Discrete choice models Flashcards
What are discrete choice models?
Discrete choice models are econometric models used to explain and predict choices between two or more discrete alternatives. They estimate the probability that an individual or entity will choose a specific option based on observable factors.
How do discrete choice models differ from continuous dependent variable models?
Unlike continuous models where outcomes take any value, discrete choice models deal with categorical outcomes (e.g., binary 0/1 or multinomial categories).
Give three real-world examples of discrete choice scenarios.
- Consumer purchasing decisions (Buy = 1, Not Buy = 0). 2. Voting choices among multiple candidates. 3. Loan default decisions (Default = 1, No Default = 0).
What are the three main types of discrete choice models?
- Linear Probability Model (LPM) 2. Probit Model 3. Logit Model
What is the Linear Probability Model (LPM)?
LPM applies Ordinary Least Squares (OLS) regression to a binary dependent variable, estimating the probability of an event occurring as a linear function of explanatory variables.
What is the general formula for the Linear Probability Model?
P(Y = 1 | X) = α + βX + u
where:
P(Y = 1 | X) is the probability that event Y occurs given X
α is the intercept,
β represents the effect of X on P(Y =1),
X represents the independent variable(s), and
u is the error term accounting for unexplained variation.
Why is LPM easy to estimate and interpret?
LPM uses OLS regression, making estimation straightforward, and the coefficient β directly represents the change in probability for a one-unit increase in X.
What are the major limitations of LPM?
- Predicted probabilities can be outside the 0-1 range. 2. Assumes constant marginal effects. 3. Suffers from heteroskedasticity. 4. Residuals are not normally distributed.
How does the Probit model improve on LPM?
The Probit model ensures probabilities stay between 0 and 1 by assuming a cumulative normal distribution function (CDF) instead of a linear function.
What is the general formula for the Probit model?
P(Y = 1 | X) = Φ(β0 + β1X), where:
P(Y = 1 | X) is the probability that event Y occurs given X,
Φ represents the standard normal cumulative distribution function (CDF),
β0 is the intercept,
β1 represents the effect of X on the probit index, and
X represents the independent variable(s).
Why are Probit model coefficients difficult to interpret?
The coefficients represent changes in the probit score rather than direct probability changes, requiring conversion using the normal CDF.
What are the advantages of the Probit model?
- Ensures probabilities remain between 0 and 1.
- Captures non-linearity in decision-making.
- Corrects heteroskedasticity issues.
What are the main limitations of the Probit model?
- Coefficients require additional computation for interpretation.
- Requires Maximum Likelihood Estimation (MLE), making it computationally complex.
How does the Logit model differ from the Probit model?
The Logit model assumes a logistic distribution instead of a normal distribution, ensuring probabilities stay between 0 and 1.
What is the general formula for the Logit model?
P(Y = 1 | X) = 1 / (1 + e^-(β0 + β1X)), where:
P(Y = 1 | X) is the probability that event Y occurs given X,
β0 is the intercept, β1 represents the effect of X on the log-odds of Y occurring,
X represents the independent variable(s),
e is Euler’s number (~2.718), and the denominator ensures probabilities stay within the 0-1 range.
How do Logit model coefficients differ from LPM and Probit?
Logit coefficients represent log odds instead of probabilities. A one-unit increase in X changes the odds of Y = 1 by e^β.
What are the advantages of the Logit model?
- Keeps probabilities between 0 and 1.
- Handles non-linearity better than LPM.
- Provides easier interpretation using odds ratios.
What are the limitations of the Logit model?
- Requires MLE for estimation.
- Coefficients must be transformed for direct interpretation.
Why are Probit and Logit models preferred over LPM?
LPM has theoretical limitations, such as predicting probabilities outside the 0-1 range. Probit and Logit models provide more reliable probability estimates.
What is the key difference between the Probit and Logit models?
The Probit model assumes a normal distribution, while the Logit model assumes a logistic distribution, leading to slightly different probability curves.
