Cultural innovations, including language, exhibit regional adoption patterns. Two primary mechanisms are proposed: identity effects (adopting behaviors signaling demographic identities) and network effects (spread through homophilous networks). Existing research often focuses on one mechanism, neglecting their interaction. This study hypothesizes that network and identity play complementary roles, with network effects driving urban spread and identity effects driving rural spread. The researchers aim to demonstrate that modeling lexical innovation requires integrating both network and identity effects to accurately capture the geographic patterns of adoption, particularly considering the complexities of urban-rural diffusion.

Existing literature on cultural innovation diffusion often attributes regional adoption to either identity or network effects. Identity-centric models emphasize strong-tie diffusion among demographically similar individuals, while network-centric models focus on weak-tie diffusion through broader networks. However, these models often struggle to explain the differing diffusion patterns observed in urban versus rural areas. Urban centers tend to be diverse and adopt innovations earlier, while rural areas exhibit more homogenous adoption patterns where innovations signal local identities. The challenge lies in the limited models that explicitly integrate network and identity dynamics, especially regarding the urban-rural spread.

The researchers developed an agent-based model to simulate the diffusion of new words on Twitter. The model incorporates network structure derived from a 10% sample of Twitter data (2012-2020), focusing on reciprocal mentions to define tie strength. Agent identities are inferred from user locations and census data, covering five categories (location, race/ethnicity, socioeconomic status, languages spoken, and political affiliation). Each word's identity is assigned based on the demographics of its early adopters. The diffusion process simulates agents' decisions to adopt a word based on factors like attention fading, novelty, stickiness, relevance (identity congruence), variety of exposure, and relatability (identity similarity of network neighbors). The model parameters are fitted to empirical data from 76 neologisms identified on Twitter. Three counterfactual models were simulated: network-only, identity-only, and a null model (shuffled network and no identity). Model evaluation compared simulated and empirical spatial distributions using Lee's L and spatiotemporal pathways between counties using Bayesian likelihood.

The study found that the Network+Identity model significantly outperformed the counterfactual models in predicting both the spatial distribution and spatiotemporal pathways of new word adoption. The Network+Identity model demonstrated "broadly similar" adoption regions to Twitter data (mean Lee's L > 0.15) and substantially higher likelihood of observed pathways compared to other models. Specifically: 1. **Overall Diffusion:** The Network+Identity model best predicted the geographic distribution and spread of new words across all areas, highlighting the importance of integrating both factors. 2. **Urban-Urban Diffusion:** The Network-only model best explained the spread of words between urban counties, indicating weak-tie diffusion was dominant. Empirical pathways were strongest when network pathways were heavy and identity pathways were light, consistent with weak-tie diffusion among dissimilar individuals. 3. **Rural-Rural Diffusion:** The Identity-only model best predicted diffusion within rural counties, supporting the strong-tie diffusion hypothesis. Empirical pathways were strongest when both network and identity pathways were heavy, highlighting the importance of shared identity in rural areas. 4. **Urban-Rural Diffusion:** The Network+Identity model was necessary to best predict the diffusion between urban and rural counties, signifying the interplay of both network and identity in bridging these geographical contexts. Diffusion in this context seemed to incorporate aspects of both weak-tie and strong-tie mechanisms. 5. **Urban-Rural Dynamics:** Urban-rural differences emerged from the model's interaction of network and identity, suggesting that these differences are not simply due to factors like population density or tie distribution. The Null model underperformed all other models, demonstrating that the interplay of network and identity is crucial, not just structural factors alone.

The findings strongly support the hypothesis that network and identity play complementary and interacting roles in the spatial diffusion of linguistic innovation. The superiority of the Network+Identity model demonstrates that omitting either factor leads to incomplete understanding of diffusion patterns. The urban-rural differences in diffusion mechanisms are not simply due to structural differences in networks but are driven by the distinct ways individuals use networks and identities to spread and adopt linguistic innovations. Weak-tie diffusion dominates in urban environments due to the diversity of connections, while strong-tie diffusion predominates in rural areas owing to the importance of shared identity. The model provides a framework for understanding how these complementary processes generate observed spatial patterns, particularly the heterogeneity between urban and rural settings.

This study underscores the critical need for integrating both network and identity effects in models of cultural diffusion. The agent-based model successfully captures the observed spatial patterns of lexical innovation by accounting for the complementary roles of network and identity in urban and rural contexts. Future research can expand this model to other types of cultural innovations, explore additional factors influencing diffusion, and investigate cross-national or cross-cultural applicability.

The study relied on a 10% sample of Twitter data, which might not fully represent the overall population. The inference of agent identities from census data involves potential ecological fallacies. The model includes several simplifying assumptions, such as the representation of identities and the mechanism of word adoption, which could be further refined. The focus on reciprocal mentions limits the scope of network connections considered.