The socio-economic and managerial value of social media information diffusion

Social media platforms have become transformative infrastructures that not only mediate business interactions but also shape how societies produce, circulate, and evaluate information. They influence how opinions form, brands engage with consumers, and markets respond to collective sentiment. Prior research in information systems and digital media has examined these effects from multiple perspectives, including knowledge dissemination [11–13], content virality and emotional contagion [3,14,15], platform affordances and algorithmic visibility [16], and network and misinformation dynamics [10,17]. Collectively, this stream of work demonstrates that social media is a double-edged phenomenon amplifying visibility and engagement, while creating reputational and informational risks [5,18].

However, much of the existing literature conceptualizes user engagement activities, such as retweets, likes, and comments—as independent or additive behaviors. This reductionist view overlooks how these actions dynamically interact to shape diffusion trajectories and collective attention. For instance, prior research highlights the role of emotional content in driving virality [3], yet this framework does not address how cross-behavioral interactions (e.g., commenting versus liking) alter diffusion outcomes. Similarly, existing studies illustrate how digital affordances influence visibility [16], but do not consider the competitive interplay among multiple, parallel streams of information that coexist within algorithmic feeds.

Building on this backdrop, our study advances the literature by theorizing and empirically modeling how distinct engagement activities—retweets, comments, and likes—jointly shape information diffusion and visibility within highly competitive, algorithmically curated environments. Using data from Sina Weibo’s Hot Search List, we capture the interaction and competition among parallel posts under the same trending topic, offering insights into how attention is fragmented or reinforced across concurrent cascades. This perspective extends the understanding of social media diffusion from a business performance issue to a broader socio-technical phenomenon with implications for digital governance, public discourse management, and the future sustainability of online attention economies.

Understanding and forecasting user engagement dynamics on social media

Understanding and forecasting user engagement on social media has become a central concern in both information systems and marketing research, as these behaviors drive not only content popularity but also the broader circulation of ideas, values, and influence in digital ecosystems [19–21]. Prior studies have applied a wide range of predictive approaches, from traditional regression models [22,23] to machine learning algorithms [24–26] and deep learning architectures [27]. While these models have advanced our ability to predict engagement outcomes and assess content virality, most focus on a single type of user behavior, such as retweets or comments in isolation.

Yet, user engagement on social platforms is inherently interactive and interdependent. Different behaviors—retweeting, commenting, and liking—do not occur independently but continuously influence each other in shaping diffusion trajectories. For instance, prior research has applied deep learning to predict user interactions [28], yet it does not examine how multiple engagement types co-evolve over time. Similarly, existing studies focus on predicting virality through retweets alone [27], overlooking how comments or likes may moderate diffusion intensity or redirect user attention.

To address these limitations, our study explicitly models the dynamic interdependencies among engagement behaviors within social media posts. By integrating these interactions into a hybrid Hawkes–Transformer framework, we combine the interpretability of temporal point processes with the adaptive learning ability of deep neural networks. This integration not only improves forecasting accuracy but also yields deeper insight into the behavioral and algorithmic mechanisms driving social engagement and diffusion. Beyond predictive performance, this approach contributes to digital foresight—advancing our understanding of how engagement patterns evolve and how platforms might govern or sustain meaningful interaction in the future attention economy.

Analytical modeling of event-driven diffusion processes

Analytical models based on temporal point processes particularly the Hawkes process, have become powerful tools for examining how events unfold and influence one another over time. In social media contexts, these models capture the temporal dependencies among engagement events such as retweets, comments, and likes, illustrating how prior interactions increase the likelihood of subsequent ones [8,29]. The Hawkes framework thus offers a theoretically grounded approach to modeling self-exciting behaviors, in which each user action generates feedback that shapes the momentum of diffusion. Researchers in information systems have applied Hawkes processes to model retweet cascades and information spread, emphasizing their ability to represent cascading and path-dependent dynamics [8,9].

However, most existing studies rely on univariate formulations that capture a single behavior—typically retweets—while overlooking how different engagement types interact simultaneously. Furthermore, information cascades are often treated as independent processes, ignoring the possibility that multiple posts on the same topic may compete or reinforce one another within algorithmic feeds. These simplifications limit our ability to understand the complex attention ecology that governs social diffusion.

