Handbook of Regression Modeling in People Analytics

Description

Despite the recent rapid growth in machine learning and predictive analytics, many of the statistical questions that are faced by researchers and practitioners still involve explaining why something is happening. Regression analysis is the best ‘swiss army knife’ we have for answering these kinds of questions. This book is a learning resource on inferential statistics and regression analysis. It teaches how to do a wide range of statistical analyses in both R and in Python, ranging from simple hypothesis testing to advanced multivariate modelling. Although it is primarily focused on examples related to the analysis of people and talent, the methods easily transfer to any discipline. The book hits a ‘sweet spot’ where there is just enough mathematical theory to support a strong understanding of the methods, but with a step-by-step guide and easily reproducible examples and code, so that the methods can be put into practice immediately. This makes the book accessible to a wide readership, from public and private sector analysts and practitioners to students and researchers. Key Features: • 16 accompanying datasets across a wide range of contexts (e.g. academic, corporate, sports, marketing) • Clear step-by-step instructions on executing the analyses. • Clear guidance on how to interpret results. • Primary instruction in R but added sections for Python coders. • Discussion exercises and data exercises for each of the main chapters. • Final chapter of practice material and datasets ideal for class homework or project work. Cover Half Title Title Page Copyright Page Contents Foreword by Alexis Fink Introduction 1. The Importance of Regression in People Analytics 1.1. Why is regression modeling so important in people analytics? 1.2. What do we mean by ‘modeling’ ? 1.2.1. The theory of inferential modeling 1.2.2. The process of inferential modeling 1.3. The structure, system and organization of this book 2. The Basics of the R Programming Language 2.1. What is R? 2.2. How to start using R 2.3. Data in R 2.3.1. Data types 2.3.2. Homogeneous data structures 2.3.3. Heterogeneous data structures 2.4. Working with dataframes 2.4.1. Loading and tidying data in dataframes 2.4.2. Manipulating dataframes 2.5. Functions, packages and libraries 2.5.1. Using functions 2.5.2. Help with functions 2.5.3. Writing your own functions 2.5.4. Installing packages 2.5.5. Using packages 2.5.6. The pipe operator 2.6. Errors, warnings and messages 2.7. Plotting and graphing 2.7.1. Plotting in base R 2.7.2. Specialist plotting and graphing packages 2.8. Documenting your work using R Markdown 2.9. Learning exercises 2.9.1. Discussion questions 2.9.2. Data exercises 3. Statistics Foundations 3.1. Elementary descriptive statistics of populations and samples 3.1.1. Mean, variance and standard deviation 3.1.2. Covariance and correlation 3.2. Distribution of random variables 3.2.1. Sampling of random variables 3.2.2. Standard errors, the t-distribution and confidence intervals 3.3. Hypothesis testing 3.3.1. Testing for a difference in means (Welch’s t-test) 3.3.2. Testing for a non-zero correlation between two variables t-test for correlation) 3.3.3. Testing for a difference in frequency distribution between different categories in a data set (Chi-square test) 3.4. Foundational statistics in Python 3.5. Learning exercises 3.5.1. Discussion questions 3.5.2. Data exercises 4. Linear Regression for Continuous Outcomes 4.1. When to use it 4.1.1. Origins and intuition of linear regression 4.1.2. Use cases for linear regression 4.1.3. Walkthrough example 4.2. Simple linear regression 4.2.1. Linear relationship between a single input and an outcome 4.2.2. Minimising the error 4.2.3. Determining the best fit 4.2.4. Measuring the fit of the model 4.3. Multiple linear regression 4.3.1. Running a multiple linear regression model and interpreting its coefficients 4.3.2. Coefficient confidence 4.3.3. Model ‘goodness-of-fit’ 4.3.4. Making predictions from your model 4.4. Managing inputs in linear regression 4.4.1. Relevance of input variables 4.4.2. Sparseness (‘missingness’) of data 4.4.3. Transforming categorical inputs to dummy variables 4.5. Testing your model assumptions 4.5.1. Assumption of linearity and additivity 4.5.2. Assumption of constant error variance 4.5.3. Assumption of normally distributed errors 4.5.4. Avoiding high collinearity and multicollinearity between input variables 4.6. Extending multiple linear regression 4.6.1. Interactions between input variables 4.6.2. Quadratic and higher-order polynomial terms 4.7. Learning exercises 4.7.1. Discussion questions 