An Introduction to Generalized Linear Models by Annette J. Dobson PDF

By Annette J. Dobson

ISBN-10: 0412311003

ISBN-13: 9780412311000

ISBN-10: 0412311100

ISBN-13: 9780412311109

ISBN-10: 1489972528

ISBN-13: 9781489972521

Carrying on with to stress numerical and graphical equipment, An advent to Generalized Linear types, 3rd Edition offers a cohesive framework for statistical modeling. This re-creation 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 types (GLMs) sooner than concentrating on tools for interpreting specific types of info. It covers basic, Poisson, and binomial distributions; linear regression types; classical estimation and version becoming tools; and frequentist equipment of statistical inference. After forming this beginning, the authors discover a number of linear regression, research of variance (ANOVA), logistic regression, log-linear types, survival research, multilevel modeling, Bayesian types, and Markov chain Monte Carlo (MCMC) tools.

Using well known statistical software program courses, this concise and available textual content illustrates useful techniques to estimation, version becoming, and version comparisons. It comprises examples and routines with whole info units for almost all of the versions covered.

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Additional info for An Introduction to Generalized Linear Models

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Response variables Y 1 , ••• , Y N which are assumed to share the same distribution from the exponential family; 2. , J 3. l,) = x;p where This chapter concludes with three examples of generalized linear models. 1 Linear model One special case is the linear model y = xp + e where the elements e, of e are independent and all have the distribution N(O, a 2 ). e. l,. All the models discussed in Chapter 2 are of this form. 2 Historical linguistics Consider a language which is the descendant of another language as, for example, modern Greek is a descendant of ancient Greek, or the Romance languages are descendants of Latin.

Theoretical results for generalized linear models are given by Fahrmeir and Kaufman (1985). The basic idea is that if is a consistent estimator of a parameter 8 and var (e) is the variance of the estimator then for large samples the following results hold, at least approximately: e 1. e is an unbiased estimator of (] (because for a consistent estimator E( e) approaches 8 as the sample size becomes large); 2. The statistic e- e V[var (e)] N(O, 1); or equivalently, the distribution Normal has the standard distribution with one degree chi-squared a has statistic square of the of freedom 50 Inference ce- 8) 2 A " ~-XI var ( 8) The generalization of these results to p parameters is as follows.

5 respectively), we need to know the sampling distribution of the minima of the sums of squares. By analogous arguments to those used in the previous example, it can be shown that (S 1/a 2 ) ~ X~K- 4 and if H 0 is correct then (S 0 /a 2 ) ~ X~K- 3 . In each case the number of degrees of freedom is the number of observations minus the number of parameters estimated. 2 which is certainly not statistically significant, so the data do not provide evidence against the hypothesis {3 1 = {3 2 and we have reason for preferring the simpler Model 0.

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An Introduction to Generalized Linear Models by Annette J. Dobson

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