The Model Thinker: What You Need to Know to Make Data Work for You (pp. 13-25)Chapter 2: Why Model?Types of ModelsEmbodiment ApproachAnalogy ApproachAlternative Reality ApproachGood ModelsThe Seven Uses of ModelsREDCAPEReasonExplainDesignCommunicateActPredictExplore
Knowing reality means constructing systems of transformations that correspond, more or less adequately, to reality.
- Jean Piaget
Aims to capture reality and stresses realism
Typically focus on he important parts and either strip away unnecessary dimensions or lump them together
Aims to abstract from reality
Tries to capture the essence of a process, system, or phenomenon, without necessarily strictly adhering to reality
The "favorite classroom example" is a model which makes an estimate about the amount of leather you might find in a cowhide.
When a physicist assumes way friction but otherwise makes realistic assumptions, she takes the embodiment approach. When an economist represents competing firms a different species and defines produce niches, she makes an analogy. She does so using a model developed to embody a different system.
No bright line differentiates the embodiment approach from the analogy approach.
Purposely does not represent or capture reality
Functions as analytic and computational playgrounds in which we can explore possibilities
These models allow researchers to imagine new things and test out-of-the-box hypotheses
Allows us to ask questions like:
Models should be communicable and tractable
Communicable means that a models would be describable in some formal language like mathematics or computer code
We also need to provide formal definitions of conceptual terms like beliefs or preferences
How tractable something is means how amenable it is to analysis — we should be able to test the model
Good models should also be described as simply as possible
This principal is often referred to as Ockham's Razor
|Reason||To identify conditions and deduce logical implications|
|Explain||To provide (testable) explanations for empirical phenomena|
|Design||To choose features of institutions, policies, and rules|
|Communicate||To relate knowledge and understandings|
|Act||To guide policy choices and strategic actions|
|Predict||To make numerical and categorical predictions of future and unknown phenomena|
|Explore||To investigate possibilities and hypotheticals|
When constructing a model, we identify the most important actors, entities, and relevant characteristics. We then attempt to describe how they interact and aggregate, which enables us to conclude what should follow from what, and why. This allows us to improve our reasoning about what we are studying. However, to do this we need formal logic.
Formal logic allows us to:
Simpson's paradox — individual subpopulations can contain a larger percentage of women than men but the total population can still contain a larger percentage of men
Parrondo's paradox — it is possible for two losing bets, when played alternately, to produce a positive expected return
Friendship paradox - most people have fewer friends than their friends have, on average
We should not dismiss these examples as mathematical novelties. Each has practical applications: efforts to increase the population of women could backfire, combinations of losing investments could win, and the total length of a network of electric lines, pipelines, ethernet lines, or roads could be reduced by adding more nodes.
Uncover mathematical relationships
Reveal the conditionality of truths (most important)
Logic can show us when our models will break and under what conditions they will thrive
Critics of models sometimes say that we are simply repackaging what we already know into fancy math
What this misses, however, is the conditional form that models offer
If we try to lead our lives or manage others by unconditional rules, we find ourselves lost in a sea of opposite proverbs. Are two heads better than one? Or, do too many cooks spoil the broth?
|Two heads are better than one||Too many cooks spoil the broth|
|He who hesitates is lost||A stitch in time saves nine|
|Tie yourself to the mast||Keep your options open|
|The perfect is the enemy of the good||Do it well or not at all|
|Actions speak louder than words||The pen is mightier than the sword|
(Examples above are taken from the text.)
Models provide clear logical explanations for empirical phenomena
Physical phenomena are much more predictable than social phenomena
The most effective models explain both straightforward outcomes and puzzling ones
As for the claim that models can explain anything: it is true, they can. However, a model-based explanation includes formal assumptions and explicitly causal chains. Those assumptions and causal chains can be taken to data. A model that claims that high levels of criminal behavior can be explained by low probabilities of being caught can be test.
Models aid in design by providing frameworks within which we can contemplate the implications of choices
By creating models you can test specific frameworks to understand how different types of designs lead to specific conditional outcomes
Page provides the example of the FCC creating a model for auctioning radio licenses
By creating a common representation, models improve communication
acceleration— and does so concisely in equation form
Formally defining abstract concepts like political ideology offer this same precision within communication
We can also define abstract concepts in different ways, ideology can be defined based on voting records or text analysis of speeches, for example
These models allow us to clearly compare entities based on the constructed "scale" — i.e. politician is more liberal than politician
While it is always possible that some of these mathematical constructions are not perfect, this is why we test them against data
The great end of life is not knowledge but actions.
— Francis Bacon
Important decisions made by governments and institutions typically rely on models. Very important decisions rely on very sophisticated models.
Network models were made of the financial institutions at play during the 2008 bail out to inform which banks to help
Physical models may be built to inform policymakers decisions as well
The general take away here is that models can be helpful for showing if it makes sense to do or not do something specific in the real world. This (to me at least) ties closely to the Design section.
In perhaps the most famous example of applying an explanatory model to predict, the French mathematician Urban Le Verrier applied the Newtonian laws created to explain planetary movements to evaluate the discrepancies in the orbit of Uranus. He discovered the orbits to be consistent with the presence of a large planet in the out region of the solar system. On September 18, 1846, he sent his prediction to the Berlin Observatory. Five days later, astronomers located the planet Neptune exactly where Le Verrier had predicted it would be.
However, prediction explanation!
Models can predict without explaining and vice versa
Models are used to explore intuitions and possibilities
Abandoning constraints of reality can spur creativity
What if we make all buses free?
What if we let students choose which assignments determine their course grades?
Exploration sometimes can also simply mean comparing common assumptions across domains
Notes by Matthew R. DeVerna