction effect is determined by the sign of the cross-partial derivative of the interaction term which depends not only on the sign of the coefficients of the basis functions (𝛽′𝑠 in Figure 4), but also on the reflective pair involved in the interaction term. We outline the derivation of the crosspartials for the expansion in Equation (11) in Figure 4. The top panel of Figure 3 presents the resulting surface. The interaction effects are only present in regions where the slope of the surface changes with an increase in either or both media involved, in other words for non-zero terms of the corresponding product. The remaining regions reflect the main effects which can be easily observed by slicing the surface parallel to the axis representing the medium of interest. For ease of exposition, the main effect regions (zero interactions), positive and negative interactions are marked with “𝝄,” “+,” and “-” respectively. - - Figure 4 about here - The antagonistic effect occurs at higher spending levels for both media, consistent with our interaction supersaturation explanation. Two more observations emerge from the examination of Regional TV-Internet interaction response surface. First, the interaction effect is 22

asymmetric. In other words, each medium does not contribute equally to the interaction. To illustrate, we calculated the effect of an incremental allocation of $10K to both media under three scenarios. In the first scenario the allocation is evenly split between two media at $50K each, in the second $10K is shifted to regional TV for an allocation of $60K (with $40K allocated to internet), and in the third $10K is shifted to internet for an allocation of $60K (with $40K allocated to regional TV). Sales contributions due to the interaction for the corresponding scenarios are shown in Figure 5. In the even split scenario, the contributions are symmetric as expected from our discussion on asymmetric effects. However, when the allocation is shifted by $10K to each medium, the contribution corresponding to the shift to the Internet is much bigger than that for regional TV. In fact, a $10K allocation “gain” for the Internet leads to a gain in contribution whereas the same allocation “gain” for regional TV leads to a loss in contribution. Hence, internet emerges as the dominant medium in the asymmetric interaction. It should be noted that the decrease in the contribution to the interaction effect with increased allocation to Regional TV does not imply a negative interaction, but rather that the interaction effect is weakened if the incremental budget is allocated to the non-dominant medium (Regional TV). Interestingly, the illustration shows that the “low-budget” medium (internet) is the dominant medium in the interaction, suggesting that such media may offer a different pace and modality which can moderate saturation from high-budget media and lift the interaction effect as a result. Second, the dominant medium in the interaction is an ancillary one; in other words, although it does not have a direct (main) effect, it has a strong catalytic interaction effect, at least at moderate spending levels, consistent with Raman and Naik (2004). This underlines the importance of the interaction effects and the role of low budget media in leveraging such effects. - - Figure 5 about here - 23

DISCUSSION AND IMPLICATIONS To facilitate the discussion, we further summarize our findings on synergistic and antagonistic effects in a “synergy-antagonism” matrix presented in Table 4. In this matrix, above-diagonal elements correspond to synergistic effects of a media pair, whereas below-diagonal elements correspond to antagonistic effects. Each element in the matrix contains two entries: one records the average percent spending across all analyzed cases (Table 3) that produces synergistic (antagonistic) effects for the media pair, and the other records the frequency of incidence of synergistic (antagonistic) effects for the media pair. For example, there are a total of 5(3) observed incidences of synergistic (antagonistic) effects between National TV and Regional TV, corresponding to a joint 40(15) percent of media spending. The rows (columns) of the matrix are organized following the “high/low” budget designation of the media discussed earlier. The first three rows (columns) are occupied by high budget media (National and Regional TV, Newspapers), and the rest of the rows (columns) by low budget media (Newspapers, Internet, Outdoor, Radio). Although the matrix summarizes the findings of our study, it can be used by managers for the purposes of monitoring the incidence of synergistic and antagonistic effects (along with the corresponding allocations) across different campaigns. - - Table 4 about here - The following observations emerge from the examination of the matrix: 1)

On average 44% of allocation to any media pair produces synergistic effects whereas

