R Statistics Cookbook

Over 100 recipes for performing complex statistical operations with R 3.5

Francisco Juretig

• Publisher: Packt Publishing
• Year: 2019
• Print ISBN:
  9781789802566
• Edition: 1
• eBook ISBN:
  9781789802924
• Topic: Computer Science
• Subtopic: Computer Science General
• Index: Computer Science

Solve real-world statistical problems using the most popular R packages and techniques

Key Features

• Learn how to apply statistical methods to your everyday research with handy recipes
• Foster your analytical skills and interpret research across industries and business verticals
• Perform t-tests, chi-squared tests, and regression analysis using modern statistical techniques

Book Description

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.

What you will learn

• Become well versed with recipes that will help you interpret plots with R
• Formulate advanced statistical models in R to understand its concepts
• Perform Bayesian regression to predict models and input missing data
• Use time series analysis for modelling and forecasting temporal data
• Implement a range of regression techniques for efficient data modelling
• Get to grips with robust statistics and hidden Markov models
• Explore ANOVA (Analysis of Variance) and perform hypothesis testing

Who this book is for

If you are a quantitative researcher, statistician, data analyst, or data scientist looking to tackle various challenges in statistics, this book is what you need! Proficiency in R programming and basic knowledge of linear algebra is necessary to follow along the recipes covered in this book.

Getting Started with R and Statistics

In this chapter, we will cover the following recipes:

• Maximum likelihood estimation
• Calculation 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 plots 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
• Modelling sequences with the TraMineR package
• Clustering sequences with the TraMineR package
• Displaying geographical data with the leaflet package

Introduction

In this chapter, we will introduce a wide array of topics regarding statistics and data analysis in R. We will use quite a diverse set of packages, most of which have been released over recent years.

We'll start by generating random numbers, fitting distributions to data, and using several packages to plot data. We will then move onto sampling, creating diagrams with the DiagrammeR package, and analyzing sequence data with the TraMineR package. We also present several techniques, not strictly related to statistics, but important for dealing with advanced methods in R—we introduce the Rcpp package (used for embedding highly efficient C++ code into your R scripts) and the R6 package (used for operating with R6 classes, allowing you to code using an object-oriented approach in R).

Technical requirements

We will use R and its packages, that can be installed via the install.packages() command, and we will indicate which ones are necessary for each recipe in the corresponding Getting ready section.

Maximum likelihood estimation

Suppose we observe a hundred roulette spins, and we get red 30 times and black 70 times. We can start by assuming that the probability of getting red is 0.5 (and black is obviously 0.5). This is certainly not a very good idea, because if that was the case, we should have seen nearly red 50 times and black 50 times, but we did not. It is thus evident that a more reasonable assumption would have been a probability of 0.3 for red (and thus 0.7 for black).

The principle of maximum likelihood establishes that, given the data, we can formulate a model and tweak its parameters to maximize the probability (likelihood) of having observed what we did observe. Additionally, maximum likelihood allows us to calculate the precision (standard error) of each estimated coefficient easily. They are obtained by finding the curvature of the log-likelihood with respect to each parameter; this is obtained by finding the second-order derivatives of the log-likelihood with respect to each parameter.

The likelihood is essentially a probability composed of the multiplication of several probabilities. Multiplying lots of probabilities is never a good idea, because if the probabilities are small, we would very likely end up with a very small number. If that number is too small, then the computer won't be able to represent it accurately. Therefore, what we end up using is the log-likelihood, which is the sum of the logarithms of those probabilities.

In many situations, we also want to know if the coefficients are statistically different from zero. Imagine we have a sample of growth rates for many companies for a particular year, and we want to use the average as an indicator of whether the economy is growing or not. In other words, we want to test whether the mean is equal to zero or not. We could fit that distribution of growth rates to a Gaussian distribution (which has two parameters,

), and test whether

(estimated

) is statistically equal to zero. In a Gaussian distribution, the mean is

. When doing hypothesis testing, we need to specify a null hypothesis and an alternative one. For this case, the null hypothesis is that this parameter is equal to zero. Intuition would tell us that if an estimated parameter is large, we can reject the null hypothesis. The problem is that we need to define what large is. This is why we don't use the estimated coefficients, but a statistic called the Z value—this is defined as the value that we observed divided by the standard error. It can be proven that these are distributed according to a Gaussian distribution.

So, once we have the Z value statistic, how can we reject or not reject the null hypothesis? Assuming that the null hypothesis is true (that the coefficient is equal to zero), we can compute the probability that we get a test statistic as large or larger than the one we got (these are known as p-values). Remember that we assume that the coefficients have fixed values, but we will observe random deviations from them in our samples (we actually have one sample). If the probability of finding them to be as large as the ones that we observed is small, assuming that the true ones are zero, then that implies that luck alone can't explain the coefficients that we got. The final conclusion in that case is to reject the null hypothesis and conclude that the coefficient is different from zero.

Getting ready

The bbmle package can be installed using the install.packages("bbmle") function in R.

How to do it...

In this exercise, we will generate a 1000 random gamma deviates with its two parameters set to shape=20 and rate=2. We will then estimate the two parameters by using the mle2 function in the bbmle package. This function will also return the Z values, and the p-values. Note that we need to assume a distribution that we will use to fit the parameters (in genera...

Table of contents

• Title Page
• Copyright and Credits
• About Packt
• Contributors
• Preface
• Getting Started with R and Statistics
• Univariate and Multivariate Tests for Equality of Means
• Linear Regression
• Bayesian Regression
• Nonparametric Methods
• Robust Methods
• Time Series Analysis
• Mixed Effects Models
• Predictive Models Using the Caret Package
• Bayesian Networks and Hidden Markov Models
• Other Books You May Enjoy