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G89.2229 Lect 11W
G89.2229 Lect 1W
G89.2229 Multiple Regression
Week 11 (Wednesday)
Logistic Regression Review
Maximum Likelihood Estimates
Probit Regression and Example
Model Fit
Logistic Regression Review
Additive probability models are often not ideal.
p is bounded by [0,1].
Log odds of p [w(p)] has nice properties.
Unbounded, with w(p)=0 for p=.5.
Important equations
Logistic Example: Clinic Only
Maximum Likelihood Estimates
Strategy: Choose guesses for regression weights that makes the outcome seem likely under the model.
We use simple binomial probability theory to calculate the likelihood.
Choose some probability starting values
Calculate how likely each observation is under the initial probabilities
Summarize the overall likelihood
Modify the model to improve the likelihood
Review of Binomial Probability
What is the likelihood of rolling a "1" on a single die
What is the likelihood of rolling "snake eyes" with two dice
1/6
Review of Binomial Probability
What is the likelihood of rolling one "1" and one value other than "1"
What is the probability of Y (where Y is 1 when die is "1" and 0 otherwise)
Review of Binomial Probability
Suppose Suppose Y is a binary random variable with probability p. What is the probability of Y
Suppose that r=SY, where n observations are summed. What is probability of SY =r
Summarizing Likelihood
Probabilities of rare events get small.
The probability that a particular sample will have a specific pattern of values is very small.
Products of probabilities get exponentially smaller
Keeping track of these small numbers is facilitated by taking logs.
Ln likelihoods sum (whereas likelihoods need to be multiplied)
Example
This Excel spreadsheet shows how the regression coefficients change the fitted probabilities.

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