Home > data science, math education, statistics > What is a model?

What is a model?

September 28, 2012

I’ve been thinking a lot recently about mathematical models and how to explain them to people who aren’t mathematicians or statisticians. I consider this increasingly important as more and more models are controlling our lives, such as:

  • employment models, which help large employers screen through applications,
  • political ad models, which allow political groups to personalize their ads,
  • credit scoring models, which allow consumer product companies and loan companies to screen applicants, and,
  • if you’re a teacher, the Value-Added Model.
  • See more models here and here.

It’s a big job, to explain these, because the truth is they are complicated – sometimes overly so, sometimes by construction.

The truth is, though, you don’t really need to be a mathematician to know what a model is, because everyone uses internal models all the time to make decisions.

For example, you intuitively model everyone’s appetite when you cook a meal for your family. You know that one person loves chicken (but hates hamburgers), while someone else will only eat the pasta (with extra cheese). You even take into account that people’s appetites vary from day to day, so you can’t be totally precise in preparing something – there’s a standard error involved.

To explain modeling at this level, then, you just need to imagine that you’ve built a machine that knows all the facts that you do and knows how to assemble them together to make a meal that will approximately feed your family. If you think about it, you’ll realize that you know a shit ton of information about the likes and dislikes of all of your family members, because you have so many memories of them grabbing seconds of the asparagus or avoiding the string beans.

In other words, it would be actually incredibly hard to give a machine enough information about all the food preferences for all your family members, and yourself, along with the constraints of having not too much junky food, but making sure everyone had something they liked, etc. etc.

So what would you do instead? You’d probably give the machine broad categories of likes and dislikes: this one likes meat, this one likes bread and pasta, this one always drinks lots of milk and puts nutella on everything in sight. You’d dumb it down for the sake of time, in other words. The end product, the meal, may not be perfect but it’s better than no guidance at all.

That’s getting closer to what real-world modeling for people is like. And the conclusion is right too- you aren’t expecting your model to do a perfect job, because you only have a broad outline of the true underlying facts of the situation.

Plus, when you’re modeling people, you have to a priori choose the questions to ask, which will probably come in the form of “does he/she like meat?” instead of “does he/she put nutella on everything in sight?”; in other words, the important but idiosyncratic rules won’t even be seen by a generic one-size-fits-everything model.

Finally, those generic models are hugely scaled- sometimes there’s really only one out there, being used everywhere, and its flaws are compounded that many times over because of its reach.

So, say you’ve got a CV with a spelling error. You’re trying to get a job, but the software that screens for applicants automatically rejects you because of this spelling error. Moreover, the same screening model is used everywhere, and you therefore don’t get any interviews because of this one spelling error, in spite of the fact that you’re otherwise qualified.

I’m not saying this would happen – I don’t know how those models actually work, although I do expect points against you for spelling errors. My point is there’s some real danger in using such models on a very large scale that we know are simplified versions of reality.

One last thing. The model fails in the example above, because the qualified person doesn’t get a job. But it fails invisibly; nobody knows exactly how it failed or even that it failed. Moreover, it only really fails for the applicant who doesn’t get any interviews. For the employer, as long as some qualified applicants survive the model, they don’t see failure at all.

  1. Jonathan
    September 28, 2012 at 9:07 am

    Great post on an interesting and important topic..

    A few random reactions. As you know the Black Scholes model for pricing options is routinely used by people who know that most of its assumptions are wrong. In fact, it is used in a way that is inconsistent with its assumptions. That is, if is were correct, the same volatility should be used for all options but when people use it they put in different volatilities for different options. Someone (perhaps Bruno Dupire) said people were “putting the wrong number in the wrong model to get the right answer.” I think that captures it well.

    Black Scholes is also an example of another use of models — communication. People may use their own models in valuation but B-S is a useful way to communicate because everyone in the industry understands it.

    On a related subject: some people (Nassim Taleb for example) take the industry’s use of Black-Scholes to mean that people believe its assumptions to be true. But, sophisticated users of models should (and often do) use them despite the fact that they know their flaws.