Recent advances have explored hybrid approaches that integrate temporal point processes with deep learning architectures to model complex event dynamics. For example, the Recurrent Marked Temporal Point Process (RMTPP) employs recurrent neural networks to model event sequences in continuous time [30], while the Neural Hawkes Process uses continuous-time LSTM structures to learn the intensity function end-to-end [31]. More recently, Transformer-based variants such as the Transformer Hawkes Process leverage self-attention mechanisms to capture long-range temporal dependencies in event sequences [32]. More recent work continues to extend this line of research by exploring more flexible neural architectures for modeling temporal dependencies in event sequences [33]. However, these approaches generally focus on end-to-end learning of the intensity function.

Extending this line of research, we develop a retweet-centric multivariate Hawkes framework that incorporates multiple engagement behaviors—retweets, comments, and likes—together with cross-cascade competition among parallel posts. In addition, we adopt a two-stage design in which a multivariate Hawkes model is first estimated to capture interpretable behavioral dynamics, and the resulting parameters are incorporated as structured inputs into a Transformer-based prediction model. Rather than learning the intensity function end-to-end, this design emphasizes interpretability and the explicit modeling of cross-cascade competition, providing a more comprehensive depiction of digital diffusion as an interdependent, event-driven process.

Summary and research gap

Prior research on social media information diffusion has provided valuable insights into content virality, engagement forecasting, and event-based diffusion modeling using frameworks such as the Hawkes process. Yet, two critical gaps remain largely unexplored. First, most studies treat engagement behaviors—such as retweets, comments, and likes—as isolated mechanisms, overlooking their interdependent and evolving nature in shaping diffusion trajectories. Second, existing models often assume that information cascades operate independently, neglecting the competitive and reinforcing interactions that occur among parallel posts under the same topic. These limitations constrain our understanding of how user behaviors collectively generate, sustain, or fragment public attention within algorithmically curated environments.

To address these gaps, this study proposes a retweet-centric modeling framework that integrates multiple engagement behaviors and cross-cascade interactions between parallel information cascades. By embedding Hawkes-estimated parameters into a Transformer-based deep learning architecture, the model enhances both forecasting capability and theoretical interpretability, bridging data-driven prediction with behaviorally grounded diffusion theory. Using large-scale data from Sina Weibo, we empirically validate this approach and uncover how cross-behavioral interdependencies and cascade competition shape collective attention.

Beyond extending prior IS and diffusion research, our findings contribute to technological forecasting and social change by illuminating the mechanisms through which algorithmic mediation structures visibility, amplifies or constrains engagement, and influences the sustainability of attention in digital societies. These insights offer foresight for digital governance and strategic content management, helping platforms and organizations design healthier and more transparent attention ecosystems.

Point process and conditional intensity function

A point process can be represented by a counting process , which denotes the cumulative number of retweet events for post up to time . This counting process is right-continuous, non-decreasing, and takes non-negative integer values, with each engagement event incrementing by one. If the first engagement occurs at time and the engagement occurs , then represents the number of engagement events within the interval . In our empirical setting, we construct incremental engagement counts by measuring the number of new retweets within each one-hour interval, denoted as

In the context of Sina Weibo, user engagement events are not independent; each retweet event influence the content’s visibility and perceived popularity, thereby increasing or decreasing the likelihood of future engagements. This temporal dependency among engagement events can be effectively captured using a self-exciting point process, which explicitly models how past events influence the arrival of future events. A key distinguishing feature of point processes is their conditional intensity function , which represents the instantaneous rate at which new events are expected to occur at time , given the history of past events. In a self-exciting point process, the conditional intensity depends not only on time but also on the cumulative history of prior events, allowing the model to capture self-reinforcing dynamics in user engagement activities. Specifically, the conditional intensity can be interpreted as the instantaneous diffusion rate of content , representing the probability that a new event occurs at time , given the history of past retweet events, while comment activity enters as an influencing factor on the retweet intensity.

