Types of model

In The Starting Point, my first post on this blog, I argued that “(B) Much knowledge can be seen as … models.” That’s obvious to some degree but it raises the question of what constitutes a model.

There are at least four kinds of model: Structural, taxonomic, developmental and causal. There are also metamodels.

In The Starting Point I argued that “(A) Knowledge is most interesting and important where it is general.” Some models are very general. Thus most fundamental models in physics can apply anywhere in the universe. Some are entirely specific, eg the UK Treasury’s model of the UK economy applies only to the UK and probably for only a few years. For now I only note this distinction. It may be desirable to formalise it at some future point.

Structural models

Structural models show the structure of an actual or proposed object. They may be physical or virtual. Structural models are used in many areas including medicine, chemistry and the various kinds of engineering.

Doctors have created generic models of the body’s skeleton, nerves, blood vessels, etc. which are used in medical education and to guide surgery. In sensitive cases exploratory operations and non-invasive scans (using X-rays, ultrasound or MRI) are used to create models of an individual patient’s body. Another recent advance has been the construction of full-size

Chemists have long used structural models of molecules to help them reason about their properties and reactions. For many years they were drawn on paper or built using rods and balls but now they are increasingly likely to be electronic. Electronic models allow calculation of, eg, molecular shapes.

Engineers used to rely on drawings to communicate their designs to clients and those who have to build them. They increasingly use 3D models which also support design work and construction. During design they enable stress calculations, simulation of performance, compatibility, etc. They may generate lists of required materials, work allocations and control data for numerically-controlled tools.

Taxonomic models

A taxonomic model is a set of categories with allocation rules. These rules are usually text for use by a human classifier but may be executable. Thus, in 1999 the BBC automated the allocation of incoming news reports to its own 5,000 news categories. Journalists use these categories to select the reports they need. The system, News On-line (NEON), replaced the people who had previously done this job.

Some taxonomies are very simple. For instance, the states of matter are solid, liquid, gas and plasma. These are often stable.

Others are very large and may evolve continuously. Well-known large-scale taxonomies include:

• In science, the Periodic Table of the Chemical elements and the Linnaean taxonomy of living things.
• In business, Standard Industry codes (SIC), the UN Product Classification, the Yellow pages categories.
• In marketing, the Mosaic set of consumer profiles.
• In information retrieval, the Dewey decimal system and the Yahoo ontology.

We sometimes find that a causal model underlies a taxonomy, eg, blood groups. Sometimes this is known first; sometimes only later. Thus:

• The distinctness of the chemical elements reflects the quantum mechanics of atomic nuclei.
• The Linnaean taxonomy reflects the evolution of living things – a phenomenon that was not understood in Linnaeus’ time.
  
• The Mosaic profiles reflect people’s lifestyle choices and resources

This also applies to sub-atomic particles and blood groups but not (so far) to genres or Standard Industry codes (SIC), the Dewey decimal system or the Yahoo ontology.

Developmental models

A developmental model asserts that its subject, eg an organism or a market, must pass through a series of stages. There are many stages models. Amongst the best-known are those developed by Piaget in the area of child development.

A well-known business example is Geoffrey Moore’s market development model:

• Innovators
• Early adopters
• Chasm
• Early Majority
• Late Majority
• Laggards

(See Crossing the chasm by Geoffrey Moore).

Like a taxonomy a developmental model may be based on a causal model or may be purely empirical.

Causal models

Causal models show how events lead to consequences.

The most basic causal models are purely indicative – little more than a list of factors that predispose to a result.

At the next step up are empirical models. These models produce forecasts by extrapolating from previous experience. Many economic and financial planning models are of this kind.

The best causal models are mathematical and allow quantitative prediction of consequences. They may be tacit or explicit. Tacit causal models may be no more than correlations. Explicit causal models, eg Newtonian mechanics, include explanations.

Some models are hybrid. Typically they use theory-based formulae where they are available and empirical formulae elsewhere. The Dupuy Insitute's Tactical Numerical Deterministic Model (see separate posting) appears to be a hybrid.

A causal model requires a taxonomy as foundation. That is, the entities in the model must be clearly defined. Sometimes the taxonomy predates the causal model but some causal models, probably including the most significant ones, require some revision of the taxonomy.

Metamodels

A metamodel is a general model that says, for one or more specific models, which features are significant and, sometimes, how they are represented.

Suppose a database contains a digital model of a gearbox. Underlying the database is a schema, an executable digital listing of the kinds of data items and relationships used to store that model. This schema is the metamodel for the gearbox model and would be equally applicable to other gearboxes and, probably, to a wide range of engineered structures.

In principle there are metametamodels – but these are only needed by, for instance, people designing new database and knowledge management systems.