Home > Uncategorized > Three types of models – 5

## Three types of models – 5

It is important to understand that there are three type of models, corresponding the following diagram. The simplest type of model is a pattern in the data that we observe. A second type of model is a “mental model”. This is a structure we create in our own minds, in order to understand the patterns that we see in the observations. The third type of model is a structure of the hidden real world, which generates the patterns that we see. Some examples will be helpful in clarifying these ideas about the typology of models.

Empirical Models: The simplest kind of model consists of a pattern that we see in the observations. For example, read more

1. January 12, 2020 at 11:30 am

Why are these three seen as the only type of model? What about models based on valid theoretical understanding? These are what is actually being sought. Until theoretical validity is required, there can be no progress in any way. After all economists seem to have examined in minute detail all the wrong ways of analysis.

• January 12, 2020 at 1:49 pm

What does it mean for a model to be “theoretically valid”?

• January 12, 2020 at 2:22 pm

If all that one wishes to do is to represent a data set with a mathematical function, then any arbitrary equation can be fitted to that data set. This can be a useful model of that data set. However it has no theoretical validity at all. To even be possible of having theoretical validity a mathematical expression must conform to the quantity calculus — for aggregation, quantities must have identical physical units — multiplication and division of quantities is unrestricted — the taking of logarithms and the raising to non-integer powers of quantities is forbidden. Those are the requirements for possible theoretical validity. The final requirement is to demonstrate that the representation conforms to the empirical data. Those requirements provide theoretical validity.

2. January 12, 2020 at 2:36 pm

What you describe is EXACTLY what I categorize as a mental model — theoretical structures which generate predictions matching observed reality.

• January 12, 2020 at 4:30 pm

In your blog you say “All that matters about mental models is that they should provide a match to the observations. It does not matter whether or not they match the true structures of reality which produce the observations.”

I believe that what you are describing above is a null set. I am describing a quantitative relationship which I took to be not what you had intended to be within your class of mental models. If what I have described as theoretical validity is achieved then it will describe the true structures of reality.

3. January 13, 2020 at 2:06 am

You are expressing a standard misconception which is the subject of this sequence of post — if a mental (theoretical) model provides a good match to observed phenomena and forecasts well, then it MUST match hidden underlying real world structures. Read my posts on the Simpson’s Paradox to understand why this is not true. Hidden structures of reality are NOT DIRECTLY observable, and hence one can NEVER be sure that one has them correctly – knowledge of real world is always tentative. Mental models differ in terms of WHAT they try to do — Kantian models try to match the PHENOMENA, and abandon the attempt to match the Noumena (hidden structures of reality). Now it is TRUE that one can never be sure whether or not one has captured the hidden structures, but NONETHELESS we must make the attempt.

4. January 13, 2020 at 10:20 am

I do not believe that I have misconceived this. I am applying physical scientific thinking, Scientists know that their ideas may not be the whole truth but the test is are they good enough. That is all that is required to be considered as valid. Not the absolute truth you seem to be requiring. I only seek good enough. Take as example, Newton’s theory of gravitation and relativity. Even when we know that Newton is, by the standard of the absolute truth, wrong, we continue to use the theory for most normal purposes as true. Only if precise timing in different gravitational fields and for speeds close to that of light do Einstein and Newton differ. This example is an example of a Lakotosian progressive research programme with Einstein developing Newton’s theory further. Economists seem not to understand the significance of validity being NOT invalidated by the empirical evidence.

5. January 13, 2020 at 10:33 am

If you want to understand philosophy of science, I strongly recommend that you read Bhaskar’s Critical Realism A good intro text is by Andrew Collier: Critical Realism: An Introduction to Roy Bhaskar’s Philosophy. My discussion is grounded in this theory, and without understanding critical realism, you will be unable to understand what I am saying.

• January 13, 2020 at 11:13 am

As a physical scientist, I well understand critical reasoning. However, what I do not understand is why economists refer to authority rather than examine issues critically. When you use the term mental model, I took it to mean qualitative rather than quantitative analysis. I have been referring to mathematical forms meeting the standards of the quantity calculus. That seems to be very different to what you seem to be discussing.

6. January 15, 2020 at 7:24 pm

I quote: “mental models differ in terms of WHAT they try to do — Kantian models try to match the PHENOMENA, and abandon the attempt to match the Noumena (hidden structures of reality). Now it is TRUE that one can never be sure whether or not one has captured the hidden structures, but NONETHELESS we must make the attempt.”

I’m afraid I cannot see the distinction that Asad Zaman is trying to make. How would a scientist who is trying to explain phenomena conduct herself differently from one trying to “explain reality”? . In trying to match phenomena, the scientist is presumably trying to express or expose the structure or natural laws that generate the phenomena. How do you “match the Noumena” without matching the phenomena?

7. January 16, 2020 at 1:05 am

@Gerald Holtham – see my posts on Simpson’s Paradox on the WEA Pedagogy Blog for SEVERAL examples of how imagined structures of reality can produce a perfect match to observable data without matching each other or matching reality.