Unlike traditional multivariate Hawkes processes, which typically construct separate intensity functions for each engagement type (e.g., and ), this study adopts a retweet-centric approach. Specifically, we define a single conditional intensity function for information diffusion, focusing on the occurrence of retweet events as the primary indicator of content diffusion. In this framework, comments do not have an independent intensity function. Instead, their influence is incorporated into the retweet intensity function, capturing their potential role in affecting future retweet likelihood. This modeling approach simplifies the representation of engagement dynamics while preserving the essential interactions between retweets and comments, aligning with the core nature of social media information diffusion, which is directly driven through retweets.

Given that Sina Weibo does not provide timestamps for likes, we are unable to directly model the temporal dynamics of likes using a point process framework. Instead, we incorporate the cumulative number of likes into the baseline intensity μᵢ, treating it as a post-specific constant rather than a time-varying component. This formulation allows μᵢ to differ across posts based on observed audience engagement, as shown below:

where represents the total number of likes for post i observed at the end of the 10-hour observation window and is treated as a time-invariant scalar. Before incorporating likes, the baseline intensity reduces to = μ₀. The term μ₀ captures inherent differences in post visibility, such as variation in the poster’s social network size. The second term, , reflects the overall level of audience interest associated with the post.

Finally, the conditional is interpreted as the diffusion rate of information and is defined as follows:

(1)

where is a non-negative conditional intensity function, and represents the history of past retweet events for post up to time , while comment activity is incorporated as an influencing factor on the retweet intensity.

Multivariate self-exciting process

The self-exciting process is a fundamental model in point process theory, where past events increase the likelihood of future events by raising the conditional intensity function. This formulation assumes that the impact of historical events decays monotonically over time, typically following an exponential decay function, but accumulates additively to reinforce future event occurrences.

In the context of social media information diffusion, retweets serve as the primary mechanism driving content spread. Each retweet expands a post’s audience by introducing it to new users, thereby increasing visibility and accelerating further engagement. Since information propagation depends on reaching larger networks, retweets directly contribute to the self-reinforcing diffusion process, a classic self-exciting phenomenon.

While retweets consistently promote diffusion, comments can have a dual effect. High comment volume may enhance content visibility and increase the chances of further retweets. However, critical or controversial comments may signal content saturation or generate negative sentiment, reducing retweet likelihood. Additionally, comments may shift user focus from spreading content to discussing it, potentially slowing down the diffusion process.

Traditional multivariate Hawkes models typically assign independent intensity functions to different engagement types (e.g., and ), modeling them as parallel but separate processes. However, in reality, retweets and comments are inherently interdependent, jointly shaping content visibility and information spread.

To better capture this interdependence of engagement activities influencing retweet behavior, our model adopts a retweet-centric self-exciting and cross-cascade mutual-exciting process. In this model, retweets serve as the primary self-exciting mechanism, directly driving information diffusion by expanding a post’s audience reach. Meanwhile, comments are incorporated as an additional engagement mechanism, potentially influencing the visibility of a post and its likelihood of being retweeted. Rather than modeling comments as an independent process, their impact is embedded into the retweet intensity function to better capture their influence on retweet behavior.

Specifically, the self-exciting point process models information diffusion by capturing how retweet events, together with comment activity, influence the likelihood of future retweets. Therefore, in addition to the dynamic baseline intensity , we introduce two self-excitation components, as shown in Equation (2).

First, retweet events trigger self-excitation, reinforcing information diffusion over time. Each retweet event at time contributes an additional positive excitatory effect that decays exponentially as time progresses. This effect is not permanent but gradually decays over time (as shown in Fig 6). This decay is modeled using an exponential kernel function:, with and > 0.

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Fig 6. Illustration of the self-exciting point process.

Each past retweet event generates an excitatory effect that decays exponentially over time, contributing to the cumulative conditional intensity.

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Second, unlike traditional multivariate Hawkes models that assign an independent intensity function to comments, our model embeds their effect within the retweet intensity function. In this way, comments are incorporated as an additional self-excitation component that may indirectly influence content diffusion by affecting the likelihood of retweets. Specifically, a comment event at time also generates an effect for future retweets, which may be either excitatory or suppressive, and follows a similar exponential decay function. The resulting conditional intensity function is expressed as:

(2)

where >0, and all past retweet and comment times satisfy . The parameters . The retweet-induced parameter captures the self-excitation effect of retweets, such that each past retweet increases the likelihood of future retweets. In contrast, the comment-induced parameter is not sign-restricted, allowing for both reinforcing () and suppressive () effects, depending on whether comments promote further diffusion or divert user attention away from retweeting.

