Problems with Centrality Measures in Psychopathology Symptom Networks: Why Network Psychometrics Cannot Escape Psychometric Theory.

Understanding patterns of symptom co-occurrence is one of the most difficult challenges in psychopathology research. Do symptoms co-occur because of a latent factor, or might they directly and causally influence one another? Motivated by such questions, there has been a surge of interest in network analyses that emphasize the putatively direct role symptoms play in influencing each other. In this critical paper, we highlight conceptual and statistical problems with using centrality measures in cross-sectional networks. In particular, common network analyses assume that there are no unmodeled latent variables that confound symptom co-occurrence. The traditions of clinical taxonomy and test development in psychometric theory, however, greatly increase the possibility that latent variables exist in symptom data. In simulations that include latent variables, we demonstrate that closeness and betweenness are vulnerable to spurious covariance among symptoms that connect subgraphs (e.g., diagnoses). We further show that strength is redundant with factor loading in several cases. Finally, if a symptom reflects multiple latent causes, centrality metrics reflect a weighted combination, undermining their interpretability in empirical data. Our results suggest that it is essential for network psychometric approaches to examine the evidence for latent variables prior to analyzing or interpreting patterns at the symptom level. Failing to do so risks identifying spurious relationships or failing to detect causally important effects. Altogether, we argue that centrality measures do not provide solid ground for understanding the structure of psychopathology when latent confounding exists.

Identification of causal effects with latent confounding and classical additive errors in treatment.

In this paper, we discuss the identifiability and estimation of causal effects of a continuous treatment on a binary response when the treatment is measured with errors and there exists a latent categorical confounder associated with both treatment and response. Under some widely used parametric models, we first discuss the identifiability of the causal effects and then propose an approach for estimation and inference. Our approach can eliminate the biases induced by latent confounding and measurement errors by using only a single instrumental variable. Based on the identification results, we give guidelines for determining the existence of a latent categorical confounder and for selecting the number of levels of the latent confounder. We apply the proposed approach to a data set from the Framingham Heart Study to evaluate the effect of the systolic blood pressure on the coronary heart disease.

Higher-Order Least Squares: Assessing Partial Goodness of Fit of Linear Causal Models.

We introduce a simple diagnostic test for assessing the overall or partial goodness of fit of a linear causal model with errors being independent of the covariates. In particular, we consider situations where hidden confounding is potentially present. We develop a method and discuss its capability to distinguish between covariates that are confounded with the response by latent variables and those that are not. Thus, we provide a test and methodology for partial goodness of fit. The test is based on comparing a novel higher-order least squares principle with ordinary least squares. In spite of its simplicity, the proposed method is extremely general and is also proven to be valid for high-dimensional settings. Supplementary materials for this article are available online.

A new method for estimating the probability of causal relationships from observational data: Application to the study of the short-term effects of air pollution on cardiovascular and respiratory disease.

In this paper we investigate which airborne pollutants have a short-term causal effect on cardiovascular and respiratory disease using the Ancestral Probabilities (AP) procedure, a novel Bayesian approach for deriving the probabilities of causal relationships from observational data. The results are largely consistent with EPA assessments of causality, however, in a few cases AP suggests that some pollutants thought to cause cardiovascular or respiratory disease are associated due purely to confounding. The AP procedure utilizes maximal ancestral graph (MAG) models to represent and assign probabilities to causal relationships while accounting for latent confounding. The algorithm does so locally by marginalizing over models with and without causal features of interest. Before applying AP to real data, we evaluate it in a simulation study and investigate the benefits of providing background knowledge. Overall, the results suggest that AP is an effective tool for causal discovery.

Estimating bounds on causal effects in high-dimensional and possibly confounded systems.

We present an algorithm for estimating bounds on causal effects from observational data which combines graphical model search with simple linear regression. We assume that the underlying system can be represented by a linear structural equation model with no feedback, and we allow for the possibility of latent confounders. Under assumptions standard in the causal search literature, we use conditional independence constraints to search for an equivalence class of ancestral graphs. Then, for each model in the equivalence class, we perform the appropriate regression (using causal structure information to determine which covariates to adjust for) to estimate a set of possible causal effects. Our approach is based on the IDA procedure of Maathuis et al. (2009), which assumes that all relevant variables have been measured (i.e., no latent confounders). We generalize their work by relaxing this assumption, which is often violated in applied contexts. We validate the performance of our algorithm in simulation experiments.

Bayesian Estimation of Causal Direction in Acyclic Structural Equation Models with Individual-specific Confounder Variables and Non-Gaussian Distributions.

Several existing methods have been shown to consistently estimate causal direction assuming linear or some form of nonlinear relationship and no latent confounders. However, the estimation results could be distorted if either assumption is violated. We develop an approach to determining the possible causal direction between two observed variables when latent confounding variables are present. We first propose a new linear non-Gaussian acyclic structural equation model with individual-specific effects that are sometimes the source of confounding. Thus, modeling individual-specific effects as latent variables allows latent confounding to be considered. We then propose an empirical Bayesian approach for estimating possible causal direction using the new model. We demonstrate the effectiveness of our method using artificial and real-world data.