    Of course, as you also know, models can go wildly wrong or lead people to horrible behavior. Most often, I think this is willful so the model is not really a source of the problem. The rating agencies models are a case in point. They were used to sell junk mortgages securities to unwitting buyers. But, in this case, as with the Value-Added model, it is probably intentional misuse because it is in the users interest.


  2. Aaron
    September 28, 2012 at 9:19 am

    Who doesn’t like to put nutella on everything?


  3. suevanhattum
    September 28, 2012 at 9:24 am

    And it may be that your ‘spelling error’ was the unconventional name of a company, or project, or book, or …, which you spelled correctly. As in “Helped the rock band, Townails, with its promotions.” (Yep, the computer has helpfully underlined Townails in red for me.)


  4. September 28, 2012 at 10:18 am

    Mix in to all this a tendency for people to very quickly start treating broad models, not as rough guidelines, but as infallible and better informed than us. In reaction to the inevitable chaos are those who want to use no models at all–which is impossible and is really just a “never use models” model. Plus, stupidity and immorality can make the best of models do horrible things.


  5. ppbnvnt
    September 28, 2012 at 3:04 pm

    Accepting the fallibility of models without getting paranoid is really difficult.

    Years ago, around the time of the mad cow disease mess I was talking to a doctor on the posibilities of ever catching the disease. IIRC, there was a moment she said that she was sure she would never get it because she only bought argentinian meat. I said that I had already heard on an argentinian mad cow case on TV, to which she replied that that was impossible because in Argentina cows graze freely instead of eating fodder.

    How did the argentinian cow get the disease then? Easy. Because she wasn’t argentinian. The farmer had imported the cows from a 3rd country and falsified the paperwork.

    Now suppose you are a spanish police high ranking government official and there is a pacific protest rally surounding the congress which is very annoying to your interests and you want to quickly get rid of it. Freedom of expression laws forbid you from breaking it up unless the protesters get violent. How can you get it done? Easy. Command undercover police officers to start a riot.



  6. Chyhe
    September 28, 2012 at 5:03 pm

    Hi Cathy! You are the best. I’m keeping my fingers crossed that your schedule frees up for summer 2013. we are not as boring as we look.


  7. Michael Hudson
    September 30, 2012 at 1:56 pm

    This is very clear, Cathy.
    I’ve copied it for my students.
    Michael Hudson


  8. October 3, 2012 at 10:04 pm

    Econometric models have many fatal flaws, convenient assumptions and self benefiting estimates which can be manipulated easily by the model’s creators to produce the results desired by their benefactors – almost always corporations, corporate minions and financial elites. These models are worse than useful, specially in the present time when they are considered relevant and valuable by being able to “explain” past major calamities even when they fail to predict a single future event – like the largest most disasterous financial bubble of all time which threatens all developed world economies, for instance.
    Regardless of the fact that these econometric models have failed to predict anything in the long term and precious little in the short term, they still have credence and are referred to when evaluating economic proposals!?
    It seems to me that the major advantage of these models is that they can be manipulated to “show” that by shifting ever more wealth to the top few percent of wealthiest individuals that somehow economies will recover. Obviously the popular definition of recover refers to Wall Street NOT Main Street. When they predict Main Street recovery the results are always ever more wealth shifted upwards to the top income producers (earners would be misleading because this group ‘earns’ nothing they loot everything) first and foremost with middle classes having to adjust living standards down to facilitate “recovery”.
    Why do we need models? We know what fuels a real economic ‘recovery’ – it is consumer demand for goods and services produced in country, full stop! There is simply no other metric which can predict or outcome which can produce economic recovery.
    Battling models which give us the choice between two or more vitally flawed econometric models which are not expected to predict future outcomes but may explain past outcomes!? This is what we are talking about!
    The unnecessary, confusing, and partial realities and the self serving convenient assumptions which populate these models seem strangely to add to their credibility, again – even though they are not capable of predicting economic anything.
    Economic solutions are basically simple – increase consumer demand and the economy will improve; decreases in consumer demand will produce economic stagnation and recession/depression. Who cares about manipulated models which very few understand and which fail to predict the serious errors in policy which, surprise surprise, produce economic disasters for the majority and unimagined increases in wealth – through transfers of wealth from middle classes – for the wealthiest few?


  1. September 30, 2012 at 7:37 am
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