Practicing R for Statistical Computing (2023)

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Practicing R for Statistical Computing R faqs

The book “Practicing R for Statistical Computing” is designed to provide a comprehensive introduction to R language for data presentation, manipulation, and statistical data analysis. The book covers fundamentals of data structures in R language such as vectors, matrices, arrays, and lists, along with techniques for exploratory data analysis, the transformation of the data, and its manipulation. The book explains basic statistical concepts and demonstrates their implementation including descriptive statistics, graphical representation of data, probability, popular probability distributions, and hypothesis testing. It also explores linear and non-linear modeling, model selection, and diagnostic tools available in R.

Practicing R for Statistical Computing

The book also covers flow control and conditional computation using ‘if’ conditions and loops. A useful discussion is also done about functions and resources for further learning. It provides an extensive list of functions grouped according to statistics classification, which can be helpful for both statisticians and R programmers. The use of different graphic devices, high-level and low-level graphical procedures, and adjustment of parameters are also explained. Throughout the book, R commands, functions, and objects are printed in different fonts for understanding and easy identification. The possible standard errors, warnings, and mistakes by users in the R language are also discussed and classified, and explanations on how to prevent them are given.

Chapter-wise downloadable R code files from Practicing R for Statistical Computing are:

Chapter 1: R Language: Introduction

Chapter 2: Obtaining and Installing R Language

Chapter 3: Using R as a Calculator

Chapter 4: Data Mode and Data Structure

Chapter 5: Working with Data

Chapter 6: Descriptive Statistics

Chapter 7: Probability and Probability Distributions

Chapter 8: Confidence Intervals and Comparison Tests

Chapter 9: Correlation & Regression Analysis

Chapter 10: Graphing in R

Chapter 11: Control Flow: Selection and Iteration

Chapter 12: Functions and R Resources

Chapter 13: Common Errors and Mistakes

Chapter 14: Functions for Better Programming

Chapter 15: This chapter lists the widely used built-in functions (No R code exists)

Chapter 16: This chapter lists several important R packages (No R code exists)

Authors:

Muhammad Aslam is Professor in the Department of Statistics at Bahauddin Zakariya University,

Muhammad Imdad Ullah is an Assistant Professor in the Department of Statistics at Ghazi University,

Muhammad Aslam is a Professor at the Department of Statistics at Bahauddin Zakariya University, Multan, Pakistan. He holds a Ph.D. in Statistics, a Master’s degree in Statistics, and a Post-Graduate Diploma in Computer Programming and Computing Statistics from the same university. He also completed his Post-Doctorate from the Institut de Mathematiques de Bourgogne, Dijon, France.

Professor Aslam’s research is mainly focused on regression analysis and statistical inference, with a particular interest in simulation studies using computer programming. With more than 25 years of teaching experience, he has published more than 120 research articles in several prestigious international journals. Nine research scholars have completed their Ph.D. degrees under his guidance. Muhammad Imdad Ullah, the co-author of this book, is among these scholars. 

Muhammad Imdad Ullah is an Assistant Professor at the Department of Statistics, Ghazi University, Dera Ghazi Khan, Pakistan. He received his Ph.D. degree from Bahauddin Zakariya University. He has also earned a Post-Graduate Diploma in Computer Programming and Computing Statistics. His Ph.D. work is about the development of R packages addressing linear regression models with the issue of multicollinearity. This work led to the development of three R packages—mctest, lmridge, and liureg —and three research articles based on these packages were published in The R Journal. His area of expertise includes computer programming and statistical computations. With over 14 years of teaching experience, he has authored 11 research publications.

Practicing R Language for Statistical Copmuting

Learn Statistics and Data Analysis

The Poisson Regression in R

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The Poisson regression model should be used when the dependent (response) variable is in the form of counts or values of the response variables following a Poisson distribution. In R, glm() function can be used to perform Poisson regression analysis.

Note that the lm() function performs simple and multiple linear regression models when the dependent variable is continuous.

Poisson Regression Models in R Language

Statistical models such as linear or Poisson regression models can be performed easily in R language.

The Poisson regression is used to analyze count data.

