2nd edition. — New York: Springer, 2021. — 471 p.
Regression analysis of cause effect relationships is increasingly the core of medical and health research. This work is a 2nd edition of a 2017 pretty complete textbook and tutorial for students as well as recollection / update bench and help desk for professionals. It came to the authors' attention, that information of history, background, and purposes, of the regression methods addressed were scanty. Lacking information about all of that has now been entirely covered. The editorial art work of the first edition, however pretty, was less appreciated by some readerships, than were the original output sheets from the statistical programs as used. Therefore, the editorial art work has now been systematically replaced with original statistical software tables and graphs for the benefit of an improved usage and understanding of the methods. In the past few years, professionals have been flooded with big data. The Covid-19 pandemic gave cause for statistical software companies to foster novel analytic programs better accounting outliers and skewness. Novel fields of regression analysis adequate for such data, like sparse canonical regressions and quantile regressions, have been included.
Preface to the Second Edition
Preface to the First Edition
Introduction, History, and Background
Extension of Regression Theories and Terminologies
More Modern Times
Data Example
Defining the Intercept ``a´´ and the Regression Coefficient ``b´´ from the Regression Equation y = a + bx
Correlation Coefficient (R) Varies Between - and +
Computing R, Intercept ``a´´ and Regression Coefficient ``b´´: Ordinary Least Squares and Matrix Algebra
SPSS Statistical Software for Windows for Regression Analysis
A Significantly Positive Correlation, X Significant Determinant of Y
Simple Linear Regression Uses the Equation y = a+bx
Multiple Regression with Three Variables Uses Another Equation
Real Data Example
SPSS Statistical Software for Windows for Regression Analysis
Summary of Multiple Regression Analysis of Variables
Purposes of Multiple Linear Regression
Multiple Regression with an Exploratory Purpose, First Purpose
Multiple Regression for the Purpose of Increasing Precision, Second Purpose
Multiple Regression for Adjusting Confounding, Third Purpose
Multiple Regression for Adjusting Interaction, Fourth Purpose
Introduction, History and Background
Logistic Regression
Cox Regression
Logistic Regression
Cox Regression
Introduction, History, and Background
High Performance Regression Analysis
Example of a Multiple Linear Regression Analysis as Primary Analysis from a Controlled Trial
Example of a Multiple Logistic Regression Analysis as Primary Analysis from a Controlled Trial
Example of a Multiple Cox Regression Analysis as Primary Analysis from a Controlled Trial
Introduction, History, and Background
Binary Poisson Regression
Negative Binomial Regression
Probit Regression
Tetrachoric Regression
Quasi-Likelihood Regressions
Introduction, History, and Background
Multinomial Regression
Ordinal Regression
Negative Binomial and Poisson Regressions
Random Intercepts Regression
Logit Loglinear Regression
Hierarchical Loglinear Regression
Introduction, History, and Background
Cox with Time Dependent Predictors
Segmented Cox
Interval Censored Regression
Autocorrelations
Polynomial Regression
Introduction, History, and Background
Little if any Difference Between Anova and Regression Analysis
Paired and Unpaired Anovas
Introduction, History, and Background
Repeated Measures Anova (Analysis of Variance)
Repeated Measures Anova Versus Ancova
Repeated Measures Anova with Predictors
Mixed Linear Model Analysis
Mixed Linear Model with Random Interaction
Doubly Repeated Measures Multivariate Anova
Introduction, History, and Background
Restructuring Categories into Multiple Binary Variables
Variance Components Regressions
Contrast Coefficients Regressions
Introduction, History, and Background
Regression Analysis with Laplace Transformations with Due Respect to Those Clinical Pharmacologists Who Routinely Use it
Laplace Transformations: How Does it Work
Laplace Transformations and Pharmacokinetics
Introduction, History, and Background
Semi Variography
Correlation Levels Between Observed Places and Unobserved Ones
The Correlation Between the Known Places and the Place ``?´´
Markov Regression
Introduction, History, and Background
Path Analysis
Structural Equation Modeling
Bayesian Networks
Introduction, History, and Background
Multivariate Analysis of Variance (Manova)
Canonical Regression
Chapter : More on Poisson Regressions
Introduction, History, and Background
Poisson Regression with Event Outcomes per Person per Period of Time
Poisson Regression with Yes / No Event Outcomes per Population per Period of Time
Poisson Regressions Routinely Adjusting Age and Sex Dependence, Intercept-Only Models
Loglinear Models for Assessing Incident Rates with Varying Incident Risks
Introduction, History, and Background
Linear Trend Testing of Continuous Data
Linear Trend Testing of Discrete Data
Introduction, History, Background
Optimal Scaling with Discretization and Regularization versus Traditional Linear Regression
Automatic Regression for Maximizing Relationships
Introduction, History, and Background
Linear and the Simplest Nonlinear Models of the Polynomial Type
Spline Modeling
Chapter : More on Nonlinear Regressions
Introduction, History, and Background
Testing for Linearity
Logit and Probit Transformations
``Trial and Error´´ Method, Box Cox Transformation, ACE /AVAS Packages
Sinusoidal Data with Polynomial Regressions
Exponential Modeling
Spline Modeling
Loess Modeling
Appendix
Chapter : Special Forms of Continuous Outcomes Regressions
Kernel Regressions
Gamma and Tweedie Regressions
Robust Regressions
Introduction, History, and Background
Example
Deming Regression
Passing-Bablok Regression
Chapter : Regressions, a Panacee or at Least a Widespread Help for Clinical Data Analyses
Introduction, History, and Background
How Regressions Help You Make Sense of the Effects of Small Changes in Experimental Settings
How Regressions Can Assess the Sensitivity of your Predictors
How Regressions Can be Used for Data with Multiple Categorical Outcome and Predictor Variables
How Regressions Are Used for Assessing the Goodness of Novel Qualitative Diagnostic Tests
How Regressions Can Help you Find out about Data Subsets with Unusually Large Spread
Maximum Likelihood Estimation
Autocorrelations
Weighted Least Squares
Two Stage Least Squares
Robust Standard Errors
Generalized Least Squares
Introduction, History, and Background
Data Example with a Continuous Outcome, More on the Principles of Regression Trees
Automated Entire Tree Regression from the LDL Cholesterol Example
Chapter : Regressions with Latent Variables
Introduction, History, and Background
Factor Analysis
Partial Least Squares (PLS)
Discriminant Analysis
Introduction, History, and Background
Data Example
Introduction, History, and Background
Principles of Principal Components Analysis and Optimal Scaling, a Brief Review
Principal Components Analysis
Optimal Scaling with Spline Smoothing
Optimal Scaling with Spline Smoothing Including Regularized Regression Using Either Ridge, Lasso, or Elastic Net Shrinkages
Introduction, History, and Background
Statistical Model
Step 1 - Smoothing
Step 2 - Functional Principal Components Analysis (FPCA)
Step 3 - Regression Analysis
Applications in Medical and Health Research
Introduction, History, and Background
Traditional Linear and Robust Linear Regression Analysis
Quantile Linear Regression Analysis