21% produces antagonistic effects (summary box). Thus, we establish that synergy, a central concept of IMC and cross-media advertising, is not the de facto outcome. On the upside, the incidence and allocation concerning synergistic effects are double the size of those for the antagonistic effects. 24

2)

Antagonistic effects invariably involve at least one high-budget medium and almost

exclusively the TV medium (national and regional). Only the entries corresponding to the first three columns (high-budget media) below the diagonal of the matrix (antagonistic effects) are populated. This provides informal support for our supersaturation argument. High-budget media are more likely to be saturated due to audience replication and this carries to the interactions in which they are involved to produce antagonistic effects (Taylor et al. 2013). 3)

Despite the risk of antagonistic effects (previous point), high-budget media are still

capable of producing synergistic effects. The difference between producing a synergistic versus an antagonistic effect for high budget media may very well be determined by message (in)consistency and complementarity, a point that will be elaborated below. 4)

Interactions between low-budget media (Newspapers, Internet, Outdoor, Radio) produce

only synergistic effects, even though some of them do not produce any direct (main) effects (Internet, Outdoor, Radio). The entries on the right-hand side of the matrix below the diagonal are empty (no antagonistic effects). This confirms the ancillary role of low-budget media in producing a catalytic effect and their ability to provide leverage for sales response as illustrated in the Yoplait case. The above observations provide a strong basis for discussion. High-budget media, as expected, play a pivotal role and may prove both a “blessing” and a “curse” given their involvement in both synergistic and antagonistic effects. Two potential reasons for this duality of effects are supersaturation and message content (see Bass et al. 2007, for the latter). As discussed in the Background and Conceptualization section, while high-budget media are inevitably more likely to produce antagonism due to their potential for overexposure, their visibility may help create synergies possibly on the condition of message consistency and complementarity. For 25

instance, although national TV advertising is typically more strategic (image oriented) and regional TV advertising is more tactical (informational), consistent messaging through a unified umbrella theme (commonality) could boost the image-information complementarity of the two types of advertising (Batra and Keller 2016). This could explain why we find that more interactions between regional and national TV produce synergistic effects (5) and at a higher combined spending allocation (40%) than antagonistic effects (3 at 15%). On the other hand, potentially contradictory message themes may produce antagonistic effects, as evidence has shown for the case of a single (TV) medium (Bass et al. 2007). Thus, message consistency could be the key in producing synergies even between high-budget media. Indeed, most successful multimedia campaigns of recent years (AdAge 2015), such as Wieden+Kennedy’s “The Man You Man Could Smell Like” campaign for Old Spice and Ogilvy & Mather’s “Campaign for Real Beauty” for Dove, effectively use multiple executions and media channels to communicate a unified message to the audience. This is consistent with the encoding variability view (Unnava and Burnkrant 1991). The findings on the role of low-budget media are encouraging. They suggest that such media can be leveraged through interactions to produce significant synergistic effects in an ancillary, catalytic fashion (Raman and Naik 2004). In many instances, such effects are produced when two such media combine, and done so at low risk since no antagonistic effects occur (lower right-hand side of the matrix). Hence, the use of low-budget media can be a strategic choice resulting in win-win situations (synergy with no antagonism). This could be due to the change of pace and modality low-budget media can offer to offset the saturation due to the highbudget media.

26

Two more observations from our findings, beyond the synergy-antagonism matrix, are worth discussing. One is that antagonistic effects may not only occur at high spending levels, as a result of potential interaction supersaturation, but also at low spending levels (Table 3). In other words, low spending levels may not result simply in zero interaction effects (due to the existence of thresholds) but may even produce antagonistic effects. This could be due to the possibility of “noise” generated by media at low spending levels. More specifically, low spending levels may not allow for sufficient repetition and hence comprehension of messages communicated through a medium (e.g. Belch 1982; Cacioppo and Petty 1979; Mitchell and Olson 1977). Thus, the “signal” communicated through the medium will be noisy and may create an adverse, antagonistic, when interacting with other media due to audience confusion. It should be noted that this proposed mechanism for antagonistic effects is distinct from message inconsistency. In the case of inconsistency, messages are comprehended but because they are conflicting they cause antagonism. In the case of noise, a message is not comprehended and can lead to antagonism due to the lack of clarity and confusion it creates. An alternative explanation for antagonistic effects at low spending levels is competitive interference, which we do not account for. Future research should test such potential explanations for this phenomenon using individual-level data to further help managers identify conditions for antagonistic effects. Finally, the notion of asymmetries and medium dominance in the interaction effect suggests that managers can strategically leverage dominant media to boost the sales performance of their brands where the total is truly more than the sum of the parts. The MARS methodology can help managers identify the dominant media through the analysis of the interaction response surface, along the lines of our illustration in Figure 5. The good news for managers is that such

