Population size predicts lexical diversity, but so does the mean sea level - why it is important to correctly account for the structure of temporal data

TL;DR

This paper highlights the importance of correctly modeling temporal dependencies in data analysis, demonstrating how neglecting this can lead to spurious correlations, and proposes simple transformations to address this issue.

Contribution

It reveals how improper temporal modeling causes false relationships in linguistic and environmental data and offers practical solutions for correct analysis.

Findings

Incorrect models produce spurious correlations between population size and lexical diversity.

Transforming time series data can mitigate issues caused by temporal dependencies.

Proper modeling of temporal structure is crucial for valid inferences in longitudinal studies.

Abstract

In order to demonstrate why it is important to correctly account for the (serial dependent) structure of temporal data, we document an apparently spectacular relationship between population size and lexical diversity: for five out of seven investigated languages, there is a strong relationship between population size and lexical diversity of the primary language in this country. We show that this relationship is the result of a misspecified model that does not consider the temporal aspect of the data by presenting a similar but nonsensical relationship between the global annual mean sea level and lexical diversity. Given the fact that in the recent past, several studies were published that present surprising links between different economic, cultural, political and (socio-)demographical variables on the one hand and cultural or linguistic characteristics on the other hand, but seem to suffer from exactly this problem, we explain the cause of the misspecification and show that it has profound consequences. We demonstrate how simple transformation of the time series can often solve problems of this type and argue that the evaluation of the plausibility of a relationship is important in this context. We hope that our paper will help both researchers and reviewers to understand why it is important to use special models for the analysis of data with a natural temporal ordering.