Statistical Models

Question 1

How can statistical models be described?

Answer 1

1. All models are simplifications (thus both limiting and enabling) —> doctrine of elementarism vs. wholism -> all models are wrong, but some are useful
2. Models serve both understanding and prediction.

Question 2

What is a model‘s utility!

Answer 2

1. Alithea: unhiding what might otherwise remain hidden

2. Adequatio Intellectus: providing insight

Question 3

What are three modeling languages?

Answer 3

1. verbal
2. mathematical: we capture models theough mathematics to add greater precision (eg. game theory)
3. computational: we translate the mathematical model into syntax that yields bumeric estimates

Question 4

What is the generic form of a mathematical model?

Answer 4

h(y,O) = f(x,B)

y is the outcome variable
x is a predictor of the outcome variable
f and h are functions
B and O are parameters that are typically unknown

Question 5

What are examples of mathematical models?

Answer 5

1. Exponential: small marginal effect (L)
2. linear
3. logistic: steep decline (S umgekehrt)
4. radical: opposite pattern od exponential

Question 6

What is a discrete change?

Answer 6

If we change the predictor by a unit, assuming all else remains equal, then y changes by … Units (je nach Modell)

Question 7

What is a marginal effect?

Answer 7

A change in predictor x, assuming all else remains equal, then there is a rate of change given by limes.

Question 8

What are the attributes of statistical models?

Answer 8

Statistical models are mathematical models with two distinctive characteristics:

1. Empirical: data generating process
2. stochastic: uncertainty due to incompleteness of the model

Question 9

What are the ingredients of statistical model?

Answer 9

Following generalized linear modeling framework:

1. Distribution
2. Outcome
3. Linear Predictor
4. Link Function

Question 10

What does the distribution so?

Answer 10

It captures the stochastics
defined over how we think y behaves
should comply with the support if Y

Question 11

What is the outcome?

Answer 11

One or more parameters that are driven by the predictors

Not all parameters have to be outcomes, some parameters are nuisance parameters (they drive the distribution but are if no theoretical interest)

Question 12

What is the linear predictor?

Answer 12

A function that is linear in the parameters: parameters occur as multiplicative weights in an additive function (B0 + B1X1 +….)

Question 13

What is a link function?

Answer 13

The link function connects an outcome of interest to a linear predictor.

Question 14

How can models be seen as truth, when they are limited and possibly distorting?

Answer 14

greek word aletheia=unhiddenness
-> a model can be seen as truth insofar as it makes unhidden aspects od the situation being nodelled that were previously hidden

greek word adequatio intellectus: the model does not depend on being the whole truth but simply on wherher it is adequate to reveal some aspects of reality to our insight.

Question 15

What are the five stages in statistical modelling?

Answer 15

1. Identification: process of finding or choosing an appropriate model for a given situation (e.g. conceptual or empirical or eclectic)
2. Estimation and fitting: moving from the general model to the specific numerical form = fitting. process of assigning numerical values to parameters = Estimation.
3. Validation: value and validity
4. Application:
5. Iteration:

Question 16

What are sources of uncertainty in modelling?

Answer 16

• Identification Uncertainty: possibility of error in the identification process
• the world changes -> models will become more uncertain over time
• Data: Sampling variation