Chapter 6 demonstrates one way that RIO can be used for exploratory data analysis: identifying statistically significant interaction terms. We show how exploring the relationships among cases offers important insights into the relationships between variables.

Chapter 1 introduces the general logic and motivations behind turning regression models “inside out.” Here, we explain how Regression Inside Out (RIO) facilitates a case-oriented approach to regression, detail the benefits of such an approach, and provide a roadmap for the rest of the book.

Chapter 3 demonstrates how the mathematics of turning Ordinary Least Squares (OLS) regression inside out can be generalized to Generalized Linear Models (GLM) including logistic, Poisson, negative binomial, random intercept, and fixed effects models.

Chapter 10 concludes our book, outlining the benefits of a case-oriented approach to regression. We review key substantive findings from the analyses presented in previous chapters and highlight directions for future research.

Chapter 5 shows how the methods introduced in the preceding chapters can be used to gain novel substantive and theoretical insights. We show how RIO can be used to identify multiple storylines implied by a single regression model by examining cases (or sets of cases) that contribute to the regression model in otherwise unseen ways. We illustrate RIO’s substantive benefits through empirical analyses of (1) the effects of regional integration on inequality, (2) the social determinants of health, and (3) the correlates of dog ownership.

Chapter 8 demonstrates how RIO allows analysts to incorporate the case-oriented logic of configurational comparative analysis into a regression framework. We contrast regression with qualitative comparative analysis (QCA), discuss key benefits of QCA, and outline a comparative configurational approach to regression. We illustrate how RIO can be used to realize some of the benefits of configurational comparative analysis through (1) a macro-comparative analysis of education-based inequality in political participation and (2) an analysis of the correlates of poverty using nationally representative data from the United States.

Chapter 4 explores methods for turning model variance inside out. We discuss the logic and limitations of decomposing variance to the level of cases and introduce two distinct approaches to obtaining case-level contributions to the model variance: the squared residuals approach and the leave-one-out approach.

This chapter provides a primer on the logic of Bayesian updating and shows how it is used for answering causal queries. We illustrate with applications to correlational and process-tracing inferences.

We illustrate Bayesian mixed methods with causal models through a reexamination of the model of inequality and democratization and of institutions and growth introduced in Chapter 8. We show how to use updated population models to draw both population- and case-level inferences, demonstrate situations in which learning is minimal and in which it is more substantial, and illustrate how the probative value of case-level evidence can be empirically established through model updating.

We turn to the problem of choosing between going “wide” and going “deep”: between seeking a little bit of information on a large number of cases versus studying a smaller number of cases intensively. We outline a simulation-based approach to identify the optimal mix of breadth and depth. Simulations suggest that going deep is especially valuable where confounding is a concern, for queries about causal pathways, and where models embed strong beliefs about causal effects. We also find that there are diminishing marginal returns to each strategy and that depth often provides the greatest gains when we have cross-case evidence on only a modest number of cases.