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To date, statistics has tended to be neatly divided into two theoretical approaches or frameworks: frequentist (or classical) and Bayesian. Scientists typically choose the statistical framework to analyse their data depending on the nature and complexity of the problem, and based on their personal views and prior training on probability and uncertainty. Although textbooks and courses should reflect and anticipate this dual reality, they rarely do so. This accessible textbook explains, discusses, and applies both the frequentist and Bayesian theoretical frameworks to fit the different types of statistical models that allow an analysis of the types of data most commonly gathered by life scientists. It presents the material in an informal, approachable, and progressive manner suitable for readers with only a basic knowledge of calculus and statistics. Statistical Modeling with R is aimed at senior undergraduate and graduate students, professional researchers, and practitioners throughout the life sciences, seeking to strengthen their understanding of quantitative methods and to apply them successfully to real world scenarios, whether in the fields of ecology, evolution, environmental studies, or computational biology.
The Conceptual Basis for Fitting Statistical Models
General Introduction
Statistical Modeling: A short historical background
Estimating Parameters: The main purpose of statistical inference
Applying the Generalized Linear Model to Varied Data Types
The General Linear Model I: Numerical explanatory variables
The General Linear Model II: Categorical explanatory variables
The General Linear Model III: Interactions between explanatory variables
Model Selection: One, two, and more models fitted to the data
The Generalized Linear Model
When the Response Variable is Binary
When the Response Variable is a Count, Often with Many Zeros
Further Issues Involved in the Modeling of Counts
Models for Positive, Real-Valued Response Variables: Proportions and others
Incorporating Experimental and Survey Design Using Mixed Models
Accounting for Structure in Mixed/Hierarchical Models
Experimental Design in the Life Sciences: The basics
Mixed Hierarchical Models and Experimental Design Data