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

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

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

Ulf H. Olsson The Logit Model The Logistic Function

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

Ulf H. Olsson The Logit Model

Ulf H. Olsson Logit Model for P i

Ulf H. Olsson Simple Example

Ulf H. Olsson Simple Example

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

Ulf H. Olsson The Logit Model (example) Estimate a model to predict the probability that a person has a job, given yrs. at a university and score at the dancing contest. (data see SPSS-file:Binomgra1.sav)

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:

Ulf H. Olsson Introduction to the ML-estimator

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

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