A model is a usable description of how a system is believed to work. It is a simplification of reality, with unnecessary detail excluded. Good models describe key aspects of how systems work. Bad models misrepresent reality. A model can be created using words, combinations of images and words, physical models, diagrams, and mathematics.

Physical models

The technical meaning of the word “model” is identical to the understanding you had as a child. Consider a model of Copenhagen’s harbor, built out of Lego. This is a model in the same way as an equation can be a model: it is something designed to look like the real thing, but it is not actually the real thing.

Word models

Many models exist as sentences. For example, the economic concept of the demand curve posits that:

Demand is a function of price.

Graphical models

Models can be combinations of images and words. A simple example is:

A more complicated graphical model is the means-end chain shown below, which shows how preferences for specific features of wine-based soft drinks (shown at the bottom) “ladder” up to benefits desired, which in turn ladder up to values that are important to people.

Causal diagrams

Causal diagrams are a type of graphical model where arrows indicate what causes what. For example, the idea that demand for a good is a function of price is expressed as:

A more complex model may specify the mechanism by which an input affects an outcome. For example, the hierarchy of effects model of advertising says that advertising influences sales by making more people aware, changing their attitude, prompting them to want to buy, and encouraging their final decision to purchase:

Equations

For most areas of application, the ultimate model is one where a model can be expressed using mathematics, as in the following equation:

$Sales = 121 + 4.1 × $Advertising expenditure

Such models are the end-goal of most efforts at science as they are most precise, which makes them both more useful in practice and easier to check.  This should not be inferred as meaning that all models should be expressed mathematically: when a model is expressed mathematically it is often harder to understand, which can lead to errors. For example, causal diagrams are often better for understanding causality than are equations (see Pearl, Judea (2009), Causality: Models, Reasoning and Inference: Cambridge University Press; 2nd Edition).

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