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3. A GLM is fitted to independent binary observations {y;} using the log link, log(T) = xẞ, i = 1,...,n, (xio, Xi1, " where Ti = E(y) denotes the probability of success, x¿ = Xip) is a vector of predictors and B = (30, ẞ1,..., ßp) is a vector of unknown parameters (a) Explain what issues may arise from use of the log link for binary observations. (b) Write down the log-likelihood of ẞ and show that the (j,k) element of the expected information matrix is given by n Πί -Xijxik (1 − πi) i=1 (You should derive from scratch. Do not quote any results from the lecture notes.)

3. A GLM is fitted to independent binary observations {y;} using the log link, log(T) = xẞ, i = 1,...,n, (xio, Xi1, " where Ti = E(y) denotes the probability of success, x¿ = Xip) is a vector of predictors and B = (30, ẞ1,..., ßp) is a vector of unknown parameters (a) Explain what issues may arise from use of the log link for binary observations. (b) Write down the log-likelihood of ẞ and show that the (j,k) element of the expected information matrix is given by n Πί -Xijxik (1 − πi) i=1 (You should derive from scratch. Do not quote any results from the lecture notes.)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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3. A GLM is fitted to independent binary observations {y;} using the log link, log(T) = xẞ, i = 1,...,n, (xio, Xi1, " where Ti = E(y) denotes the probability of success, x¿ = Xip) is a vector of predictors and B = (30, ẞ1,..., ßp) is a vector of unknown parameters (a) Explain what issues may arise from use of the log link for binary observations. (b) Write down the log-likelihood of ẞ and show that the (j,k) element of the expected information matrix is given by n Πί -Xijxik (1 − πi) i=1 (You should derive from scratch. Do not quote any results from the lecture notes.)
Transcribed Image Text:3. A GLM is fitted to independent binary observations {y;} using the log link, log(T) = xẞ, i = 1,...,n, (xio, Xi1, " where Ti = E(y) denotes the probability of success, x¿ = Xip) is a vector of predictors and B = (30, ẞ1,..., ßp) is a vector of unknown parameters (a) Explain what issues may arise from use of the log link for binary observations. (b) Write down the log-likelihood of ẞ and show that the (j,k) element of the expected information matrix is given by n Πί -Xijxik (1 − πi) i=1 (You should derive from scratch. Do not quote any results from the lecture notes.)
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