Book Image

R Statistics Cookbook

By : Francisco Juretig
2 (2)
Book Image

R Statistics Cookbook

2 (2)
By: Francisco Juretig

Overview of this book

R is a popular programming language for developing statistical software. This book will be a useful guide to solving common and not-so-common challenges in statistics. With this book, you'll be equipped to confidently perform essential statistical procedures across your organization with the help of cutting-edge statistical tools. You'll start by implementing data modeling, data analysis, and machine learning to solve real-world problems. You'll then understand how to work with nonparametric methods, mixed effects models, and hidden Markov models. This book contains recipes that will guide you in performing univariate and multivariate hypothesis tests, several regression techniques, and using robust techniques to minimize the impact of outliers in data.You'll also learn how to use the caret package for performing machine learning in R. Furthermore, this book will help you understand how to interpret charts and plots to get insights for better decision making. By the end of this book, you will be able to apply your skills to statistical computations using R 3.5. You will also become well-versed with a wide array of statistical techniques in R that are extensively used in the data science industry.

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Table of Contents (12 chapters)
Preface
Preface
Who this book is for
What this book covers
To get the most out of this book
Sections
Get in touch
Free Chapter
1
Getting Started with R and Statistics
Getting Started with R and Statistics
Introduction
Technical requirements
Maximum likelihood estimation
Calculating densities, quantiles, and CDFs
Creating barplots using ggplot
Generating random numbers from multiple distributions
Complex data processing with dplyr
3D visualization with the plot3d package
Formatting tabular data with the formattable package
Simple random sampling
Creating diagrams via the DiagrammeR package
C++ in R via the Rcpp package
Interactive plots with the ggplot GUI package
Animations with the gganimate package
Using R6 classes
Modeling sequences with the TraMineR package
Clustering sequences with the TraMineR package
Displaying geographical data with the leaflet package
2
Univariate and Multivariate Tests for Equality of Means
Univariate and Multivariate Tests for Equality of Means
Introduction
The univariate t-test
The Fisher-Behrens problem
Paired t-test
Calculating ANOVA sum of squares and F tests
Two-way ANOVA
Type I, Type II, and Type III sum of squares
Random effects
Repeated measures
Multivariate t-test
MANOVA
3
Linear Regression
Linear Regression
Introduction
Computing ordinary least squares estimates
Reporting results with the sjPlot package
Finding correlation between the features
Testing hypothesis
Testing homoscedasticity
Implementing sandwich estimators
Variable selection
Ridge regression
Working with LASSO
Leverage, residuals, and influence
4
Bayesian Regression
Bayesian Regression
Introduction
Getting the posterior density in STAN
Formulating a linear regression model
Assigning the priors
Doing MCMC the manual way
Evaluating convergence with CODA
Bayesian variable selection
Using a model for prediction
GLMs in JAGS
5
Nonparametric Methods
Nonparametric Methods
Introduction
The Mann-Whitney test
Estimating nonparametric ANOVA
The Spearman's rank correlation test
LOESS regression
Finding the best transformations via the acepack package
Nonparametric multivariate tests using the npmv package
Semiparametric regression with the SemiPar package
6
Robust Methods
Robust Methods
Introduction
Robust linear regression
Estimating robust covariance matrices
Robust logistic regression
Robust ANOVA using the robust package
Robust principal components
Robust Gaussian mixture models with the qclust package
Robust clustering
7
Time Series Analysis
Time Series Analysis
Introduction
The general ARIMA model
Seasonality and SARIMAX models
Choosing the best model with the forecast package
Vector autoregressions (VARs)
Facebook's automatic Prophet forecasting
Modeling count temporal data
Imputing missing values in time series
Anomaly detection
Spectral decomposition of time series
8
Mixed Effects Models
Mixed Effects Models
Introduction
The standard model and ANOVA
Some useful plots for mixed effects models
Nonlinear mixed effects models
Crossed and nested designs
Robust mixed effects models with robustlmm
Choosing the best linear mixed model
Mixed generalized linear models
9
Predictive Models Using the Caret Package
Predictive Models Using the Caret Package
Introduction
Data splitting and general model fitting
Preprocessing
Variable importance and feature selection
Model tuning
Classification in caret and ROC curves
Gradient boosting and class imbalance
Lasso, ridge, and elasticnet in caret
Logic regression
10
Bayesian Networks and Hidden Markov Models
Bayesian Networks and Hidden Markov Models
Introduction
A discrete Bayesian network via bnlearn
Conditional independence tests
Continuous and hybrid Bayesian networks via bnlearn
Interactive visualization of BNs with the bnviewer package
An introductory hidden Markov model
Regime switching in financial data via HMM
11
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Testing homoscedasticity

The ordinary least squares algorithm generates estimates that are unbiased (the expected values are equal to the true values), consistent (converge in probability to the true estimates), and with the minimal variance among unbiased estimates (when we get more data, the estimates don't change much, compared to other techniques). Also, the estimates are distributed according to a Gaussian distribution. But all of this occurs when certain conditions are met, in particular the following ones:

  • The residuals should be homoscedastic (same variance).
  • The residuals should not be correlated, which generally occurs with temporal data.
  • There is no perfect correlation between variables (or linear combinations of variables).
  • Exogeneity—the regressors are not correlated with the error term.
  • The model is linear and is correctly specified.
  • There should...
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