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GRA 6020 Multivariate Statistics; The Logit Model Introduction to Multilevel Models

GRA 6020 Multivariate Statistics; The Logit Model Introduction to Multilevel Models. Ulf H. Olsson Professor of Statistics. The Logit Model. The Logistic Function e ~ 2.7 1828 1828. The Logit Model. Logit Model for P i. Binary Response Models.

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GRA 6020 Multivariate Statistics; The Logit Model Introduction to Multilevel Models

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  1. GRA 6020Multivariate Statistics; The Logit ModelIntroduction to Multilevel Models Ulf H. Olsson Professor of Statistics

  2. The Logit Model • The Logistic Function • e ~ 2.7 1828 1828 Ulf H. Olsson

  3. The Logit Model Ulf H. Olsson

  4. Logit Model for Pi Ulf H. Olsson

  5. 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

  6. The Marginal effect Ulf H. Olsson

  7. Simple interaction Model; X-continuous and D dichotomous Ulf H. Olsson

  8. 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

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

  10. 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

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

  12. Multilevel Models More general than panel models

  13. Ulf H. Olsson

  14. School Pupil School Neighbourhood Pupil Classifying Structures Simple hierarchy Cross classifications Multiple membership Ulf H. Olsson

  15. Ulf H. Olsson

  16. Ulf H. Olsson

  17. Simple panel model Studying nine individuals and five time periodes; i= 1,2,..,9. t= 1,..,5; Y: Wages; X:Education level Ulf H. Olsson

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