Theory and methods of the multiverse: an application for panel-based models

Abstract

Multiverse analysis involves systematically sampling a vast set of model specifications, known as a multiverse, to estimate the uncertainty surrounding the validity of a scientific claim. By fitting these specifications to a sample of observations, statistics are obtained as analytical results. Examining the variability of these statistics across different groups of model specifications helps to assess the robustness of the claim and gives insights into its underlying assumptions. However, the theoretical premises of multiverse analysis are often implicit and not universally agreed upon. To address this, a new formal categorisation of the analytical choices involved in modelling the set of specifications is proposed. This method of indexing the specification highlights that the sampling structure of the multiversal sample does not conform to a model of independent and identically distributed draws of specifications and that it can be modelled as an information network instead. Hamming’s distance is proposed as a measure of network distance, and, with an application to a panel dataset, it is shown how this approach enhances transparency in procedures and inferred claims and that it facilitates the check of implicit parametric assumptions. In the conclusions, the proposed theory of multiversal sampling is linked to the ongoing debate on how to weigh a multiverse, including the debate on the epistemic value of crowdsourced multiverses.