Lecture summary and notes Advanced Empirical Methods
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Module
Advanced Empirical Methods (FEM11164)
Institution
Erasmus Universiteit Rotterdam (EUR)
Summary of all lectures including the notes the professors made, including modules 1, 2, and 3. The course is obliged in several masters (behavioural, strategy and health economics). There is no exam, so these notes should enable you to make the three assignments that capture your grade for the cou...
1. Ordered categorical variables
Examples & Model setup
Discrete variable models
Dependent variable is the categorical variable
Ordered categorical variables are in categories with clear order (not
continuous)
Examples:
- Risk preferences, self-confidence, self-assessed health
Generally:
Y = 1, 2, …, J
- You describe this data with tabulate.
- It is an underlying latent variable between minus infinity and plus
infinity, but we observe the categorical variable (different
thresholds)
- This can be visually shown like this:
,We can use the ordered logit and the ordered probit model for an ordered
categorical dependent variable. If we make a linear model for latent
continuous variable y*:
The categorical variable with the underlying latent variable:
We can choose for ordered probit or ordered logit model; the choice
depends on the error term:
- Ordered probit: u follows a std. normal distribution.
- Ordered logit: u follows a logistic distribution.
They are almost identical, not much difference.
The probability that y=j with an ordered logit model:
Pay attention to the minuses in the formula (they are correct because of
the thresholds)
The probability that y=j with an ordered probit model:
,Ordered logit model
Exponential of minus infinity is zero, so
Exponential of infinity is infinity. Infinity / infinity = 1, so
, Ordered probit model is done in the same matter as logit
Maximum Likelihood Estimation
We take the log likelihood because this simplifies the likelihood function.
Capital L over all the observations
Small 1 over 1 observation
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