GRA%206020%20Multivariate%20Statistics;%20The%20Linear%20Probability%20model%20and%20The%20Logit%20Model%20(Probit)

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GRA 6020Multivariate Statistics The Linear
Probability model and The Logit Model (Probit)

• Ulf H. Olsson
• Professor of Statistics

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Binary Response Models

• The Goal is to estimate the parameters

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The Logit Model

• The Logistic Function

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The Logistic Curve G (The Cumulative Normal
Distribution)
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The Logit Model
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Logit Model for Pi
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Simple Example
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Simple Example
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The Logit Model

• Non-linear gt Non-linear Estimation gtML
• Model can be tested, but R-sq. does not work.
  Some pseudo R.sq. have been proposed.
• Estimate a model to predict the probability

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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-fileBinomgra1.sav)

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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

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Introduction to the ML-estimator
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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

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Goodness of Fit

• The lower the better (0 perfect fit)

• Some Pseudo R-sq.

• The Wald test for the individual parameters