# Marketing mix Modelling — Interaction Effects

The marketing mix operates as a co-ordinated programme designed to achieve business imperatives. It is therefore not surprising that often the elements of the mix interact synergistically, to produce an effect greater than the sum of their individual effects.

For example, the elements of consumer promotions, like discounts, displays and co-op advertising, often have a synergistic impact lifting sales more than the sum of their individual impact on sales. Or for example, investments in marketing instruments such as theme advertising strengthen a brand’s equity, resulting in the lowering of consumers’ sensitivity to changes in price.

These interaction effects influence the sensitivity of one or more elements of the marketing mix, to changes in another element of the mix. They are captured in response functions by including an additional term (X1×X2) which represents the product of the two interacting variables.

The multiplicative model implies that the dependent variable is affected by an interaction of the variables of the marketing mix. Its functional form is written as:

$$S= e^α \prod_j^{variables} X_j^{β_j} = e^α X_1^{β_1}X_2^{β_2}X_3^{β_3} ... X_J^{β_J}, X_j >0$$

In its logarithmic form however the interaction effects are no longer explicit:

$$ln(S)=α+β_1lnX_1+β_2lnX_2+β_3lnX_3 ... +β_JlnX_J$$

If there is the need to include interaction effects after taking logs, the transcendental logarithmic (translog) model is one approach for doing so:

$$ln(S)=α+β_1lnX_1+β_2lnX_2+β_3lnX_3 ...$$ $$+β_{12}lnX_1lnX_2+β_{13}lnX_1lnX_3+β_{22}lnX_2lnX_2 ...$$ $$+β_{11}(lnX_1)^2+β_{22}(lnX_2)^2+β_{33}(lnX_3)^2 ...$$

A related notion, interdependency, exists when a company’s decisions on one element of the marketing mix impact its decisions on some of the other elements of the mix. This may result from the outcome of concerted strategies, or the trade-offs that companies need to make with limited budgets. For example, pricing decisions impact margins, which in turn may have a bearing on the brand’s budget on other instrument such as advertising. Interdependence may also exist within different forms of an instrument — conventional and online advertising for instance.

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