To ensure the stability of the model, we require the constraint , preventing the self-excitation process from diverging. This ensures that information diffusion gradually stabilizes rather than growing indefinitely. Specifically, measures the magnitude of self-excitation from retweets, while captures the directional influence of comments on retweet behavior. The parameters and govern how quickly the impact of past retweet and comment events fade over time. As a result, the diffusion rate of information for post at time depends on the cumulative effect of all past retweets, comments, and likes, allowing us to model engagement-driven content propagation within an integrated modeling framework.

Multivariate self-exciting process with cross-cascade effects

While the self-exciting process effectively models how engagement events within a single post influence retweet behavior, real-world social media dynamics are often more complex. In particular, parallel information streams comprising multiple posts under the same trending topic occur simultaneously. These parallel posts compete for user attention, and retweets of one post can influence the retweet dynamics of others. To better capture this complexity, we extend the model to analyze cascade diffusion mechanisms on Sina Weibo.

In the specification of the model, parallel cascades are operationally defined as posts belonging to the same trending topic that are active within the same 10-hour observation window. For each focal post, parameters are estimated independently using its own event history. Cross-cascade effects are incorporated by conditioning on the retweet histories of other posts within the same topic, which enter the intensity function as exogenous inputs rather than through pairwise parameterization.

In addition to the self-excitation components, as shown in Equation (3), we incorporate parallel information flows (i.e., posts under the same trending topic) that compete for user attention. For each parallel post , let denote the sequence of retweet event times associated with post , where indexes individual retweet events. These retweet events from post may influence the diffusion intensity of the focal post . In this formulation, parameters are estimated at the post level, with each post having its own parameter vector.

Cross-cascade effects are incorporated by conditioning on the retweet histories of other posts within the same topic, which enter the intensity function as exogenous inputs rather than through pairwise parameterization. The cross-cascade component is defined as a double summation. The outer summation runs over all parallel posts within the same trending topic, while the inner summation aggregates all historical retweet events from post . This structure captures the cumulative influence of retweet activity from competing posts on the focal post’s diffusion intensity.

The complete model is expressed as:

(3)

This formulation implies that the diffusion intensity of post i depends not only on its own engagement history (retweets and comments), but also on the cumulative retweet activity of competing posts within the same topic. The parameter represents the impact of the -th parallel post cascade on the diffusion intensity of the focal post . Unlike the self-excitation parameter , the cross-cascade parameter is not sign-restricted, allowing for both reinforcing and suppressive interactions across parallel posts. A positive indicates that retweet activity from post increases the diffusion intensity of post , reflecting cross-cascade amplification. In contrast, a negative suggests competition for user attention, whereby activity in post reduces the retweet likelihood of the focal post . We summarize the constraints and interpretations of all model parameters in Table 3.

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Table 3. Summary of parameter constraints and interpretations.

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In our setting, parallel cascades are defined as posts belonging to the same Hot Search topic that are active within the same 10-hour observation window. All model parameters are estimated at the post level, with each post having its own parameter vector. Cross-cascade effects are incorporated by conditioning on the retweet histories of other posts within the same topic, which enter the intensity function as exogenous inputs rather than through pairwise parameterization. This design ensures that the model captures cross-cascade interactions without introducing a combinatorial increase in the number of parameters.

Model estimation procedure and results

In our study, we employ maximum likelihood estimation (MLE) to infer the parameters of our Hawkes model. The estimation is implemented using the L-BFGS-B algorithm with box constraints. Parameters are initialized at μ₀ = 0.1, α = 0.5, β = 1.0, and γ = 0.01. The optimization terminates when the gradient norm falls below 1e-5 or after a maximum of 1,000 iterations, whichever occurs first.

Specifically, we analyze the sequence of observed event times where represents the time of the last retweet event within the interval The objective is to construct and maximize the likelihood function based on these observed data points, enabling us to accurately capture the dynamics of information diffusion in social media networks. As shown in Equation (4), the joint density function is formulated to reflect the probability of the observed sequence of retweet events, incorporating the influence of past retweet events on future occurrences. This approach provides a robust framework for understanding and predicting user engagement behavior in social media.

