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1. Statistics in the Service of Science: Don’t Let the Tail Wag the Dog

   https://doi.org/10.1007/s42113-022-00129-2  

   Singmann, Henrik; Kellen, David; Cox, Gregory E.; Chandramouli, Suyog H.; Davis-Stober, Clintin P.; Dunn, John C.; Gronau, Quentin F.; Kalish, Michael L.; McMullin, Sara D.; Navarro, Danielle J.; et al (March 2023, Computational Brain & Behavior)

   Abstract Statistical modeling is generally meant to describe patterns in data in service of the broader scientific goal of developing theories to explain those patterns. Statistical models support meaningful inferences when models are built so as to align parameters of the model with potential causal mechanisms and how they manifest in data. When statistical models are instead based on assumptions chosen by default, attempts to draw inferences can be uninformative or even paradoxical—in essence, the tail is trying to wag the dog. These issues are illustrated by van Doorn et al. (this issue) in the context of using Bayes Factors to identify effects and interactions in linear mixed models. We show that the problems identified in their applications (along with other problems identified here) can be circumvented by using priors over inherently meaningful units instead of default priors on standardized scales. This case study illustrates how researchers must directly engage with a number of substantive issues in order to support meaningful inferences, of which we highlight two: The first is the problem of coordination , which requires a researcher to specify how the theoretical constructs postulated by a model are functionally related to observable variables. The second is the problem of generalization , which requires a researcher to consider how a model may represent theoretical constructs shared across similar but non-identical situations, along with the fact that model comparison metrics like Bayes Factors do not directly address this form of generalization. For statistical modeling to serve the goals of science, models cannot be based on default assumptions, but should instead be based on an understanding of their coordination function and on how they represent causal mechanisms that may be expected to generalize to other related scenarios. 

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2. Causal Inference With Observational Data and Unobserved Confounding Variables

   https://doi.org/10.1111/ele.70023  

   Byrnes, Jarrett_E K; Dee, Laura E (January 2025, Ecology Letters)

   ABSTRACT Experiments have long been the gold standard for causal inference in Ecology. As Ecology tackles progressively larger problems, however, we are moving beyond the scales at which randomised controlled experiments are feasible. To answer causal questions at scale, we need to also use observational data —something Ecologists tend to view with great scepticism. The major challenge using observational data for causal inference is confounding variables: variables affecting both a causal variable and response of interest. Unmeasured confounders—known or unknown—lead to statistical bias, creating spurious correlations and masking true causal relationships. To combat this omitted variable bias, other disciplines have developed rigorous approaches for causal inference from observational data that flexibly control for broad suites of confounding variables. We show how ecologists can harness some of these methods—causal diagrams to identify confounders coupled with nested sampling and statistical designs—to reduce risks of omitted variable bias. Using an example of estimating warming effects on snails, we show how current methods in Ecology (e.g., mixed models) produce incorrect inferences due to omitted variable bias and how alternative methods can eliminate it, improving causal inferences with weaker assumptions. Our goal is to expand tools for causal inference using observational and imperfect experimental data in Ecology. 

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3. Longitudinal Omics Data Analysis: A Review on Models, Algorithms, and Tools

   Taheriyoun, Ali R; Ross, Allen; Safikhani, Abolfazl; Soudbakhsh, Damoon; Rahnavard, Ali (June 2025, arxiv)

   Longitudinal omics data (LOD) analysis is essential for understanding the dynamics of biological processes and disease progression over time. This review explores various statistical and computational approaches for analyzing such data, emphasizing their applications and limitations. The main characteristics of longitudinal data, such as imbalancedness, high-dimensionality, and non-Gaussianity are discussed for modeling and hypothesis testing. We discuss the properties of linear mixed models (LMM) and generalized linear mixed models (GLMM) as foundation stones in LOD analyses and highlight their extensions to handle the obstacles in the frequentist and Bayesian frameworks. We differentiate in dynamic data analysis between time-course and longitudinal analyses, covering functional data analysis (FDA) and replication constraints. We explore classification techniques, single-cell as exemplary omics longitudinal studies, survival modeling, and multivariate methods for clinical/biomarker-based applications. Emerging topics, including data integration, clustering, and network-based modeling, are also discussed. We categorized the state-of-the-art approaches applicable to omics data, highlighting how they address the data features. This review serves as a guideline for researchers seeking robust strategies to analyze longitudinal omics data effectively, which is usually complex. 

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4. Optimal designs for generalized linear mixed models based on the penalized quasi-likelihood method

   https://doi.org/10.1007/s11222-023-10279-3  

   Shi, Yao; Yu, Wanchunzi; Stufken, John (October 2023, Statistics and Computing)

   While generalized linear mixed models are useful, optimal design questions for such models are challenging due to complexity of the information matrices. For longitudinal data, after comparing three approximations for the information matrices, we propose an approximation based on the penalized quasi-likelihood method.We evaluate this approximation for logistic mixed models with time as the single predictor variable. Assuming that the experimenter controls at which time observations are to be made, the approximation is used to identify locally optimal designs based on the commonly used A- and D-optimality criteria. The method can also be used for models with random block effects. Locally optimal designs found by a Particle Swarm Optimization algorithm are presented and discussed. As an illustration, optimal designs are derived for a study on self-reported disability in olderwomen. Finally,we also study the robustness of the locally optimal designs to mis-specification of the covariance matrix for the random effects. 

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5. Distributed Bayesian Inference in Linear Mixed-Effects Models

   Srivastava, S; Xu, Y. (March 2021, Journal of computational and graphical statistics)

   null (Ed.)

   Linear mixed-effects models play a fundamental role in statistical methodology. A variety of Markov chain Monte Carlo (MCMC) algorithms exist for fitting these models, but they are inefficient in massive data settings because every iteration of any such MCMC algorithm passes through the full data. Many divide-and-conquer methods have been proposed to solve this problem, but they lack theoretical guarantees, impose restrictive assumptions, or have complex computational algorithms. Our focus is one such method called the Wasserstein Posterior (WASP), which has become popular due to its optimal theoretical properties under general assumptions. Unfortunately, practical implementation of the WASP either requires solving a complex linear program or is limited to one-dimensional parameters. The former method is inefficient and the latter method fails to capture the joint posterior dependence structure of multivariate parameters. We develop a new algorithm for computing the WASP of multivariate parameters that is easy to implement and is useful for computing the WASP in any model where the posterior distribution of parameter belongs to a location-scatter family of probability measures. The algorithm is introduced for linear mixed-effects models with both implementation details and theoretical properties. Our algorithm outperforms the current state-of-the-art method in inference on the functions of the covariance matrix of the random effects across diverse numerical comparisons. 

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