27

media are frequently low budget so incremental effects due to interactions can come at a very low cost. (Ehrenberg-Bass 2012; Enoch and Johnson 2010; Porta 2008) LIMITATIONS AND FUTURE RESEARCH A notable limitation of our study is that it does not account for message content and hence consistency, which is an important success pillar for cross-media advertising (Bass et al. 2007, Batra and Keller 2016). An additional critical factor we did not examine is competitive interference (e.g. Danaher et al. 2008), which may be a cause for antagonistic effects even at low spending levels. Content analysis of advertising messages and consideration of competitive advertising interference would shed further light into the causes of antagonistic effects, an area that has not received significant attention in terms of theoretical development. Although much effort has been expended on arguing for the synergy benefits of cross- media campaigns, more research should focus on the underlying causes of antagonism. In addition to investigating the role of the aforementioned message (in)consistency and competitive interference, future research should also test two more explanations we have offered for antagonistic effects: the “noise” explanation for low spending levels, and the supersaturation or duplicate reach explanation for high spending levels (Taylor et al 2013). In sum, we believe that the following questions can shape a useful future research agenda on antagonistic effects: a) To what extent does message (in)consistency inhibit learning and contribute to antagonistic effects? b) Does competitive interference cause antagonistic effects? c) Does low spending on a medium create “noise” in the interaction by causing a distraction and hence producing an antagonistic effect? d) Does supersaturation due to exposure in one medium cause antagonistic effects in its interaction with other media?

28

Although the use of aggregate-level data in our study was motivated on the basis of managerial decision-making practices, the previous questions need to be investigated using individual-level data. Individual-level analyses could also explore conditions that render a medium dominant in an interaction that leads to asymmetric effects as well as the role of sequential vs. simultaneous media consumption. We also acknowledge the potential for endogeneity in media spending, which however is challenging to address in an adaptively estimated nonparametric model with interactions such as MARS. Recent developments in accommodating endogeneity in Generalized Additive Models (Chib et al. 2009) can provide some guidance for future research in this matter. Finally, extensive replication of this study’s findings can provide opportunities for empirical generalizations, whereas examination of optimal allocation policies in the presence of synergistic, antagonistic and asymmetric cross-media effects can offer up valuable managerial insights. Hopefully, the resulting outcomes will broaden the existing knowledge base and fulfill the promise of cross-media advertising research.

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TABLES AND FIGURES TABLE 1 Descriptive Statistics Sales (units) Mean Std.Dev. Minimum Maximum % Allocation % “On” Count

11,051.68 3,747.23 5,754.00 22,054.00

68

National TV ($1,000)

Regional TV ($1,000)

1,963.90 5,685.64 0.00 25,495.40 70.66 29.41 68

347.10 523.38 0.00 2,602.6 12.49 69.12 68

Prius Hybrid (monthly) Magazine Newsp. Internet ($1,000) ($1,000) ($1,000) 321.85 725.13 0.00 3,125.90 11.60 33.82 68

7.02 43.07 0.00 321.60 0.30 2.94 68

Outdoor ($1,000)

Radio ($1,000)

Price ($)