(4)

From , we can derive . Substituting this into Equation (4), the likelihood function is expressed as:

(5)

Typically, the log form of the likelihood function is easier to maximize, denoted as Therefore, based on the observed data of retweet events, the log-likelihood function for estimating the parameter set is:

(6)

During the model fitting process, we analyzed the timestamps of posts, retweets, and comments for 29,316 posts. However, for 1,097 posts, the estimation procedure did not converge within a reasonable time frame. As these cases constitute only 3.74% of the dataset, we excluded them from the final analysis to ensure estimation reliability. Given the small proportion of excluded cases, their omission is unlikely to impact the accuracy of the parameter estimates. Consequently, the final sample used for parameter estimation consists of 28,219 posts.

Table 4 presents the descriptive statistics for the estimated parameters of the Hawkes model, denoted as . These estimates provide insights into the dynamics of information diffusion on Sina Weibo. The average baseline intensity is 0.362, capturing the inherent likelihood of engagement in the absence of prior triggering events. The relatively large dispersion (std. dev. = 0.831) indicates substantial heterogeneity in baseline popularity across posts. The parameter , with a mean of 0.035, captures the marginal effect of accumulated likes on the baseline diffusion intensity.

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Table 4. Descriptive statistical analysis of Hawkes model.

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Specifically, each additional like is associated with an increase of approximately 0.035 units in the baseline intensity. Because the distribution of likes is highly right skewed, we further illustrate this effect using empirical percentiles of the like distribution and the median estimated γ value reported in Table 4 (0.009). In our sample, the median post receives 106 likes, the 75th percentile receives 468 likes, and the 90th percentile receives 1,927 likes. Moving from the median to the 75th percentile corresponds to an increase of 362 likes and an increase of approximately 3.26 units in the post-specific baseline intensity. Moving from the median to the 90th percentile corresponds to an increase of 1,821 likes and an increase of approximately 16.39 units, holding other factors constant. This suggests that audience validation, as reflected by likes, plays a meaningful role in enhancing content visibility.

For self-excitation effects, the mean value of is 0.655, indicating that retweets strongly reinforce subsequent retweet activity. This effect varies substantially across posts, as reflected by the wide range of values. The corresponding decay rate has a mean of 3.430, implying that the influence of past retweets decays relatively quickly over time, leading to a rapid decline in marginal impact. To further characterize the stability of the excitation process, we compute the self-excitation ratio at the post level. The results show that this ratio is consistently below 1, with a mean of 0.29 (SD = 0.24) and a maximum value of 0.98.

For comment-induced engagement, the mean value of is −0.412, suggesting that comments, on average, negatively affect retweet diffusion. However, the observed variation indicates that this effect is heterogeneous across posts, with comments potentially exerting stronger or weaker influence depending on the context. The decay parameter , with a mean of 0.667, indicates that comment effects also diminish over time, following a similar but more persistent decay pattern compared to retweets.

For cross-cascade effects, the parameter has a mean of −0.193, suggesting that, on average, parallel information streams tend to exert a suppressive effect on each other, consistent with competition for user attention. However, the wide range of values indicates that cross-cascade interactions can also be reinforcing in certain cases. The corresponding decay parameter , with a mean of 0.859, implies that cross-cascade effects persist longer than self-excitation effects before dissipating. Because the comment-induced and cross-cascade parameters are intentionally unrestricted in sign, intensity non-negativity is determined by the total fitted intensity after all model components are combined, rather than by the α₁ / β₁ branching-stability condition alone. We therefore conduct an ex post intensity validation by reconstructing λᵢ(t) for each post using the baseline intensity, retweet self-excitation, comment effect, and cross-cascade effect, evaluated at observed event times and on a regular grid within the 10-hour observation window. The fitted total intensity remains non-negative throughout the observation window for approximately 99.7% of posts. The remaining 87 posts, approximately 0.3% of the estimated sample, show numerical violations and are excluded from the final estimation sample.

Fig 7 illustrates the temporal evolution of the average Hawkes intensity across all posts. Initially, the intensity declines sharply, reflecting the rapid decay of user engagement shortly after a post is published. This pattern is consistent with the self-exciting nature of social media interactions, where engagement spikes immediately following a post but gradually diminishes over time.

