Summary We extend the omitted variable bias framework with a suite of tools for sensitivity analysis in regression models that does not require assumptions on the functional form of the treatment assignment mechanism nor on the distribution of the unobserved confounders, naturally handles multiple confounders, possibly acting non‐linearly, exploits expert knowledge to bound sensitivity parameters and can be easily computed by using only standard regression results. In particular, we introduce two novel sensitivity measures suited for routine reporting. The robustness value describes the minimum strength of association that unobserved confounding would need to have, both with the treatment and with the outcome, to change the research conclusions. The partial R2 of the treatment with the outcome shows how strongly confounders explaining all the residual outcome variation would have to be associated with the treatment to eliminate the estimated effect. Next, we offer graphical tools for elaborating on problematic confounders, examining the sensitivity of point estimates and t‐values, as well as ‘extreme scenarios’. Finally, we describe problems with a common ‘benchmarking’ practice and introduce a novel procedure to bound the strength of confounders formally on the basis of a comparison with observed covariates. We apply these methods to a running example that estimates the effect of exposure to violence on attitudes toward peace.

Propensity score matching and weighting are popular methods when estimating causal effects in observational studies. Beyond the assumption of unconfoundedness, however, these methods also require the model for the propensity score to be correctly specified. The recently proposed covariate balancing propensity score (CBPS) methodology increases the robustness to model misspecification by directly optimizing sample covariate balance between the treatment and control groups. In this paper, we extend the CBPS to a continuous treatment. We propose the covariate balancing generalized propensity score (CBGPS) methodology, which minimizes the association between covariates and the treatment. We develop both parametric and nonparametric approaches and show their superior performance over the standard maximum likelihood estimation in a simulation study. The CBGPS methodology is applied to an observational study, whose goal is to estimate the causal effects of political advertisements on campaign contributions. We also provide open-source software that implements the proposed methods.

We propose the use of Kernel Regularized Least Squares (KRLS) for social science modeling and inference problems. KRLS borrows from machine learning methods designed to solve regression and classification problems without relying on linearity or additivity assumptions. The method constructs a flexible hypothesis space that uses kernels as radial basis functions and finds the best-fitting surface in this space by minimizing a complexity-penalized least squares problem. We argue that the method is well-suited for social science inquiry because it avoids strong parametric assumptions, yet allows interpretation in ways analogous to generalized linear models while also permitting more complex interpretation to examine nonlinearities, interactions, and heterogeneous effects. We also extend the method in several directions to make it more effective for social inquiry, by (1) deriving estimators for the pointwise marginal effects and their variances, (2) establishing unbiasedness, consistency, and asymptotic normality of the KRLS estimator under fairly general conditions, (3) proposing a simple automated rule for choosing the kernel bandwidth, and (4) providing companion software. We illustrate the use of the method through simulations and empirical examples.

Abstract& Recently, a number of investigators have examined the neural loci of psychological processes enabling the control of visual spatial attention using cued-attention paradigms in combination with event-related functional magnetic resonance imaging. Findings from these studies have provided strong evidence for the involvement of a fronto-parietal network in attentional control. In the present study, we build upon this previous work to further investigate these attentional control systems. In particular, we employed additional controls for nonattentional sensory and interpretative aspects of cue processing to determine whether distinct regions in the fronto-parietal network are involved in different aspects of cue processing, such as cue-symbol interpretation and attentional orienting. In addition, we used shorter cue-target intervals that were closer to those used in the behavioral and event-related potential cueing literatures. Twenty participants performed a cued spatial attention task while brain activity was recorded with functional magnetic resonance imaging. We found functional specialization for different aspects of cue processing in the lateral and medial subregions of the frontal and parietal cortex. In particular, the medial subregions were more specific to the orienting of visual spatial attention, while the lateral subregions were associated with more general aspects of cue processing, such as cue-symbol interpretation. Additional cue-related effects included differential activations in midline frontal regions and pretarget enhancements in the thalamus and early visual cortical areas. &

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