Asparouhov T., Muthén L.K., Muthen B. Regression and mediation analysis using Mplus

Muthén & Muthén, 2016. — 266 p.The inspiration to write this book came from many years of teaching about Mplus and answering questions on Mplus Discussion and Mplus support. It became clear that once people leave school, it is difficult to keep up with the newest methodology. The purpose of this book is to provide researchers with information that is not readily available to them and that we believe is important for their research. Many topics such as linear regression analysis; mediation analysis; causal inference; regression analysis with categorical, count, and censored outcomes; Bayesian analysis; and missing data analysis have entire books devoted to them. This book does not attempt to replace these books but rather to give useful and manageable summaries of these topics and show how the analyses are implemented in Mplus. The technical level is kept at a minimum but still requires an introductory statistics background and a good background in regression.
Chapter 1 covers linear regression analysis including regression with an interaction, multiple-group analysis, missing data on covariates, and heteroscedasticity modeling. Chapter 2 covers mediation analysis with a continuous mediator and a continuous outcome including moderated mediation. Chapter 3 covers special topics in mediation analysis that are not normally found in books on mediation analysis. These include Monte Carlo simulation studies of mediation and moderated mediation, model misspecification due to omitted variables and confounders, instrumental variable estimation, sensitivity analysis, multiple group analysis of moderated mediation, and measurement error. Chapter 4 covers causal inference based on counterfactuals for mediation analysis with a continuous mediator and a continuous outcome. Chapter 5 covers regression analysis for categorical dependent variables including binary, ordinal, and nominal variables. Chapter 6 covers regression analysis for a count dependent variable including the following models: Poisson, Poisson with a random intercept, zero-inflated Poisson, negative binomial, zero-inflated negative binomial, two-part (hurdle) with zero-truncation, and varying-exposure. Chapter 7 covers regression analysis for a censored dependent variable including the following models: censored-normal (tobit), censored-inflated, sample selection (Heckman), two-part, and switching regressions. Chapter 8 covers causal inference for mediation analysis with a binary outcome and a continuous mediator, a count outcome and a continuous mediator, a two- part outcome and a continuous mediator, a binary and an ordinal mediator, a nominal mediator, and a mediator with measurement error. Chapter 9 discusses Bayesian analysis and uses it to estimate several mediation examples which show how it can be used as an alternative to maximum likelihood estimation. Chapter 10 discusses several approaches to missing data modelling including missing completely at random (MCAR), missing at random (MAR), and not missing at random (NMAR) including selection modeling.