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The preference for simple explanations, known as the parsimony principle, has long guided the development of scientific theories, hypotheses, and models. Yet recent years have seen a number of successes in employing highly complex models for scientific inquiry (e.g., for 3D protein folding or climate forecasting). In this paper, we reexamine the parsimony principle in light of these scientific and technological advancements. We review recent developments, including the surprising benefits of modeling with more parameters than data, the increasing appreciation of the context-sensitivity of data and misspecification of scientific models, and the development of new modeling tools. By integrating these insights, we reassess the utility of parsimony as a proxy for desirable model traits, such as predictive accuracy, interpretability, effectiveness in guiding new research, and resource efficiency. We conclude that more complex models are sometimes essential for scientific progress, and discuss the ways in which parsimony and complexity can play complementary roles in scientific modeling practice. 

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. 

Abstract van Doorn et al. (2021) outlined various questions that arise when conducting Bayesian model comparison for mixed effects models. Seven response articles offered their own perspective on the preferred setup for mixed model comparison, on the most appropriate specification of prior distributions, and on the desirability of default recommendations. This article presents a round-table discussion that aims to clarify outstanding issues, explore common ground, and outline practical considerations for any researcher wishing to conduct a Bayesian mixed effects model comparison.