134.50 428.61 0.00 2,994.70 4.80 80.88 68

0.85 4.90 0.00 28.80 0.03 2.94 68

3.81 31.40 0.00 258.90 0.13 1.47 68

25,275.04 757.47 23,692.50 27,080.00

11.37 17.25 0.00 85.90 0.80 82.35 68

0.00 0.00 0.00 0.00 0.00 0.00 68

0.00 0.00 0.00 0.00 0.00 0.00 68

22,561.69 1,263.69 19,462.00 25,042.50

68

Civic Hybrid (monthly) Mean Std.Dev. Minimum Maximum % Allocation % “On” Count

2,119.76 1,218.99 187.00 5,433.00

68

492.30 1258.287 0.00 6943.08 35.26 58.89 68

737.70 1157.603 0.00 5198.60 52.89 60.29 68

152.11 240.82 0.00 844.60 10.90 48l.53 68

2.69 22.19 0.00 183.00 0.10 1.47 68

68

Yoplait (weekly) Sales ($)

Mean Std.Dev. Minimum Maximum % Allocation % “On” Count

1,592,291 332,229 672,150 2,392,565

573

National TV ($1,000) 1,129.80 721.69 0.00 3,292.10 56.55 96.51 573

Regional TV ($1,000) 1074.50 517.24 0.00 3,116.90 35.28 99.30 573

Magazine ($1,000)

Newsp. ($1,000)

Internet ($1,000)

Outdoor ($1,000)

Radio ($1,000)

Mean Price ($)

Mean Promo.

Mean Feature/ Display

Mean Coupon

102.49 317.84 0.00 3,231.80 5.13 21.82 573

1.05 7.46 0.00 125.10 0.05 4.36 573

54.47 119.93 0.00 1,256.80 2.73 61.08 573

0.21 2.85 0.00 63.50 0.01 1.75 573

4.28 18.57 0.00 329.60 0.21 20.94 573

2.08 0.12 1.79 2.49

0.21 0.07 0.03 0.49

0.10 0.05 0.00 0.34

0.00 0.01 0.00 0.09

573

573

573

573

1.62 19.24 0.00 326.60 0.11 2.09 573

14.27 39.95 0.00 252.60 1.00 33.33 573

2.15 0.22 1.69 3.10

0.20 0.06 0.05 0.44

0.08 0.03 0.01 0.23

0.00 0.00 0.00 0.04

573

573

573

573

Danone (weekly) Mean Std.Dev. Minimum Maximum % Allocation % “On” Count

1,444,260 304,151 619,190 2,154,951

573

991.30 977.91 0.00 4,510.40 69.17 85.51 573

252.60 254.85 0.00 1,650.90 17.63 94.24 573

157.28 435.16 0.00 4,107.00 10.97 26.35 573

3.88 26.07 0.00 272.30 0.27 4.71 573

34

12.20 23.68 0.00 202.20 0.85 57.77 573

Budlight (weekly) Sales ($)

Mean Std.Dev. Minimum Maximum % Allocation % “On” Count

1,491,614 315,148 873,417 3,410,401

Mean Std.Dev. Minimum Maximum % Allocation % “On” Count

1,017,090 147,481 740,936 1,787,705

Mean Std.Dev. Minimum Maximum % Allocation % On Count

731,816 148,198 478,395 1,573,455

Mean Std.Dev. Minimum Maximum % Allocation % On Count

798,681 155,633 484,433 1,547,789

573

573

573

573

National TV ($1,000)

Regional TV ($1,000)

Magazine ($1,000)

2,724.4 2,582.61 0.00 16,975.60 84.10 100.00 573

250.60 149.60 19.60 1,323.09 7.74 100.00 573

96.50 208.14 0.00 1,326.40 2.98 37.17 573

19.71 138.83 0.00 1,959.60 0.61 40.84 573

1,986.40 2,071.80 0.00 15,162.60 80.34 99.65 573

165.10 135.25 0.00 727.80 6.70 100.00 573

119.37 315.26 0.00 3,702.50 4.83 31.59 573

1,885.50 1,417.68 0.00 6,438.50 79.61 98.08 573

165.50 237.41 0.00 2,327.70 6.99 100.00 573

57.34 167.73 0.00 1,680.00 2.42 23.73 573

1,837.80 1,467.37 0.00 10,847.10 80.05 98.78 573

184.08 162.67 0.00 1,203.2 8.01 100.00 573

127.01 330.41 0.00 4,449.60 5.53 33.16 573

Newsp. ($1,000)

