-By Arindam Banerjee, Professor of Marketing, IIM Ahmedabad
In a typical classroom session in the Analytics course at our business schools often times the discussion steers towards the efficacy of regression-based models. Issues such as “fit” of the model, the interpretation of the parameters of the predictor variables, the hurdles in interpretation created by issues such as multi-collinearity are discussed and many plausible resolutions are debated in an animated manner. Very rarely does a perfect solution emerge from these discussions.
In theory, a model is supposed to be a summarized representation of the real phenomenon. Hence, the expectation is that models should be, a) “complete” in their explanation of the real-life phenomenon, b) simple for users to appreciate the phenomenon and, c) sufficiently reliable to predict future scenarios perfectly. Most social interactions are, however way too complex to be amenable to a simplified yet perfect summary, as is demanded by business users. In fact, the very simplification process in model building (a necessary input for understanding and managerial diagnosis and control) is the reason for the partialness of the explanation. Complex social phenomena usually have complex explanation and therefore the process of simplification in model building for the purpose of better understanding will necessarily create an imperfect model - which is “part” explanatory and consequently imperfect in prediction.
Net-of-net, while it is desirable to build models which provide razor-sharp explanation of the phenomenon of interest, and also predict with reasonable accuracy, such model building ventures are idealistic. Most practical situations impose a compromise; analysts and their stakeholders have to prioritize i.e., choose what is more important to them, a) a partial but palatable explanation of the phenomenon or, b) a more reliable prediction at least in the near term. Whichever objective is more pertinent for the contextual requirement should drive the model building process.
Models that Explain
Such models are used primarily for the diagnosis of certain social behavior. They are also referred to as the process of discovering or the identification of causes of a phenomenon. For instance, in market behaviour, a common query is to find the extent to which changing prices affect demand. This is usually done by estimating a price “elasticity” coefficient of demand in a regression model. Though a relatively simple problem, the discovery of the price effect leads to many more questions than they answer that the procedure unravels. Does a price-sensitive market behaviour mean that lowering prices will have a positive impact on demand? Hard to say, since there may be many other parameters (identified or hidden) that affect demand and therefore manipulating one parameter can only provide an average impact on the demand. Therefore, while the price sensitivity of the market is an important finding from the model, the exact nature of how demand will play out depends on many other complex interactions among market forces that the model is rarely able to extract fully. Quite likely, the “fit” of these diagnostic models is low – an indication that the models are simple but partial summarization of market phenomenon. Such model rarely provide confidence in their ability to exactly predict demand as the market parameters change.
Description of market phenomena requires high degree of confidence in the relationship between demand and the pertinent market parameters. Therefore, identifying the relationship between cause (price) and effect (demand) through the parameter estimates in a regression model is very important. Multi-collinearity is a common problem that hampers this process. Most readers would appreciate the problem as one where the estimates shift frequently due to the high level of correlation among various causal parameters (like price changes and advertising changes happen simultaneously). Therefore, multi-collinearity is a critical problem that requires a satisficing resolution in diagnostic models.
Models that predict
The primary function of these models is to predict the outcome as changes happen to the causal parameters (or forecast outcome in the future). In this kind of model, the objective is to attain an acceptable level of accuracy of the predicted outcome, i.e., how close is the estimated outcome close to the actual value. In these situations, the “fit” of the model is very critical to ensure a baseline level of confidence in the model output. Most prediction (forecasting) models are developed using regression algorithms that ensure that the information contained in the training data is optimally matched using a complex mathematical formula. The important point is the ability to match the contour of the data well with a complicated and often times inexplicable mathematical function. Care is taken to ensure no “overfitting” of the model that may reduce the ability of the model to match quality testing parameters on data beyond the training set.
While the intended purpose here is not to explain the process of building sophisticated ML models, the point we would like to emphasize is that prediction models require a relatively more complicated “summary” of data that many times does not lend itself to easy interpretation. But the purpose of prediction is served. The quality check for the model is not its diagnostic ability, but whether it can reliably churn out an exact estimate of the outcome as changes happen in the future. Multi-collinearity, a formidable hurdle in diagnostic models as explained earlier, is of secondary importance over here. The critical elements to test the superiority of prediction models are, a) the “fit” to the training data and, b) the ability to predict well in a validation sample. No wonder, sophisticated Neural network algorithms used for prediction are never questioned for their (in)ability to explain the phenomenon that they are supposed to model and forecast.
Set your Modeling Objective beforehand
In conclusion, while empirical models are meant to provide a suitable summary of the information contained in the data, they are never perfect in satisfying the objectives of the user group. Good prediction models often require highly complex algorithms to meet reasonable quality standards. However, their complex characteristics do not lend themselves to the simple storytelling of the phenomenon that business leaders appreciate. Therefore, simpler models that provide a digestible but partial view of the marketplace are rarely good for prediction purposes. That should be obvious given that most human behaviour (which is central to business dealings) are fairly complex and do not have complete and comprehensible explanations. Therefore, the practical way to find a resolution is to decide on a primary objective – “explain” or “predict” and develop models accordingly to suit the purpose. Otherwise, we may be trying to build models to attain multiple objectives without much success and, that is not useful for most business enterprises.
Arindam Banerjee is a Professor of Marketing at IIM Ahmedabad. SAGE is the proud publisher of his book “Business Analytics"
Check out the SAGE textbook here.