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Binary Response Models for Multivariate Statistics

Dive into the Logit and Probit models to estimate parameters for binary response data. Learn about the Logistic Curve, ML estimation, and partial effects analysis. Discover significance testing and model fitting methods.

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Binary Response Models for Multivariate Statistics

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

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

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

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

  5. The Logit Model Ulf H. Olsson

  6. Logit Model for Pi Ulf H. Olsson

  7. Simple Example Ulf H. Olsson

  8. Simple Example Ulf H. Olsson

  9. 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 Ulf H. Olsson

  10. 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: Ulf H. Olsson

  11. Introduction to the ML-estimator Ulf H. Olsson

  12. 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 Ulf H. Olsson

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

  14. The Wald Test Ulf H. Olsson

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

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