Leeflang, Wittink, Wedel and Naert (2000) classify models according to their primary purpose or intended use.
They distinguish:

• Descriptive models. These models intend to describe decision processes of managers or customers.
• Predictive models.   These models forecast or predict future events or outcomes.
• Normative models.   These models are used to obtain recommended or optimal courses of action.

Descriptive models are not restricted for decision problems. For example one can describe the market by the structure of brand loyalty.
By predictive models we mean models for forecasting or prediction future events. For example, a firm may want to predict sales for brand, under alternative prices, advertising spending levels and package sizes.

Indeed, one can argue that for a model to have valid normative implications, it must have predictive value and at least some descriptive power. However, a descriptive model need not have normative implications and a predictive model may not be useful for normative considerations. They also point out that it is often logical to proceed from a descriptive to a predictive and then to a normative model. In other situations, a descriptive model may be sufficient. Forecasting or prediction does not always mean answering “what if” type of questions, such as, how the demand changes if price is increased by 10 percent. In some brand choice models, the structure of brand loyalty and switching is summarized in a transition probability matrix.

Normative or Prescriptive models –has one of its outputs as recommended course of action. For example, the objective function in a media allocation model may be the optimization of profit.

Demand models make up a special class of predictive models. We refer to the demand model when we have a performance variable related to the level of demand. Many demand models belong to the subset of predictive models. In a demand model, the performance variable is a measure of demand. This performance variable may depend on a number of other variables, such as marketing decision variables employed by the firm and its competitors. We distinguish individual demand models and aggregate demand models.

Aggregate demand may refer to:

1. The total number of units of a product category purchased by the population of all spending units. The corresponding demand model is called a model of industry sales, or a model of product class.
2. The total number of units of a particular brand purchased by the population of all spending units. The demand model is then a brand sales model.
3. The number of units of a particular brand purchased by the total population relative to the total number of units purchased of the product class, in which case the demand models is a market share model.

Gatignon and Robertson (1986) identify three types of models, which differ in Their objectives and implications:

Theoretical models. These models offer a mathematical description of a process in which some constructs are systematically joined to others. The objective is to generate theoretical propositions that appropriately describe the possible influence of variables on the diffusion pattern and diffusion rate. These descriptions are the raison d’être of theoretical models and should Provide suggestions to managers.

Normative models. These models also start with a description and assume functional relationships among the variables that affect the diffusion process. The behavioral assumptions may be less complex than those of theoretical models, given that the objective is not to make descriptive propositions but to develop optimal marketing strategies. An objective function for the firm is determined and the model implications are expressed with respect to variables incorporated into the model .

Empirical models. The objective of these models is to fit data and test a Specific theoretical proposition or a complete model. Marketing has focused more on empirical and normative than on theoretical Models.