Internet ($1,000)

Outdoor ($1,000)

Radio ($1,000)

103.84 224.36 0.00 1,196.80 3.21 23.04 573

2.05 16.08 0.00 191.30 0.06 2.09 573

Budweiser (weekly) 41.24 41.70 118.16 194.82 128.53 239.94 0.00 0.00 0.00 2,526.50 2,001.60 1,562.00 1.67 1.69 4.78 51.83 97.56 23.04 573 573 573

0.40 5.35 0.00 85.00 0.02 0.70 573

42.08 79.84 0.00 1,055.90 1.30 91.45 573

Mean Promo.

Mean Feature/ Display

Mean Coupon

21.22 3.67 16.69 27.34

0.19 0.05 0.07 0.39

0.20 0.04 0.08 0.39

0.00 0.00 0.00 0.01

573

573

573

573

22.31 8.89 13.60 73.83

0.16 0.08 0.03 0.43

0.15 0.09 0.03 0.43

0.00 0.02 0.00 0.20

573

573

573

573

Price ($)

Coors Light (weekly) 46.76 182.26 82.83 410.10 0.00 0.00 1,157.20 2,449.10 1.97 7.70 73.82 23.04 573 573

20.99 22.82 0.00 139.40 0.89 74.87 573

18.69 1.21 16.70 21.05

0.21 0.04 0.12 0.35

0.23 0.07 0.13 0.44

0.00 0.00 0.00 0.01

573

573

573

573

Miller Lite (weekly) 42.52 55.53 31.97 134.16 190.56 86.94 0.00 0.00 0.00 1,684.70 3,635.90 682.80 1.85 2.42 1.39 59.69 97.73 23.04 573 573 573

17.07 22.62 0.00 194.30 0.74 77.84 573

18.44 1.82 15.48 25.26

0.19 0.09 0.03 0.60

0.20 0.12 0.04 0.61

0.00 0.00 0.00 0.01

573

573

573

573

9.86 45.73 0.00 667.50 0.42 39.62 573

35

TABLE 2 Variable Importance Ranking Controls Variables Magazine

Newspaper

National TV

Regional TV

Radio*

Internet*

Outdoor*

BEER

YOGUR T

AUTO

(Surviving Shrinkage)

NA

Toyota Prius Hybrid

3

NA

1

Honda Civic Hybrid

1

NA

2

Yoplait

2

NA

3 2

4

1

3

1

3

2

Danone

4

Budlight

4

5

1

3

Budweiser

6

2

5

1

Coors Light

6

2

3

Miller Lite

7

1

6

2

NA

36

NA

Lag sales, spring , price, competitor sales Lag sales, summer, promotions, coupons, price, Lag sales, promotions, competitor sales

2

Lag sales, summer, price, promotions

4

3

Lag sales, summer, spring, coupon, price

5

1

4

Lag sales, summer, competitor sales

4

5

3

Lag sales, summer, spring, price, promotions

Denotes variable did not survive shrinkage Denotes the variable did not enter the MARS model due to low coefficient-of-variation or zero spending

Note: Asterisk (*) denotes commonly ancillary media (effective only through interactions)

NA

Lag sales, spring, summer, government incentives, price

TABLE 3 Interaction Surfaces Prius

Civic Regional TV

National TV

[0,502)

[502,2603]

NI

+

[0,25495]

%Antagonistic

0%

National TV

%Synergistic

Internet 80%

[0,86]

% Antagonistic

0%

[0,758)

[758,6943]

+

NI

%Synergistic

10%

Magazines

National TV % Antagonistic

[0,6943) 20%

[0,168)

[168,844]

