Generalized Linear Models and Extensions: Fourth Edition

Generalized linear models (GLMs) are a type of statistical model that extends linear regression to non-Gaussian or discrete response variables. They are based on the exponential family of distributions and can be fitted in Stata using the glm command. GLMs offer advantages such as model diagnostics that are calculated and interpreted similarly regardless of the assumed distribution. The theory of GLMs involves showing how they are special cases of the exponential family, deriving maximum likelihood (ML) estimators and standard errors, and demonstrating how iteratively reweighted least squares is a consequence of ML estimation using Fisher scoring.

\n Format: Paperback / softback
\n Length: 598 pages
\n Publication date: 28 June 2018
\n Publisher: Stata Press
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Generalized linear models (GLMs) are a powerful tool for analyzing data with non-Gaussian or discrete response variables. They extend the traditional linear regression framework by allowing for more flexible and complex models. The foundation of GLM theory lies in the exponential family of distributions, a vast and diverse class that encompasses a wide range of models, including logit, probit, and Poisson models. While these models can be fitted in Stata using specialized commands, fitting them as GLMs with Statas glm command offers several advantages. One of the key benefits is that model diagnostics, such as residual plots, leverage the properties of the exponential family, making them applicable regardless of the specific distribution assumed.

In this text, we will delve into the theoretical aspects of GLMs, exploring how they are derived from the exponential family and how they can be used to model a wide range of phenomena. We will also discuss the computational aspects of GLMs, focusing on Stata, a popular statistical software package. Hardin and Hilbe provide a comprehensive guide to fitting GLMs in Stata, covering topics such as model selection, parameter estimation, and interpretation of results. They also introduce the concept of iteratively reweighted least squares (IRLS), a method of parameter estimation that is closely related to ML estimation and offers additional insights into the estimation process.

By understanding the principles of GLMs and their application in Stata, researchers can gain a deeper understanding of their data and make more informed decisions based on their findings. GLMs are a versatile tool that has found applications in various fields, including social sciences, economics, and health sciences. Whether you are working with binary or continuous response variables, GLMs can help you uncover patterns, relationships, and insights that would otherwise be hidden.

In conclusion, this text provides a comprehensive and accessible introduction to GLMs, covering both theoretical and computational aspects. It is an essential resource for researchers and practitioners interested in analyzing data with non-Gaussian or discrete response variables. By leveraging the power of GLMs and Stata, researchers can gain a deeper understanding of their data and make more informed decisions that can have a significant impact on their fields.

\n Weight: 1242g\n
Dimension: 187 x 241 x 41 (mm)\n
ISBN-13: 9781597182256\n
Edition number: 4 New edition\n