3. Linear Models | Mastering Scientific Computing with R

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Table Of Contents

Mastering Scientific Computing with R

By : Paul Gerrard

3.6 (7)

Mastering Scientific Computing with R

3.6 (7)

By: Paul Gerrard

Overview of this book

If you want to learn how to quantitatively answer scientific questions for practical purposes using the powerful R language and the open source R tool ecosystem, this book is ideal for you. It is ideally suited for scientists who understand scientific concepts, know a little R, and want to be able to start applying R to be able to answer empirical scientific questions. Some R exposure is helpful, but not compulsory.

Preface

Preface

What this book covers

What you need for this book

Who this book is for

Conventions

Reader feedback

Customer support

Free Chapter

1. Programming with R

1. Programming with R

Data structures in R

Loading data into R

Basic plots and the ggplot2 package

Flow control

Functions

General programming and debugging tools

Summary

2. Statistical Methods with R

2. Statistical Methods with R

Descriptive statistics

Probability distributions

Fitting distributions

Hypothesis testing

Summary

3. Linear Models

3. Linear Models

An overview of statistical modeling

Linear regression

Analysis of variance

Generalized linear models

Generalized additive models

Linear discriminant analysis

Principal component analysis

Clustering

Summary

4. Nonlinear Methods

4. Nonlinear Methods

Nonparametric and parametric models

The adsorption and body measures datasets

Theory-driven nonlinear regression

Visually exploring nonlinear relationships

Extending the linear framework

Nonparametric nonlinear methods

Nonparametric methods with the np package

Summary

5. Linear Algebra

5. Linear Algebra

Matrices and linear algebra

The physical functioning dataset

Basic matrix operations

Triangular matrices

Matrix decomposition

Applications

Summary

6. Principal Component Analysis and the Common Factor Model

6. Principal Component Analysis and the Common Factor Model

A primer on correlation and covariance structures

Datasets used in this chapter

Principal component analysis and total variance

Formative constructs using PCA

Exploratory factor analysis and reflective constructs

Summary

7. Structural Equation Modeling and Confirmatory Factor Analysis

7. Structural Equation Modeling and Confirmatory Factor Analysis

Datasets

The basic ideas of SEM

Matrix representation of SEM

SEM model fitting and estimation methods

Comparing OpenMx to lavaan

Summary

8. Simulations

8. Simulations

Basic sample simulations in R

Pseudorandom numbers

Monte Carlo simulations

Monte Carlo integration

Rejection sampling

Importance sampling

Simulating physical systems

Summary

9. Optimization

9. Optimization

One-dimensional optimization

Linear programming

Quadratic programming

General non-linear optimization

Other optimization packages

Summary

10. Advanced Data Management

10. Advanced Data Management

Cleaning datasets in R

String processing and pattern matching

Floating point operations and numerical data types

Memory management in R

Missing data

The Amelia package

The mice package

Summary

Index

Index

Linear regression

Regression analysis is a statistical method used to estimate the relationship among continuous variables. Linear regression is the simplest and most frequently used type of regression analysis. The aim of linear regression is to describe the response variable y through a linear combination of one or more explanatory variables x1, x2, x3, …, xp. In other words, the explanatory variables get weighted with constants and then summarized. For example, the simplest linear model is y = a + bx, where the two parameters a and b are the intercept and slope, respectively. The model formula for this relationship in R is y ~ x. Note that all parameters are left out. So, if our linear model was y = a + bx + cz, then our model formula will be y ~ x + z.

Plotting a slope

Before going into a detailed example of linear regression analysis, I think it's worth going over how to plot a slope (or the change in y divided by the change in x). Say you wanted to plot a slope given the Cartesian coordinates...

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