%Synergistic

NI 0%

Magazines

Internet* % Antagonistic

Yoplait

[0,86] 0%

% Antagonistic

Radio % Antagonistic

Note:

[0,126) [126,1256] 20%

[0,21.8) [21.8,108] 5%

[80,844]

NI %Synergistic

+ 90%

Danone

Regional TV [700,3117] NI + NI % Synergistic 5% [0,700)

Internet*

[0,80)

Regional TV % Antagonistic

Regional TV [0,698) [698,3117] NI NI NI % Synergistic 0%

Radio* % Antagonistic

Asterisk (*) denotes ancillary media (effective only through interactions) 𝑁𝐼 marks regions with no interactions present

37

[0,426) [426,1651] 15%

[0,55) [55,252] 0%

National TV [0,1729) [1729,4510] NI NI NI % Synergistic 0% National TV [0,1709) [1709,4510] NI NI + NI % Synergistic 30%

Budweiser

Budlight

Newspaper

National TV

Newspaper*

[0,1.3) [1.3,1959)

% Antagonistic

0%

Coors Light

[0,1360)

[1360,15950]

NI NI % Synergistic

NI +

National TV 90%

% Antagonistic

[0,1165) [1165,15162) 85%

[0,83)

[83,2526]

NI NI % Synergistic

NI -

Regional TV % Antagonistic

0% Outdoor

Regional TV

Regional TV

National TV % Antagonistic

[0,976) [976,1360) [1360,14950] 5%

% Antagonistic

[0,314)

[314,1323]

NI NI NI % Synergistic

+ NI

Outdoor* % Antagonistic

[0,293) [293, 1562] 0%%

[0,6.8)

[6.8, 728]

NI NI % Synergistic

NI +

Outdoor 80%

% Antagonistic

Regional TV

[1360,15950] Newspaper

Outdoor

[0,1196]

-

% Antagonistic

NI

[0,72) [72,2526] 15%

[0,109)

[109,727]

NI % Synergistic

NI NI

Internet % Antagonistic

Newspaper* % Antagonistic

10%

[0,6.4) [6.4,1959) 0%

% Synergistic

% Antagonistic

[0,785) [785,1326) 5%

[0,6.8) [6.8, 728] 25%

National TV [0,4278) [4278,15163] NI + + % Synergistic 65%

[0,406) [406, 1562] 75%

National TV [0,96) [96,15163] NI + NI % Synergistic 25%

[0,898) [898,3702] 0%

Regional TV [0,345) [345,727] NI + NI NI % Synergistic 15%

0%

Regional TV [0,314) [314,1323] NI NI NI + % Synergistic 75% National TV

Magazine

[0,221) [221, 2450] 35%

National TV [0,2100) [2100, 6438] + NI % Synergistic 5%

[0,86) [86,600] 10%

Outdoor [0,221) [221, 2450] NI NI + % Synergistic 75%

Regional TV % Antagonistic

Outdoor*

[0,1360)

[1360,15950]

NI % Synergistic

NI NI

% Antagonistic

0% Magazines* % Antagonistic

0%

Magazine* [0,205) [205, 1050] NI NI NI + % Synergistic 70%

0%

National TV [0,1020) [1020,6438] NI NI + NI % Synergistic 15%

0% Internet

% Antagonistic

[0,221) [221, 2450] 0%

Regional TV* [0,177) [177,2327] NI NI NI + % Synergistic 85%

5%

National TV [0,1360)

[0,177) [177,1200] 0%

National TV [0,2100) [2100,6438] NI + NI NI % Synergistic 10%

[0,86) [86,600]

% Antagonistic

Internet % Antagonistic

[0,86) [86,600]

