Simple Mathematical Models
When studying models, it is helpful to identify broad categories of models. Classification of individual models into these categories tells us immediately some of the essentials of their structure. There are several methodologies for classification of mathematical models, below mention some of these.
One division between models is based on the type of outcome they predict. Deterministic models ignore random variation, and so always predict the same outcome from a given starting point. On the other hand, the model may be statistical in nature and so may predict the distribution of possible outcomes. Such models are said to be stochastic.
A second method of distinguishing between types of models is to consider the level of understanding on which the model is based. The simplest explanation is to consider the hierarchy of organisational structures within the system being modelled. A model, which uses a large amount of theoretical information, generally describes what happens at one level in the hierarchy by considering processes at lower levels these are called mechanistic models, because they take account of the mechanisms through which changes occur. In empirical models, no account is taken of the mechanism by which changes to the system occur. Instead, it is merely noted that they do occur, and the model tries to account quantitatively for changes associated with different conditions.
Next points for classification of models concern the nature of mathematical apparatus used in models. We can speak about continuous/discrete, linear/nonlinear etc. scales.
These divisions, deterministic/stochastic, mechanistic/empirical etc., represent extremes of a range of model types. In between lie a whole spectrum of real model types.