Elements of model building:

The classic approach to model building consists of 3 major parts:
1. specification
2. parameterization
3. validation

1. Specification(representation or structure) is the representation of the most important elements of the real world system in mathematical terms. This involves two major steps:

1. Specifying the variables to be included in the model, and making the distinction between those to be explained (the dependent variables) and those providing the explanation (the explanatory or independent variables). For example to explain market share of brand (dependent variable) we could propose following explanatory variables: price, advertising expenditures, promotions, distribution, quality, and measure this variables for the brand and for competing brands. Often this also involves a choice of statistical distribution of those variables, or a distribution of error term of the dependent variable.

2. A second aspect is the specification of a functional relationship between the variables. For example, the effects of explanatory variable can be linear or non-linear, immediate or/and lagged, additive or multiplicative. A choice among those options may be based of priori reasoning. Additive relationship, for example, implies that the explanatory variable do not interact, while the multiplicative assumes specific type of interaction. Also s-shaped function indicates increasing returns to scale for low values of an explanatory variable and decreasing returns for high values.

2. Parameterization (or estimation) is the determination of parameter estimates for a model. For this data often is available or may be available without great effect, but should be careful with such data. May be “unobserved” or “latent” variables. Attitudes about products, intentions to purchase, feelings. Sometimes such unobserved variables are omitted from the model, as in the stimulus-response models: the models with no behavioral details. Alternatively one can develop instruments to measure the unobserved variables, either directly or as a function of observed or indicator variables.

Apart from the collection issues we have to identify techniques to be applied for extracting estimates of the model parameters from the data collected.

3. Validation:

Validation criteria for model building can relate to:
The model structure (specification)
The data quality
The estimation method
The applicability of statistical tests
The model’s relative performance, against alternative models
The relevance of model results to intended use

The idea of model selection is what we often have alternative models specifications, and we use data to distinguish between the alternatives. The superiority of one model over another may depend on the product category and on competitive conditions but also on the quality of the data. Even though theoretical arguments should inform the model specifications, in marketing, we want the empirical results to be not only consistent with what sound arguments dictate, but also with how marketplace behaves subsequent to model testing. With new data, the question is whether extent models apply, and with new models the question is whether the proposed specification outperforms prevailing benchmarks. In marketing the empirical research almost always includes a measure of predictive validity.