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Fig 7. Average Hawkes intensity over time.

The figure shows the estimated conditional intensity of retweets, reflecting the instantaneous rate of engagement over the 10-hour period.

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Between two and six hours after posting, the intensity decline slows, suggesting a stabilization phase in which engagement continues at a lower, more stable rate. Notably, after approximately six hours, the average intensity reaches its lowest point, indicating that most engagement activity has subsided. However, a slight upward trend emerges beyond this point, suggesting that secondary interactions, such as follow-up comments or renewed interest, contribute to a minor resurgence in engagement.

This temporal pattern highlights the importance of the initial engagement window in shaping diffusion dynamics. The sharp early decline emphasizes the need for content creators to maximize visibility during the first few hours after posts. Additionally, the slight late-stage increase in intensity suggests opportunities for re-engagement strategies, such as reposting or encouraging discussions to sustain audience interest.

Parameter robustness and goodness-of-fit

The accuracy of these parameters is crucial as they directly influence the model’s ability to capture the temporal dynamics and interaction effects of information diffusion. Moreover, ensuring that the estimated parameters adhere to expected statistical patterns provides a solid foundation for using these parameters as prior knowledge in data-driven prediction models, such as deep learning, thereby enhancing both their interpretability and predictive reliability.

To assess parameter robustness and theoretical alignment, we employ Kernel Density Estimation (KDE) to examine their empirical distributions. While KDE-based assessments do not directly quantify goodness-of-fit, they serve as an essential diagnostic tool for identifying potential estimation biases or data-driven anomalies. The KDE plot allows us to assess key statistical properties, such as central tendency, dispersion, skewness, and multimodality. By analyzing parameters like dynamic baseline intensity ( and ), self-excitation (), and cross-excitation (), we evaluate whether the estimated values accurately reflect observed diffusion patterns. As shown in S1–S8 Figs, the results reveal multimodal distributions for certain parameters, suggesting heterogeneity in user engagement and content virality. Additionally, the KDE distributions closely match empirical data, confirming the robustness of the parameter estimation process.

To further complement this diagnostic evaluation, we also conduct a formal goodness-of-fit test for the point process model using the residual point method, based on Papangelou’s random time-change theorem. The cumulative intensity process is expressed as:

1. The corresponding transformed counting process is:
2. .

If the model accurately captures the characteristics of retweet data on Sina Weibo, the estimated arrival times of retweet events for a given piece of content should result in inter-arrival residuals:

These residuals are expected to follow an exponential distribution with a unit rate:

To provide a systematic evaluation, we compute Kolmogorov–Smirnov (KS) statistics for the rescaled inter-event times across all posts and report the results in Table 5, stratified by cascade size. Given the large sample size, generating Q-Q plots for all groups is impractical. Therefore, we select the five topics with the largest number of posts, ensuring a broad and diverse representation of the data. Q-Q plots for these groups are presented in Fig 8, offering a visual assessment of the model’s fit. For most selected groups, the data points align well with the theoretical quantiles, supporting the validity of the model’s assumptions. In particular, the majority of groups exhibit a strong fit to the exponential distribution, as evidenced by the close alignment of the data points with the theoretical line.

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Table 5. Goodness-of-fit statistics based on KS tests of time-rescaled residuals.

https://doi.org/10.1371/journal.pone.0354472.t005

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Fig 8. Q–Q plots of model residuals for the five largest topic groups.

The plots compare empirical residual quantiles with theoretical values to assess model fit.

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As expected, some topics display deviations in the tail, particularly for posts with extreme engagement levels. To further investigate this pattern, we conduct additional analyses on subsamples where heavy-tailed behavior is most likely to arise, including (i) the top 5% most viral posts (retweet volume above the 95th percentile) and (ii) the largest topic clusters. The results indicate that tail deviations are systematically more pronounced among high-virality posts, confirming that heavy-tailed engagement is concentrated in extreme diffusion cases. However, despite these deviations, the exponential decay specification continues to provide a strong overall fit across the majority of observations.

