Mastering Scientific Computing with R

Paul Gerrard, Radia M. Johnson

• Publisher: Packt Publishing
• Year: 2015
• ISBN:
  9781783555253
• Topic: Ciencia de la computación
• Subtopic: Lenguajes de programación

Mastering Scientific Computing with R

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Table of Contents

Mastering Scientific Computing with R

Credits

About the Authors

About the Reviewers

www.PacktPub.com

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Why subscribe?

Free access for Packt account holders

Preface

What this book covers

What you need for this book

Who this book is for

Conventions

Reader feedback

Customer support

Downloading the example code

Downloading the color images of this book

Errata

Piracy

Questions

1. Programming with R

Data structures in R

Atomic vectors

Operations on vectors

Lists

Attributes

Factors

Multidimensional arrays

Matrices

Data frames

Loading data into R

Saving data frames

Basic plots and the ggplot2 package

Flow control

The for() loop

The apply() function

The if() statement

The while() loop

The repeat{} and break statement

Functions

General programming and debugging tools

Summary

2. Statistical Methods with R

Descriptive statistics

Data variability

Confidence intervals

Probability distributions

Fitting distributions

Higher order moments of a distribution

Other statistical tests to fit distributions

The propagate package

Hypothesis testing

Proportion tests

Two sample hypothesis tests

Unit root tests

Summary

3. Linear Models

An overview of statistical modeling

Model formulas

Explanatory variables interactions

Error terms

The intercept as parameter 1

Updating a model

Linear regression

Plotting a slope

Analysis of variance

Generalized linear models

Generalized additive models

Linear discriminant analysis

Principal component analysis

Clustering

Summary

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

Polynomial regression

Performing a polynomial regression in R

Spline regression

Nonparametric nonlinear methods

Kernel regression

Kernel weighted local polynomial fitting

Optimal bandwidth selection

A practical scientific application of kernel regression

Locally weighted polynomial regression and the loess function

Nonparametric methods with the np package

Nonlinear quantile regression

Summary

5. Linear Algebra

Matrices and linear algebra

Matrices in R

Vectors in R

Matrix notation

The physical functioning dataset

Basic matrix operations

Element-wise matrix operations

Matrix subtraction

Matrix addition

Matrix sweep

Basic matrixwise operations

Transposition

Matrix multiplication

Multiplying square matrices for social networks

Outer products

Using sparse matrices in matrix multiplication

Matrix inversion

Solving systems of linear equations

Determinants

Triangular matrices

Matrix decomposition

QR decomposition

Eigenvalue decomposition

Lower upper decomposition

Cholesky decomposition

Singular value decomposition

Applications

Rasch analysis using linear algebra and a paired comparisons matrix

Calculating Cronbach's alpha

Image compression using direct cosine transform

Importing an image into R

The compression technique

Creating the transformation and quantization matrices

Putting the matrices together for image compression

DCT in R

Summary

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

Understanding the basics of PCA

How does PCA relate to SVD?

Scaled versus unscaled PCA

PCA for dimension reduction

PCA to summarize wine properties

Choosing the number of principal components to retain

Formative constructs using PCA

Exploratory factor analysis and reflective constructs

Familiarizing yourself with the basic terms

Matrices of interest

Expressing factor analysis in a matrix model

Basic EFA and concepts of covariance algebra

Concepts of EFA estimation

The centroid method

Multiple actors

Direct factor extraction by principal axis factoring

Performing principal axis factoring in R

Other factor extraction methods

Factor rotation

Orthogonal factor rotation methods

Quartimax rotation

Varimax rotation

Oblique rotations

Oblimin rotation

Promax rotation

Factor rotation in R

Advanced EFA with the psych package

Summary

7. Structural Equation Modeling and Confirmatory Factor Analysis

Datasets

Political democracy

Physical functioning dataset

Holzinger-Swineford 1939 dataset

The basic ideas of SEM

Components of an SEM model

Path diagram

Matrix representation of SEM

The reticular action model (RAM)

An example of SEM specification

An example in R

SEM model fitting and estimation methods

Assessing SEM model fit

Using OpenMx and matrix specification of an SEM

Summarizing the OpenMx approach

Explaining an entire example

Specifying the model matrices

Fitting the model

Fitting SEM models using lavaan

The lavaan syntax

Comparing OpenMx to lavaan

Explaining an example in lavaan

Explaining an example in OpenMx

Summary

8. Simulations

Basic sample simulations in R

Pseudorandom numbers

The runif() function

Bernoulli random variables

Binomial random variables

Poisson random variables

Exponential random variables

Monte Carlo simulations

Central limit theorem

Using the mc2d package

One-dimensional Monte Carlo simulation

Two-dimensional Monte Carlo simulation

Additional mc2d functions

The mcprobtree() function

The cornode() function

The mcmodel() function

The evalmcmod() function

Data visualization

Multivariate nodes

Monte Carlo integration

Multiple integration

Other density functions

Rejection sampling

Importance sampling

Simulating physical systems

Summary

9. Optimization

One-dimensional optimization

The golden section search method

The optimize() function

The Newton-Raphson method

The Nelder-Mead simplex method

More optim() features

Linear programming

Integer-restricted opt...