lec23_slides - Generalized Linear Models 3 Maximum Likelihood in Logistic Regression I We have binary responses y1 yn and data on p explanatory

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Generalized Linear Models 3 April 24, 2019
Maximum Likelihood in Logistic Regression I We have binary responses y 1 , . . . , y n and data on p explanatory variables x ij , i = 1 , . . . , n and j = 1 , . . . , p .
Maximum Likelihood in Logistic Regression I We have binary responses y 1 , . . . , y n and data on p explanatory variables x ij , i = 1 , . . . , n and j = 1 , . . . , p . I We assume that y 1 , . . . , y n are independent Bernoulli random variables with parameters p 1 , . . . , p n .
Maximum Likelihood in Logistic Regression I We have binary responses y 1 , . . . , y n and data on p explanatory variables x ij , i = 1 , . . . , n and j = 1 , . . . , p . I We assume that y 1 , . . . , y n are independent Bernoulli random variables with parameters p 1 , . . . , p n . I We model the relationship between the response and explanatory variables by the formula log p i 1 - p i = β 0 + β 1 x i 1 + · · · + β p x ip . (1)
Maximum Likelihood in Logistic Regression I We have binary responses y 1 , . . . , y n and data on p explanatory variables x ij , i = 1 , . . . , n and j = 1 , . . . , p . I We assume that y 1 , . . . , y n are independent Bernoulli random variables with parameters p 1 , . . . , p n . I We model the relationship between the response and explanatory variables by the formula log p i 1 - p i = β 0 + β 1 x i 1 + · · · + β p x ip . (1) I Given data y 1 , . . . , y n and x ij for i = 1 , . . . , n and j = 1 , . . . , p , how can be estimate the parameters β 0 , . . . , β p .