8. January 16, 2020 at 11:39 am

In your Simpson paradox blogs, you present totally contrived examples with partial information. You do not prove your assertion “You are expressing a standard misconception which is the subject of this sequence of post — if a mental (theoretical) model provides a good match to observed phenomena and forecasts well, then it MUST match hidden underlying real world structures.”
I stand by my statement that quantitative mathematical analysis in terms consistent with the quantity calculus and that is not invalidated by empirical is aligned with the actual factors producing the effects.
I would also commend studying Popper and Lakatos as providing appropriate understanding of scientific methodologies.

9. January 16, 2020 at 12:25 pm

Since you agree with Popper, remember that he says that no scientific theory can EVER be proven. This means that whether the theory is true or not can NEVER be known. Even if a theory provides a perfect match to observed phenomena until now, it may fail tomorrow. Even if it does not fail, a better theory which is more general explains more can be found.

• January 16, 2020 at 12:43 pm

Which is exactly the fundamental basis of the scientific method and what I said about Newton and Einstein forming a Lakatosian progressive research programme. Every physical scientist knows that relativity is not the absolute truth as it can not be reconciled with quantum mechanics but this does not stop both being used in appropriate situations.

10. January 16, 2020 at 1:43 pm

“if a mental (theoretical) model provides a good match to observed phenomena and forecasts well, then it MUST match hidden underlying real world structures” This statement is FALSE. We NEVER have a guarantee that a model which matches appearances also matches hidden reality. If you go to Madame Tussaud’s Wax museum you will see many figures which appear to be human and match all observables. But there is no match on the invisible insides. This is my last comment

• January 16, 2020 at 3:24 pm

PS. Useful models will always be based on valid abstract theory. The model is simply an instance of the underlying valid abstract theory.

11. January 16, 2020 at 3:09 pm

Your first assertion is false to fact. You are equating hypothesis to theoretical and the two are completely different concepts. I described the conditions are for achieving theoretical validity above, which you are ignoring. You also do not differentiate between a model and an abstract theory. They are utterly different! To say that the above is your last comment is unfortunate as when it is pointed out to you all your errors in understanding of what true science is, would seem to be a the beginning rather than an ending. I do not seek to condemn but to help improve your understanding.

12. January 16, 2020 at 4:25 pm

Without wanting to sound presumptuous, I do agree with Popper. I accept that the best theories are provisional, at least as far as their universality is concerned, however often they may have been corroborated. I also accept that there are likely to be many theories consistent with a given finite data set though inconsistent with each other. Therefore not all of them can be true. None of that answers my question. I still think you are making a distinction without a difference. I am not arguing that a theory that matches data or phenomena must be true. I am saying the only way you can test a theory is by matching it to data. A scientist trying to explain the data with a theory is a scientist looking for what you call the underlying reality. There is no difference. The theory is the nearest we can get to the underlying reality until it is superseded. I am sorry you have made your last comment because if I misunderstand you I would be happy to be corrected.

13. January 17, 2020 at 1:56 am

@ghholtham – your comments show that you are ahead of Salter, in recognizing the possibility of multiple and conflicting theories, all perfectly matched to observable evidence. The question of WHAT ELSE DO WE HAVE, other than observational evidence, in order to verify or disprove, or otherwise advance our theories. The answer is that we start our journey in life with a HUGE amount of built in-knowledge, not given to us by observations and logic.

14. January 17, 2020 at 4:10 am

Knowledge is generated by interactions between subject and object, and is not passively created by observations

15. January 17, 2020 at 8:05 am

Have you actually read what I wrote? I gave the example of Newton and Einstein both incomplete as they actually fail at quantum levels. I will add another pair, the Ideal gas law and van der Waal’s equation.
Please give one example where conflicting theories fully describe the empirical evidence perfectly.
What do you mean by an enormous amounts of built-in-knowledge?

• January 17, 2020 at 4:40 pm

Asad Zaman has insisted that he knows that two completely different explanations are able to predict/explain the same empirical data. I have denied that this is possible. I take that by his not demonstrating two different explanations, he is admitting that his claim is actually a null set. This is a critical test. Either I am right and he is wrong OR he is right and I am wrong. Silence is highly indicate of which of those is true.

16. January 17, 2020 at 5:17 pm

Well, I am split. I agree with Frank that I do not know what Asad can mean by built-in knowledge.
On the other hand I agree with Asad there is such a thing as observational equivalence and the available data at a point in time may not discriminate among theories. A steady-state universe and a big bang theory of the universe coexisted for decades before the discovery of background radiation etc settled the debate in favour of the big bang. Right now there are different theories about the nature of so-called dark matter – including the theory that it doesn’t exist. As an economist I can tell you that the small and dirty data sets we have allow competing theories to exist for a very long time. I think we must be at cross purposes because those points seem obvious.

• January 18, 2020 at 9:24 am

The examples you mention are significant. Science is trying to explain somethings which we are not able to observe so of course it will require real imagination. However any theoretical analysis will conform to the quantity calculus. This is not what economic analysis does. Asad Zaman is defending invalid analysis. The only possible valid quantitative analyses must conform to the quantity calculus. For production theory the only possible contender is my paper, “Transient Development” RWER-81. The mathematics predicts the real production possibilities quantitatively and not the qualitative diagrams found in text books.
If Asad Zaman is right about the possibility of there being two independent quantitative explanations for the same facts, he will give an example from within economics. His failure to do so is highly indicative.