PSU STAT 544 - Quasilikelihood and GEE (22 pages)

Previewing pages 1, 2, 21, 22 of 22 page document View the full content.
View Full Document

Quasilikelihood and GEE



Previewing pages 1, 2, 21, 22 of actual document.

View the full content.
View Full Document
View Full Document

Quasilikelihood and GEE

39 views

Lecture Notes


Pages:
22
School:
Pennsylvania State University
Course:
Stat 544 - Categorical Data

Unformatted text preview:

1 Stat 544 Lecture 22 Quasilikelihood and GEE Quasilikelihood Suppose that we observe responses y1 y2 yN which we want to relate to covariates The ordinary linear regression model is yi N xTi 2 where xi is a vector of covariates is a vector of coe cients to be estimated and 2 is the error variance Now let s generalize this model in two ways Introduce a link function for the mean E yi i g i xTi We could also write this as E yi i 1 where the covariates and the link become part of the function i For example in a loglinear model we would have i exp xTi 2 Stat 544 Lecture 22 Allow for heteroscedasticity so that Var yi Vi 2 In many cases Vi will depend on the mean i and therefore on and possibly on additional unknown parameters e g a scale factor For example in a traditional overdispersed loglinear model we would have Vi 2 i 2 exp xTi A maximum likelihood estimate for under this model could be computed by a Fisher scoring procedure ML estimates have two nice theoretical properties they are approximately unbiased and highly e cient Interestingly the asymptotic theory underlying these properties does not really depend on the normality of yi but only on the rst two moments That is if the mean function 1 and the variance function 2 are correct but the distribution of yi is not normal the estimate of obtained by maximizing the normal loglikelihood from yi N i Vi is still asymptotically unbiased and e cient 3 Stat 544 Lecture 22 Quasi scoring If we maximize the normality based loglikelihood without assuming that the response is normally distributed the resulting estimate of is called a quasilikelihood estimate The iterative procedure for computing the quasilikelihood estimate called quasi scoring proceeds as follows First let s collect the responses and their means into vectors of length N 2 2 3 3 y1 1 6 6 7 7 6 y 7 6 7 6 2 7 6 2 7 6 7 7 y 6 7 6 6 7 6 7 6 7 4 4 5 5 yN N Also let V be the N N matrix with V1 VN on the diagonal and zeros elsewhere Finally let D be the N p matrix



View Full Document

Access the best Study Guides, Lecture Notes and Practice Exams

Loading Unlocking...
Login

Join to view Quasilikelihood and GEE and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view Quasilikelihood and GEE and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?