2.2 Reading

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What are the differences between a “verbal model” and a “formal model”?
As explained in the paragraph “A Brief Note on Statistical Models”, formal models are not the same as statistical models. Still, we can learn a lot from Smaldino’s approach. Write down three insights from this paper that you would like to apply to your statistical modeling during this course.

Q1:

A verbal model can be non-specific about many things
- The level of analysis
- The definitions of its parts
- The relationships within the modeled system
Verbal models can appear powerful and useful partly because they employ strategic ambiguity.
- Because verbal models are so vague, they can apparently explain many different phenomena, even contradictory ones (e.g., the Cubist chicken).
A formal model, on the other hand, seeks to rigorously define its level of analysis, parts (variables), and relationships between these parts.

Q2:

You should define the level of analysis for your model
You should clearly operationalize the parts (variables) and explicitly define the hypothesized relationships (causal, correlational, definitional) between these parts.
The act of formally defining our models is productive. We can test a well-defined model using data. We can discuss such a model among experts with relative consensus about what the model means, and we can improve it.
- These things are harder to do with vague verbal models.
Every model imposes some violence upon reality.
- I.e., every model is wrong (but some are useful).
Because a model is a simplification, by necessity, we leave out many factors.
- This simplification is a feature, not a bug. Models abstract away the uninteresting details (i.e., noise) of a phenomenon.
- Even models that are too simple to be interesting represent useful building-blocks to expand upon when creating more complex, interesting models.
Data can be used to validate a model and to refine the model into a closer approximation of reality