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There are a number of measures of direct and indirect effects in the literature. They are suitable in some cases and unsuitable in others. We describe a case where the existing measures are unsuitable and propose new suitable ones. We also…
When a linear model is adjusted to control for additional explanatory variables the sign of a fitted coefficient may reverse. Here these reversals are studied using coefficients of determination. The resulting theory can be used to…
Reciprocity--the tendency of individuals to form mutual ties--is a fundamental structural feature of many directed networks. Despite its ubiquity, reciprocity remains insufficiently integrated into statistical network models, particularly…
To estimate direct and indirect effects of an exposure on an outcome from observed data strong assumptions about unconfoundedness are required. Since these assumptions cannot be tested using the observed data, a mediation analysis should…
The coefficient of determination is well defined for linear models and its extension is long wanted for mixed-effects models. We revisit its extension to define measures for proportions of variation explained by the whole model, fixed…
We propose a new model selection criterion for mixed effects regression models that is computable when the model is fitted with a two-step method, even when the structure and the distribution of the random effects are unknown. The criterion…
Psychosocial constructs can only be assessed indirectly, and measures are typically formed by a combination of indicators that are thought to relate to the construct. Reflective and formative measurement models offer different…
Estimating the effect of intervention from observational data while accounting for confounding variables is a key task in causal inference. Oftentimes, the confounders are unobserved, but we have access to large amounts of additional…
Mediation analysis breaks down the causal effect of a treatment on an outcome into an indirect effect, acting through a third group of variables called mediators, and a direct effect, operating through other mechanisms. Mediation analysis…
Understanding causal mechanisms is crucial for explaining and generalizing empirical phenomena. Causal mediation analysis offers statistical techniques to quantify the mediation effects. Although numerous methods have been developed for…
One obstacle to ``elevating" correlation to causation is the phenomenon of confounding, i.e., when a correlation between two variables exists because both variables are in fact caused by a third variable. The situation where the confounders…
A common problem in health research is that we have a large database with many variables measured on a large number of individuals. We are interested in measuring additional variables on a subsample; these measurements may be newly…
Linear regression on network-linked observations has been an essential tool in modeling the relationship between response and covariates with additional network structures. Previous methods either lack inference tools or rely on restrictive…
A basic principle in the design of observational studies is to approximate the randomized experiment that would have been conducted under controlled circumstances. Now, linear regression models are commonly used to analyze observational…
Selective inference aims at providing valid inference after a data-driven selection of models or hypotheses. It is essential to avoid overconfident results and replicability issues. While significant advances have been made in this area for…
This chapter reviews indirect estimators of intergenerational mobility, focusing on approaches that infer parent-child or other family associations when direct income data are incomplete or unavailable. We synthesize methods based on…
We propose a set of causal estimands that we call the "mediated probabilities of causation." These estimands quantify the probabilities that an observed negative outcome was induced via a mediating pathway versus a direct pathway in a…
A parametric expression for causal natural direct and indirect effects is derived for the setting of a binary outcome with a binary mediator. The proposed effect decomposition does not require the outcome to be rare and generalizes the…
Hidden variable graphical models can sometimes imply constraints on the observable distribution that are more complex than simple conditional independence relations. These observable constraints can falsify assumptions of the model that…
Traditional models of active learning assume a learner can directly manipulate or query a covariate $X$ in order to study its relationship with a response $Y$. However, if $X$ is a feature of a complex system, it may be possible only to…