This finding suggests that heavy-tailed behavior primarily manifests in the extreme tail of a relatively small subset of posts, rather than dominating the overall temporal dynamics of engagement. In our setting, most diffusion activity is driven by rapid early-stage interactions, which are effectively captured by the exponential decay kernel. To further assess kernel adequacy, we conduct a robustness check by comparing the exponential kernel with a truncated power-law specification. We estimated both models on two critical subsamples most likely to exhibit long-tail deviations: (1) the five largest topic groups, and (2) the top 5% highest-virality posts (by retweet volume). Contrary to theoretical expectations regarding heavy-tailed distributions, the exponential kernel consistently outperformed the power-law alternative across both subsamples. For the five largest topic groups, the exponential kernel achieved a substantially lower AIC (8,467.25) compared to the power-law kernel (15,766.91). Similarly, for the top 5% viral posts, the exponential kernel exhibited superior fit (AIC = −168,161.03) versus the power-law kernel (AIC = −126,212.78).

The substantially lower KS pass rate among large cascades indicates that the exponential Hawkes specification fits ordinary and medium-scale diffusion processes more reliably than highly viral cascades. Because large cascades are more likely to involve delayed bursts, external shocks, influencer reposts, or algorithmic re-ranking, their residual processes deviate more strongly from the unit-rate exponential benchmark. Accordingly, Hawkes parameters estimated for this subgroup should be interpreted cautiously. They remain useful as structured summaries of early-stage excitation and competition, but they may not fully capture the long-tail dynamics of extreme diffusion events.

Comment sentiment analysis

To more rigorously assess the comment suppression effect, it is necessary to account for the sentiment polarity of user comments, since the observed reduction in information diffusion could otherwise be confounded by the presence of negative or controversial discourse. To disentangle the effect of comment volume from that of comment sentiment, we employ a fine-tuned BERT model (BERT-base-Chinese, optimized for social media corpora) to estimate sentiment polarity scores for the comments associated with each focal post. Specifically, for each time interval, we construct a dynamic sentiment variable defined as the proportion of negative comments among all comments accumulated for a given post up to that point. This sentiment measure is then incorporated into the model as a time-varying covariate.

Our modeling framework separates behavioral dynamics from semantic information. The Hawkes process captures the temporal and interactive patterns of user behavior without directly modeling textual semantics, whereas the Transformer prediction layer integrates the extracted sentiment information together with historical features to predict future retweet volume. The results show that the negative association between comment intensity and subsequent retweet activity remains highly robust after controlling for comment sentiment. In addition, sentiment itself plays a significant moderating role. We find a significantly negative relationship between the proportion of negative comments and future retweet volume (coefficient = −0.0412, p < 0.05). Substantively, a one-standard-deviation increase in the share of negative comments is associated with a reduction of approximately 0.0412 retweets per hour. Relative to the baseline mean of 1.2476 retweets per hour, this corresponds to a 3.30% decrease in future retweet increments. These findings suggest that a higher prevalence of negative comments further inhibits users’ willingness to propagate the focal message.

Theoretical contributions

This study contributes to the broader literature on digital communication, information diffusion, and socio-technical change by introducing a comprehensive framework that unifies multivariate self-excitation, cross-behavioral interaction, and cascade competition within a single modeling and forecasting paradigm. It advances theoretical understanding of how human engagement and algorithmic mediation jointly shape the evolution of collective attention in digital environments.

First, the study extends prior research that treats retweets, comments, and likes as independent behaviors [8,9] by modeling the interdependent and asymmetric dynamics across engagement types. We show that some interactions generate reinforcing effects (e.g., likes amplifying retweet diffusion), whereas others exhibit substitution or suppressive effects (e.g., comments moderating retweet cascades). These findings uncover a non-additive structure of social interaction, enriching theoretical perspectives on how emotional, informational, and social signals co-evolve in digital diffusion processes.

Second, we address the underexplored dynamics of cross-cascade interaction by modeling how parallel information flows under the same trending topic compete or reinforce one another. While previous research typically assumes cascades to be independent, our results reveal the competitive and fragmented nature of attention in algorithmically curated ecosystems. This perspective extends theories of attention scarcity and information competition, highlighting how digital environments increasingly mediate collective cognition and public discourse.

