Language statistics at different spatial, temporal, and grammatical scales

TL;DR

This study analyzes how language usage varies across temporal, spatial, and grammatical scales by applying rank diversity to geolocated Twitter data from eight countries. It defines $d(k)$ and models the sigmoid relationship $\Phi_{\mu,\sigma}(\log_{10} k)$ to extract the speed parameter $\mu$, then uses regression to assess scale effects and interactions. The key finding is that grammatical scale dominates variability in rank diversity, with 1-grams largely language-invariant and higher $N$-grams revealing geographic clustering; temporal scale shows a nonlinear, concave relation with $\Delta t$, and spatial scale effects depend on language. Emojis, hashtags, and mentions also follow sigmoid rank-diversity patterns, indicating cultural and topical differences; overall the work provides a quantitative framework to separate universal versus culture-specific aspects of language statistics and demonstrates meaningful interactions across scales.

Abstract

Statistical linguistics has advanced considerably in recent decades as data has become available. This has allowed researchers to study how statistical properties of languages change over time. In this work, we use data from Twitter to explore English and Spanish considering the rank diversity at different scales: temporal (from 3 to 96 hour intervals), spatial (from 3km to 3000+km radii), and grammatical (from monograms to pentagrams). We find that all three scales are relevant. However, the greatest changes come from variations in the grammatical scale. At the lowest grammatical scale (monograms), the rank diversity curves are most similar, independently on the values of other scales, languages, and countries. As the grammatical scale grows, the rank diversity curves vary more depending on the temporal and spatial scales, as well as on the language and country. We also study the statistics of Twitter-specific tokens: emojis, hashtags, and user mentions. These particular type of tokens show a sigmoid kind of behaviour as a rank diversity function. Our results are helpful to quantify aspects of language statistics that seem universal and what may lead to variations.

Figures (7)

• Figure 1: Rank evolution of some Spanish words during 2014. Note that if a word has a high rank, its trajectory takes a wider set of possible ranks compared to words with lower ranks Cocho2015.
• Figure 2: Rank diversity $d(k)$ for eight different countries at different grammatical scales $N=1,2,...,5$, $\Delta t = 24$hr,. Spanish-speaking countries are shown with solid lines, English-speaking countries with dashed lines. A) monograms, B) digrams, C) trigrams, D) tetragrams, and E) pentagrams. X-axis is shown in log scale.
• Figure 3: Different estimations of $\mu$. Measure the speed of rank diversity increment vs. different values of the temporal scale. Note that the $x$-axis is in $\log_{10}$ scale. The $N$ values represent $N$-grams (grammatical scale). Each row uses Twitter data from the country specified at the right label. Colored lines represent the different spatial scales considered.
• Figure 4: $\mu$ estimates vs. different values of the spatial scale. The top and right labels represent the same as in Fig. \ref{['fig:temp']}. Colored lines here represent the different temporal scales.
• Figure 5: Average dispersion (2) of scale $s$ for each country and a bar chart to compare them.