What is the difference between a theory and a model?

My father used to emphasize this distinction to me constantly when I was younger. He was a professor of psychology at UCLA and a published researcher. I’m trying to remember now what he said the difference is, but it’s just not coming to me. Is it basically that a theory attempts to provide a framework for predicting a system’s behavior while a model simply states that one system exhibits behavior which mirrors another system’s behavior? For example, a cockroach and a mouse exhibit the same response to a noxious stimulus, therefore the cockroach can be seen as modeling the mouse’s response, but a theory takes it one step further and attempts to explain the basis for the response? Am I in the right ballpark here, or is it something entirely different?

In my engineering world theories were used to produce a model that could predict what a system or component would do.

Don’t know if that is 100 percent correct or not though.

In a strictly mathematical sense, a theory is a set of axioms that describe some system, while a model is an instance of the theory.

An example is the natural numbers. The theory has axioms that there is a 0 and that each number has a successor and every number save 0 is a successor of something. The usual natural numbers is a model, but there are many others.

It looks like this might be similar to the use of these words in psychology and other disciplines.

Usage varies from field to field, and the difference is often not well defined (mathematics is an exception in this regard). On the whole, “theory” tends to mean something that is relatively well established, and has relatively wide scope, whereas “model” tend to mean something more tentative (and perhaps proposed more as analogy than putative fact) and that has a more restricted range of application.

Although it is perfectly possible that your father drew a clear distinction, and thought it important, I very much doubt that you would find widespread agreement about how the distinction should be applied in practice amongst psychologists, or, indeed, most other scientists.

Washoe… Hang on, your not that chimp that was raised as their child by psychologists, are you? :eek::wink:

No, but when I was an infant he was wont to take me to class with him and put me in a Skinner box, much to my mother’s perpetual chagrin. Let’s just say that Leonard Hofstadler’s jokes about his childhood invariably elicit a knowing chuckle from me.

Washoe, you are on the right track, but a little off with your examples. Consider the following (to use a psychology-based example). Let’s say you have a theory that more suicides occur in bad weather than in good weather. Based on this theory, you come up with the following mathematical model: number of monthly suicides in a given area = 1 x number of days overcast (without rain) + 2 x number of days with rain. So, if there are three overcast days and two rainy days, your model would predict seven suicides. This can be compared to the actual number to validate (or refute) your model and thus the underlying theory.

This is a highly simplified example, but it gives the basic idea. Generally, theory will drive the model, although in some cases data is examined to create a model, which in turn causes a theory to be derived. (Starting at the theory end is often referred to as theoretical research, while starting at the data end is often referred to as empirical research.)

As mentioned by another poster, usage of the terms can vary widely across disciplines (and even across practitioners within a discipline).

I would say that theories are a subset of models: Every theory is a model, but not every model is a theory. A theory is a model which has a great deal of experimental and observational support.

I think there’s alos a distinction that a theory is expected to conform to the reality of what it’s describing but a model can be acknowleged as not being a real depiction of something as long as it produces realistic results.

For example, if you’re explaining how gravity can alter space, there’s a common model used of space being a sheet of rubber and gravity being a metal ball that bend the rubber around it by its mass. Now nobody is claiming that they have a theory that the universe is actually made out of rubber and gravity is a bowling ball. It’s just a useful model for conceptualizing the real situation.

This looks exactly right, to me. Was there another question?

A theory describes “how” while a model simply describes “what”. A theory might say “If X happens, then it will cause Y” but all a model says is “Y happens if X happens”

I would call that an analogy, not a model.

As I understand it, a model is merely a simulation or set of calculations - inputs go in, and outputs are produced. Models don’t have to explain why it works or establish causation between inputs and outputs. A theory is an attempt at a real explanation or understanding.

As an example of the difference: ancient Greek astronomers had an excellent model of the stars and planets - they knew exactly what was going to be where each day, year, etc. with a small margin of error. But their theory was based on perfect circles, epicycles and a geocentric universe. They got the right predictions from a model despite the fact that it was based on all the wrong assumptions.

It wasn’t until calculus and gravity that people like Copernicus and Kepler could come up with better theories. Then the theory was used to improve the model.

What this thread can indicate is the general usage of the words, which may differ from field to field and even from person to person. However, if your father is still around, the best way to understand what he, in particular, meant by the distinction is by re-asking him.

He passed away about ten years ago.

Copernicus and Kepler were both dead by the time Newton (and Liebnitz) invented calculus and developed the law of universal gravitation.

I disagree. I think models are just things that kinda model reality but aren’t necessarily perfect. We have a model for electricity that current flows from positive to negative. It works, but it has little bearing on the reality that the charge carriers in a conductor are negatively charged and moving in the opposite direction. You get accurate equations and predictions (assuming you use electron hole carriers rather than positive carriers), but the reality is still that electrons are moving from negative to positive.

Yes, that’s (one meaning of) a model; it’s actually useful and all of the equations apply to it. The other example, with the weights and the rubber sheet, is not a model in that sense. The corresponding model with respect to gravity is “mass curves space, and motion is affected by that curvature.” It may not be true (though it would be a big shock if it weren’t), but it works, and you can describe the mass-space interaction mathematically, and get results that are consistent with observation. The rubber sheet thing only works as an analogy; there is no way to describe 3D space in terms of a stretchy surface that will actually reproduce the way mass moves. It’s like comparing electricity to a garden hose – it’s good for getting the point across, but it’s useless as a model.

The way I heard it was that a theory has only the alternative of being wrong. A model has a third option- it might be right but irrelevant.

A model is not the real thing. But it conveys ways of understanding some aspects of the real thing.

A theory is how we generalise what two or more things have in common, and is predictive.

A theory can embrace both the real thing and the model.