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GRA 6020 Multivariate Statistics; The Linear Probability model and The Logit Model (Probit) Ulf H. Olsson Professor of Statistics.

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Presentation on theme: "GRA 6020 Multivariate Statistics; The Linear Probability model and The Logit Model (Probit) Ulf H. Olsson Professor of Statistics."— Presentation transcript:

1 GRA 6020 Multivariate Statistics; The Linear Probability model and The Logit Model (Probit) Ulf H. Olsson Professor of Statistics

2 Ulf H. Olsson Binary Response Models The Goal is to estimate the parameters

3 Ulf H. Olsson The Logit Model The Logistic Function e ~ 2.71821828

4 Ulf H. Olsson The Logistic Curve G (The Cumulative Normal Distribution)

5 Ulf H. Olsson The Logit Model

6 Ulf H. Olsson Logit Model for P i

7 Ulf H. Olsson Simple Example

8 Ulf H. Olsson Simple Example

9 Ulf H. Olsson The Logit Model Non-linear => Non-linear Estimation =>ML Model can be tested, but R-sq. does not work. Some pseudo R.sq. have been proposed. Estimate a model to predict the probability

10 Ulf H. Olsson Binary Response Models The magnitude of each effect is not especially useful since y* rarely has a well-defined unit of measurement. But, it is possible to find the partial effects on the probabilities by partial derivatives. We are interested in significance and directions (positive or negative) To find the partial effects of roughly continuous variables on the response probability:

11 Ulf H. Olsson Introduction to the ML-estimator

12 Ulf H. Olsson Introduction to the ML-estimator The value of the parameters that maximizes this function are the maximum likelihood estimates Since the logarithm is a monotonic function, the values that maximizes L are the same as those that minimizes ln L

13 Ulf H. Olsson Goodness of Fit The lower the better (0 – perfect fit) Some Pseudo R-sq. The Wald test for the individual parameters

14 Ulf H. Olsson The Wald Test

15 Ulf H. Olsson Example of the Wald test Consider a simple regression model


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