Miller Lite

Magazines % Antagonistic

Internet* % Antagonistic

Newspaper % Antagonistic

[0,2.6) [2.6,1500] 0%

National TV [0,1260) [1260,10847] + + NI NI % Synergistic 1%

[0,47) [47,1684] 0%

National TV [0,895) [895,9000] NI NI NI + % Synergistic 90%

Internet* [0,2.6) Outdoor* % Antagonistic

Outdoor* % Antagonistic

Radio* % Antagonistic

Radio % Antagonistic

38

[0,16) [16,2200] 0%

National TV [0,378) [378,9000] NI NI + NI % Synergistic 5%

[0,682] 0%

+ % Synergistic

[2.6,1500] NI NI 1%

0%

Newspaper [0,47) [47,1684] NI + NI % Synergistic 95%

[0,30) [30,195] 0%

Newspaper [0,47) [47,1684] NI + NI NI % Synergistic 15%

[0,30) [30,195] 15%

Magazines [0,16) [16,2200] NI NI NI % Synergistic 0%

[0,682]

TABLE 4 Synergy-Antagonism Matrix for Media Pairs

National TV National TV Regional TV Magazine Newspaper

15 [3] 13 [2] 85 [1]

Internet Outdoor Radio

Regional TV 40 [5]

Magazine 5 [1] 15 [1]

Internet 13 [3] 5 [1] 80 [2]

15 [1] 20 [1]

*

40 [3]

Outdoor 15 [2] 83 [2]

Radio 30 [1]

95 [1] 38 [2]

15 [1]

* 5 [1]

Summary Average % of joint spending Incidence (count)

Note:

Newspaper 90 [2]

15 [1]

* Synergistic Effects 44 % 24

Antagonistic Effects 21% 13

The first entry represents the average spending % that produces synergistic (antagonistic) effects and the second entry (in brackets) denotes the incidence of synergistic (antagonistic) effects. Asterisk (*) denotes commonly ancillary media (effective only through interactions)

39

FIGURE 1 Reflected Pair of Piecewise Linear Basis Functions

FIGURE 2 Interaction Surface Resulting from the Multiplication of Two MARS Basis Functions

40

Incremental Sales ($1000)

1850

1800

1750

1700

1650

1600 3500 1550 100

3000 90

2500 80

70

2000 60

50

1500 40

30

1000 20

10

500 0

0

Regional TV Advertising ($1000)

Radio Advertising ($1000)

FIGURE 3 Pairwise Media Interactions (Yoplait)

41

Regional TV (RTV) (700)

-

+

NI

Internet (126)

-

+ 𝛽2 = −.010

𝛽1 = −.034

Negative Interaction

Positive Interaction

Basis Function 1: −.034 ∗ (𝑅𝑇𝑉 − 700)+ ∗ (126 − 𝐼𝑛𝑡𝑒𝑟𝑛𝑒𝑡)+

Basis Function 2: −.010 ∗ (𝑅𝑇𝑉 − 700)+ ∗ (𝐼𝑛𝑡𝑒𝑟𝑛𝑒𝑡 − 126)+

Generalized Specification: 𝐵𝐹1 = 𝛽1 (𝑋1 − 𝑘1 ) ∗ (𝑘2 − 𝑋2 ) = 𝛽1 (−𝑘1 𝑘2 + 𝑘1 𝑋2 + 𝑘2 𝑋1 − 𝑋1 𝑋2 )

Generalized Specification: 𝐵𝐹2 = 𝛽2 (𝑋1 − 𝑘1 ) ∗ (𝑋2 − 𝑘2 ) = 𝛽2 (𝑘1 𝑘2 − 𝑘1 𝑋2 − 𝑘2 𝑋1 + 𝑋1 𝑋2 )

Interaction Effect: (Cross-partial Derivative)

Interaction Effect: (Cross-partial Derivative) 𝜕 2 𝐵𝐹2 = 𝛽2 = −.010 𝜕𝑋1 𝜕𝑋2

𝜕2 𝐵𝐹1 𝜕𝑋1 𝜕𝑋2

= − 𝛽1 = .034

Figure 4: MARS Tree for Regional TV - Internet Interaction (Yoplait)

42

Sales Lift due to Interaction ($1000)

80 70 60 50 40 50

60 Ad Spending ($1000) Regional TV

Internet

Figure 5: Interaction Effect Due to a $10K Allocation Shift (Yoplait)

43