Introducing randomness

Many theories in the social sciences, and in marketing in particular, are based on models that seek to represent a system or situation, and hence enable researchers to make predictions of future changes and trends. Empirical studies attempt to identify how the different elements of the model influence each other, and of particular interest is how changes in one or more variables moderate changes in a focal variable.

by Hubert Gatignon and Joachim Vosgerau
Last Updated: 23 Jul 2013

Fitting data to models helps researchers to determine whether or not the models actually correspond to what is happening in real life, and hence whether the model will be of any use for predictions. But in many cases, while there is ample data, the models are not sophisticated enough to test the predictions or identify the impact of the different variables.

In this working paper, Hubert Gatignon, the Claude Janssen Chaired Professor of Business Administration and Professor of Marketing at INSEAD, and Joachim Vosgerau, Assistant Professor of Marketing at the Tepper School of Business, Carnegie Mellon University (PhD INSEAD, 2005), propose a new model, Stochastic Moderated Regression (SMR), designed to improve the efficiency and usefulness of econometric models.

The authors propose to use information contained in the stochastic nature of the moderating effects (SMR) to untangle moderating effects from the effects of other variables. This problem arises because of multicollinearity, which is inherent in models with moderating effects. Multicollinearity makes the moderator effect difficult to distinguish from the effect of the focal variable.

The authors describe a response equation and a moderating equation in addition to the traditional equation for the relationship between focal and moderating variables. SMR introduces a random element into the relationship describing the moderating effect. The random element in the moderating equation expresses the stochastic nature of the moderating effect and brings two advantages: providing additional information to make estimates more efficient; and providing information that may help to distinguish which moderating effects are significant.

The authors argue that incorporating the random element of a moderating function is essential to describe fully the moderating process being studied, and can be used to reduce the negative consequences of multicollinearity.

The authors go on to assess the benefits of SMR via a Monte Carlo simulation, considering moderating effects at different strengths, the impact of noise in the equations on error variance and the effects of sample size. They use both Ordinary Moderated Regression and SMR for each data set generated.

The results demonstrate the gains in efficiency offered by SMR and highlight the benefits of SMR where sample sizes are small and the moderating effect is noisy. The results demonstrate the drastic impact of specifying irrelevant factors on the ability to find significant relevant effects.

It becomes clear that assessing the moderating effect of variables is best carried out through a two-stage process, beginning with an estimation of the full model, and followed by re-estimating the model while excluding non significant moderating effects.

In the search for ever-increasing sophistication in theory development and in econometric models, methods to test contingent predictions are critical. The SMR method proposed in this paper begins to address the problems of estimating moderating effects, and the authors identify the optimum conditions under which to apply this technique.

Source: INSEAD Working Paper, Reference: 2006/17/MKT

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