For the Poisson model, let us consider another built-in data set warpbreaks. This data set describes the effect of wool type (A or B) and tension (Low, Medium, and High) on the number of warp breaks per loom, where a loom corresponds to a fixed length of yarn.

head(warpbreaks)

The $breaks$ variable is a response variable since it contains the number of breaks (count of breaks). The $tension$ and $type$ variables are taken as predictor variables.

pois_mod <- glm(breaks ~ wool + tension, data = warpbreaks, family = poisson)

The output from the pois_mod object is

Poisson Regression using glm()

The glm() provides eight choices for a family with the following default link functions:

FamilyDefault Link Function
binomial(link = “logit”)
gaussian(link = “identity”)
Gamma(link = “inverse”)
inverse.gaussian(link =$\frac{1}{\mu^2}$)
poisson(link = “log”)
quasi(link = “identity”, variance = “constant”)
quasibinomial(link = “logit”)
quasipoisson(link = “log”)

The detailed output (estimation and testing of parameters) can be obtained as

summary(pois_mod)
Summary Output Poisson Regression

Poisson Example

  • A number of cargo ships were damaged by waves (McCullagh & Nelder, 1989).
  • Number of deaths due to AIDs in Australia per quarter (3 month periods) from January 1983 – June 1986.
  • A number of violent incidents were exhibited over a 6-month period by patients who had been treated in the ER of a psychiatric hospital (Gardner, Mulvey, & Shaw, 1995).
  • Daily homicide counts in California (Grogger, 1990).
  • Founding of daycare centers in Toronto (Baum & Oliver, 1992).
  • Political party-switching among members of the US House of Representatives (King, 1988).
  • Number of presidential appointments to the Supreme Court (King, 1987).
  • A number of children in a classroom that a child lists as being their friend (unlimited nomination procedure, sociometric data).
  • A number of hard disk failures during a year.
  • Number of deaths due to SARs (Yu, Chan & Fung, 2006).
  • A number of arrests resulted from 911 calls.
  • A number of orders of protection were issued.

FAQs about Poisson Regression in R

  1. What function is used in R to perform Poisson Regression?
  2. Write about important arguments of glm() function in R to perform the Poisson Regression Model.
  3. Give real-life examples of data sets, for which Poisson regression may be performed.
  4. List the link function of the family.
  5. How Poisson Model is different from Linear Regression models?
Frequently Asked Questions About R Poisson Regression in R

MCQs in Statistics

Non-Linear Regression Model: A Comprehensive Guide

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The article is about using and applying Non-Linear Regression Models in R Language. In the least square method, the regression model is established in such a way that

"The sum of the squares of the vertical distances of different points (residuals) from the regression line is minimized"

When the relationship between the variables is not linear (one has a non-linear regression model), one may

  1. try to transform the data to linearize the relationship,
  2. fit polynomial or complex spline model to the data, or
  3. fit a non-linear regression to the data.

Non-Linear Regression Model

In the non-linear regression model, a function is specified by a set of parameters to fit the data. The non-linear least squares approach is used to estimate such parameters. In R, the nls() is used to approximate the non-linear function using a linear one and iteratively try to find the best parameter values.

Some frequently used non-linear regression models are listed in the Table below.

sr no.NameModel
1)Michaelis-Menten$y=\frac{ax}{1+bx}$
2)Two-parameter asymptotic exponential$y=a(1-e^{-bx})$
3)Three-parameter asymptotic exponential$y=a-be^{-cx}$
4)Two parameter Logistic$y=\frac{e^{a+bx}}{1+e^{a+bx}}$
5)Three parameter Logistic$y=\frac{a}{1+be^{-ex}}$
6)Weibull$y=a-be^{-cx^d}$
7)Gompertz$y=e^{-be^{-cx}}$
8)Ricker curves$y=axe^{-bx}$
9)Bell-Shaped$y=a \, exp(-|bx|^2)$

Let’s fit the Michaelis-Menten non-linear function to the data given below.

x <- seq(1, 10, 1)
y <- c(3.7, 7.1, 11.9, 19, 27, 38.5, 51, 67.7, 85, 102)

nls_model <- nls(y ~ a * x/(1 + b * x), start = list(a = 1, b = 1))

summary(nls_model)

The output of the above code for the Michaelis-Menten non-linear function is

#### Output
Formula: y ~ a * x/(1 + b * x)

Parameters:
   Estimate Std. Error t value Pr(>|t|)    
a  4.107257   0.226711   18.12 8.85e-08 ***
b -0.060900   0.002708  -22.49 1.62e-08 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2.805 on 8 degrees of freedom

Number of iterations to convergence: 11 
Achieved convergence tolerance: 6.354e-06

Let us plot the non-linear predicted values from 10 data points of newly generated x-values

new.data <- data.frame(x = seq(min(x), max(x), len = 10))

plot(x, y)
lines(new.data$x, predict(nls_model, newdata = new.data) )
Non-Linear Regression Models

The sum of squared residuals and the confidence interval of the chosen values of the coefficient can be obtained by issuing the commands,

sum(resid(nls_model)^2) 
# or 
print(sum(resid(nls_model)^2))
confint(nls_model) 
# or 
print(confint(nls_model))
Non=Linear Regression Models in R Output

Note that the formula nls() does not use special coding in linear terms, factors, interactions, etc. The right-hand side in the expression nls() computes the expected value to the left-hand side. The start argument contains the list of starting values of the parameter used in the expression and is varied by the algorithm.

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