An Introduction to Generalized Linear Models by Annette J. Dobson

By Annette J. Dobson

Carrying on with to stress numerical and graphical tools, An creation to Generalized Linear versions, 3rd Edition offers a cohesive framework for statistical modeling. This new version of a bestseller has been up-to-date with Stata, R, and WinBUGS code in addition to 3 new chapters on Bayesian research.

Like its predecessor, this variation offers the theoretical heritage of generalized linear versions (GLMs) ahead of concentrating on tools for studying specific varieties of facts. It covers general, Poisson, and binomial distributions; linear regression versions; classical estimation and version becoming tools; and frequentist tools of statistical inference. After forming this origin, the authors discover a number of linear regression, research of variance (ANOVA), logistic regression, log-linear types, survival research, multilevel modeling, Bayesian versions, and Markov chain Monte Carlo (MCMC) equipment.

Using well known statistical software program courses, this concise and obtainable textual content illustrates sensible methods to estimation, version becoming, and version comparisons. It comprises examples and routines with entire info units for almost all of the types lined.

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Additional resources for An Introduction to Generalized Linear Models

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In this form, the linear component µ = Xβ represents the “signal” and e represents the “noise”, random variation or “error”.

The slope parameters β1 and β2 represent the average increases in birthweight for each additional week of gestational age. 3 Birthweight (grams) and gestational age (weeks) for boys and girls. 3. β1 = β2 = β (that is, the growth rates are equal and so the lines are parallel), against the alternative hypothesis H1 : β1 = β2 . 6) E(Yjk ) = µjk = αj + βj xjk ; Yjk ∼ N(µjk , σ 2 ). 7) EXAMPLES 25 The probability density function for Yjk is 1 1 f (yjk ; µjk ) = √ exp[− 2 (yjk − µjk )2 ]. 7). The log-likelihood function is J K l1 (α1 , α2 , β1 , β2 ; y) = j=1 k=1 1 1 [− log(2πσ 2 ) − 2 (yjk − µjk )2 ] 2 2σ 1 1 = − JK log(2πσ 2 ) − 2 2 2σ J K j=1 k=1 (yjk − αj − βj xjk )2 , where J = 2 and K = 12 in this case.

We want to know if, on average, they retain a weight loss twelve months after the program. 8 Weights of twenty men before and after participation in a “waist loss” program. 0 Let Yjk denote the weight of the kth man at the jth time, where j = 1 before the program and j = 2 twelve months later. Assume the Yjk ’s are independent random variables with Yjk ∼ N(µj , σ 2 ) for j = 1, 2 and k = 1, . . , 20. (a) Use an unpaired t-test to test the hypothesis H0 : µ1 = µ2 versus H1 : µ1 = µ2 . EXERCISES 43 (b) Let Dk = Y1k −Y2k , for k = 1, .

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