4.7.2. Data exercises 5. Binomial Logistic Regression for Binary Outcomes 5.1. When to use it 5.1.1. Origins and intuition of binomial logistic regression 5.1.2. Use cases for binomial logistic regression 5.1.3. Walkthrough example 5.2. Modeling probabilistic outcomes using a logistic function 5.2.1. Deriving the concept of log odds 5.2.2. Modeling the log odds and interpreting the coefficients 5.2.3. Odds versus probability 5.3. Running a multivariate binomial logistic regression model 5.3.1. Running and interpreting a multivariate binomial logistic regression model 5.3.2. Understanding the fit and goodness-of-fit of a binomial logistic regression model 5.3.3. Model parsimony 5.4. Other considerations in binomial logistic regression 5.5. Learning exercises 5.5.1. Discussion questions 5.5.2. Data exercises 6. Multinomial Logistic Regression for Nominal Category Outcomes 6.1. When to use it 6.1.1. Intuition for multinomial logistic regression 6.1.2. Use cases for multinomial logistic regression 6.1.3. Walkthrough example 6.2. Running stratified binomial models 6.2.1. Modeling the choice of Product A versus other products 6.2.2. Modeling other choices 6.3. Running a multinomial regression model 6.3.1. Defining a reference level and running the model 6.3.2. Interpreting the model 6.3.3. Changing the reference 6.4. Model simplification, fit and goodness-of-fit for multinomial logistic regression models 6.4.1. Gradual safe elimination of variables 6.4.2. Model fit and goodness-of-fit 6.5. Learning exercises 6.5.1. Discussion questions 6.5.2. Data exercises 7. Proportional Odds Logistic Regression for Ordered Category Outcomes 7.1. When to use it 7.1.1. Intuition for proportional odds logistic regression 7.1.2. Use cases for proportional odds logistic regression 7.1.3. Walkthrough example 7.2. Modeling ordinal outcomes under the assumption of proportional odds 7.2.1. Using a latent continuous outcome variable to derive a proportional odds model 7.2.2. Running a proportional odds logistic regression model 7.2.3. Calculating the likelihood of an observation being in a specific ordinal category 7.2.4. Model diagnostics 7.3. Testing the proportional odds assumption 7.3.1. Sighting the coefficients of stratified binomial models 7.3.2. The Brant-Wald test 7.3.3. Alternatives to proportional odds models 7.4. Learning exercises 7.4.1. Discussion questions 7.4.2. Data exercises 8. Modeling Explicit and Latent Hierarchy in Data 8.1. Mixed models for explicit hierarchy in data 8.1.1. Fixed and random effects 8.1.2. Running a mixed model 8.2. Structural equation models for latent hierarchy in data 8.2.1. Running and assessing the measurement model 8.2.2. Running and interpreting the structural model 8.3. Learning exercises 8.3.1. Discussion questions 8.3.2. Data exercises 9. Survival Analysis for Modeling Singular Events Over Time 9.1. Tracking and illustrating survival rates over the study period 9.2. Cox proportional hazard regression models 9.2.1. Running a Cox proportional hazard regression model 9.2.2. Checking the proportional hazard assumption 9.3. Frailty models 9.4. Learning exercises 9.4.1. Discussion questions 9.4.2. Data exercises 10. Alternative Technical Approaches in R and Python 10.1. ‘Tidier’ modeling approaches in R 10.1.1. The broom package 10.1.2. The parsnip package 10.2. Inferential statistical modeling in Python 10.2.1. Ordinary Least Squares (OLS) linear regression 10.2.2. Binomial logistic regression 10.2.3. Multinomial logistic regression 10.2.4. Structural equation models 10.2.5. Survival analysis 10.2.6. Other model variants 11. Power Analysis to Estimate Required Sample Sizes for Modeling 11.1. Errors, effect sizes and statistical power 11.2. Power analysis for simple hypothesis tests 11.3. Power analysis for linear regression models 11.4. Power analysis for log-likelihood regression models 11.5. Power analysis for hierarchical regression models 11.6. Power analysis using Python 12. Further Exercises for Practice 12.1. Analyzing graduate salaries 12.1.1. The graduates data set 12.1.2. Discussion questions 12.1.3. Data exercises 12.2. Analyzing a recruiting process 12.2.1. The recruiting data set 12.2.2. Discussion questions 12.2.3. Data exercises 12.3. Analyzing the drivers of performance ratings 12.3.1. The employee_performance data set 12.3.2. Discussion questions 12.3.3. Data exercises 12.4. Analyzing promotion differences between groups 12.4.1. The promotion data set 12.4.2. Discussion questions 12.4.3. Data exercises 12.5. Analyzing feedback on learning programs 12.5.1. The learning data set 12.5.2. Discussion questions 12.5.3. Data exercises References Glossary Index