Third, we bridge theory-driven modeling with data-driven forecasting by embedding Hawkes-estimated temporal dependencies into a Transformer-based architecture. This hybrid integration demonstrates how behaviorally grounded statistical structures can serve as prior knowledge to inform deep learning, providing a transparent and interpretable analytical lens for complex social phenomena. It contributes to the emerging discourse on hybrid analytical intelligence, which reconciles statistical rigor with machine learning scalability for studying socio-technical systems.

Together, these contributions advance theoretical understanding of the interplay between engagement behaviors, information cascades, and algorithmic attention mechanisms, offering foresight into how human–algorithm interactions will continue to shape information visibility and diffusion in the evolving digital society.

Practical implications

Our findings provide actionable insights for platform designers, digital marketers, and social media strategists seeking to optimize engagement outcomes and manage content visibility in competitive digital environments.

First, the strong self-excitation effect of retweets suggests that early-stage engagement is critical. Platforms and marketers should monitor early retweet trajectories to predict organic virality and decide when to trigger additional promotion (e.g., influencer reposts, paid boosts). Algorithmic prioritization of content could incorporate real-time estimates of excitation intensity to dynamically allocate feed exposure.

Second, the nuanced role of comments—sometimes reinforcing, often suppressive—suggests that not all engagement is beneficial for diffusion. Firms and platforms may consider distinguishing engagement for feedback (comments) from engagement for amplification (retweets). For example, algorithmic systems could down-weight controversial or high-negativity comment threads when predicting shareability or allocating visibility.

Third, the evidence of cross-cascade suppression implies that timing content releases to avoid competition with similar posts may increase visibility. Platforms may benefit from content-staggering algorithms that manage temporal spacing among related posts to mitigate attention cannibalization within trending topics.

Fourth, the hybrid Hawkes--Transformer framework demonstrates that combining structural engagement patterns with real-time behavioral data enables more accurate and adaptive prediction of content success. This capability can support real-time dashboard tools for social media teams to adjust campaign timing, promotion intensity, and content formats based on predicted diffusion curves.

Limitations and future research

Despite its contributions, this study has several limitations that suggest avenues for future work. First, the model is grounded in behavioral event patterns but does not incorporate the semantic and cognitive dimensions of content. While we capture “how” users interact (retweet, comment, like), we do not account for “why” they interact, such as message framing, emotional tone, or cultural alignment. Future research could integrate natural language features and affective content analysis to enrich the explanatory depth of engagement mechanisms.

Second, the Hawkes--Transformer framework is developed and evaluated on Sina Weibo, a platform with specific affordances that may shape diffusion dynamics including the Hot Search ranking algorithm, Weibo’s repost-centric architecture, and China’s distinct social media user culture. The competitive cascade dynamics identified here (predominant negative cross-cascade effects within trending topics) may manifest differently on platforms with different recommendation algorithms, content moderation policies, or user interaction norms. Replication studies on Twitter/X, Reddit, or TikTok data would be needed to assess the cross-platform generalizability of our findings.

Third, another limitation relates to sample selection. Our dataset consists exclusively of posts that appeared on Sina Weibo’s Hot Search List at least once during the study period. As such, the analysis focuses on high-visibility and trending content, which may not fully represent long-tail or non-trending posts. Engagement dynamics in less visible content may differ in terms of user participation patterns, diffusion speed, and cross-cascade interactions. Therefore, the generalizability of our findings beyond trending topics is limited, and future research should validate the proposed framework using broader and more representative samples of social media content.

Fourth, the model assumes an exponential decay structure for the influence of past events, which may not fully capture long-tail or bursty diffusion patterns in social media environments. Our goodness-of-fit analysis suggests that while the exponential specification provides a strong fit for the majority of cascades, deviations are more likely to occur in a small subset of highly viral posts, where heavy-tailed engagement becomes more prominent. In such cases, more flexible kernels (e.g., power-law or Weibull) may better capture tail behavior. However, given that most diffusion activity in our setting is driven by early-stage dynamics, the exponential kernel remains an effective approximation for the dominant process. Future research could explore adaptive kernel specifications to better capture both early-stage decay and extreme tail behavior.

Finally, our hybrid framework emphasizes statistical structure and prediction, but future work could extend it to decision-making contexts, such as adaptive content scheduling, real-time engagement interventions, or A/B testing of content strategies based on predicted engagement and diffusion dynamics.