Analysis of Communication Effects of Media Agenda Synergy: A Hidden Markov Model-Based Approach to Modeling the Timing of Media Releases

Abstract

Based on Agenda-Setting Theory, Media Agenda Synergy (MAS) can enhance the communication effectiveness of public issues (e.g., climate change, social justice, and public health) through the information resonance and agenda complementarity among cross-media platforms, thus reconstructing the public perception. In this paper, we focus on the dynamic impact of cross-media agenda synergy on public agenda intensity and innovatively propose a “HMM-Granger” hybrid modeling framework for Media Agenda Synergy: Firstly, we quantify the causal weights of agenda shifting based on the deconstruction of the nonlinear time-series dependence of multisource media data by using LSTM neural networks. Secondly, the state transfer probability matrix of the Hidden Markov Model reveals the dual paths of “explicit collaboration” (e.g., issue resonance) and “implicit competition” (e.g., agenda masking) in media agenda coordination. The results of this study show that the Agenda Synergy between mainstream media and social media during major events can generate an Agenda Multiplier Effect, resulting in a significant increase in the intensity of the public agenda. This study provides a computable theoretical paradigm for Inter-Media Agenda Network modeling and data-driven decision support for optimizing opinion guidance strategies.

1. Introduction

Agenda-Setting Theory, initially proposed by McCombs and Donald Shaw in 1972, elucidates the mechanism through which the media influences the public’s perception of issues by selecting what to report (Coleman et al., 2009; M. E. McCombs & Shaw, 1972). In the context of sustainable development in social, environmental, and economic domains, the media assume an indispensable role through agenda setting and opinion guidance, particularly in the areas of environmental protection, social equity, and health. The communication strategies and collaborative effects of these media entities have a profound and far-reaching impact (Andrews & Caren, 2010). However, with the advent of new media and social media, the process of media agenda-setting has evolved into a dynamic and collaborative endeavor, where public perceptions and behaviors are shaped through the interaction and competition among various platforms and media. This transformation has led to an increase in the complexity and dynamism of the media landscape, thereby underscoring the significance of inter-media collaboration and competition in shaping public opinion.

In this paper, we focus on the structure and dynamics of the Chinese media system, which is shaped by political centralization, state-led communication, cultural traditions, and content regulation. These structural features create a distinct agenda-setting environment in the context of digital transformation. According to the ’List of Sources for Internet News Information Units’ issued by China’s Cyberspace Administration in 2021, official online media can be categorized into central media (e.g., Xinhua News Agency, People’s Daily), official media (e.g., government departments such as the CDC or the Central Publicity Department), and regional media (e.g., Beijing Daily, Shenyang Daily). Central media are affiliated with top-level political bodies; official media serve as channels for institutional communication; and regional media are operated by local authorities.

In addition to these institutional outlets, we also include key opinion leaders and the public in our analysis. This broader classification adopts a functional perspective on media participation in digital platforms. Drawing on Chadwick’s concept of a hybrid media system (Chadwick, 2017), the non-institutional actors, such as verified users and ordinary citizens can influence the attention of the issue by posting, sharing, and framing content. While their role differs from traditional media, they function as observable participants in the agenda-setting process on platforms like Weibo. In this study, the term media actors refers broadly to both institutional organizations (such as central, official, and regional media) and non-institutional participants (such as KOLs and the public), who all contribute to shaping agendas on Weibo.

In the context of major events (i.e., those involving political sensitivity or significant social impact), various forms of media interact with one another to promote the formation and dissemination of public opinion (Guo, 2019). During the 2020 outbreak of COVID-19 in China, for instance, various media actors—namely central media, official media, regional media, and key opinion leaders—collaborated to shape the public’s perception of the epidemic through a coordinated agenda. This collaborative effort, dubbed the Inter-Media Agenda Network, employed strategies such as “issue relay,” “complementary framing,” and “discourse resonance,” effectively guiding public opinion (Guo, 2019; Lan et al., 2025). For instance, People’s Daily, a prominent media actor, disseminated health and safety guidelines on microblogging platforms, effectively influencing the public’s cognitive framing of the epidemic by underscoring scientific epidemic prevention, government effectiveness, and collectivist values. Official media actors played a predominant role in policy interpretation, while social media platforms enhanced public engagement on the issue through user-generated content, gradually fostering a consensus. Consequently, examining the interplay between media agendas and their influence on public opinion emerges as a pivotal subject to enhance the comprehension of the communication dynamics within contemporary media (Chen et al., 2020).

The profound impact of artificial intelligence (AI) algorithms and information recommendation systems on media agenda setting has prompted researchers to explore the integration of Agenda-Setting Theory with big data analysis and machine learning models. This endeavor aims to enhance our comprehension of the formation and dissemination mechanisms of public opinion in contemporary society. The application of emerging technologies has furnished researchers with more data and technical support for empirical studies of agenda setting and the impact of agenda collaboration. However, in complex media communication environments, interactions between media are often nonlinear, and linear models are difficult to capture the more complex dynamic characteristics (Tank et al., 2021). In addition, high-dimensional data in media communication also increases the complexity of causal analysis.

In this paper, we propose a two-pronged approach that integrates Granger causality analysis to illuminate the interactions among diverse media and their potential influence on public opinion agendas. We then leverage the state transfer property of Hidden Markov Chains to enhance the feasibility of analyzing and predicting media agenda setting. This approach also enables the examination of agenda interactions and collaborations among various media actors during major social events. A central focus of this study is the promotion of public opinion on issues (e.g., climate change, public health, social justice, etc.) through collaborative mechanisms to guide and engage the public. This paper’s main contributions are as follows:

(1)

We innovatively propose an “HMM-Granger” hybrid model framework for Media Agenda Synergy, which provides a computable theoretical paradigm for modeling the Inter-Media Agenda Network.

(2)

We take media agenda collaboration as the object of study and reveal the direction of agenda setting among media through Hidden Markov Chains.

(3)

We validate a series of news on the microblogging platform, calculate the accuracy of the media release sequences of the news obtained by our prediction method, and explore the specific reasons behind the data, which suggests that our method is valid to a certain extent.

The rest of the paper is structured as follows: Section 2 provides a comprehensive review of the existing literature related to media agenda setting and collaboration. Section 3 describes the dataset we use. Section 4 introduces our proposed HMM–Granger mixed modeling framework. Section 5 outlines how to capture and quantify the nonlinear Granger causality among media. Section 6 analyzes the contribution of the introduction of Hidden Markov Chains to media agenda setting and to the function of media agenda collaboration. Section 7 summarizes the paper and provides directions for future research. Section 8 contains a discussion of the limitations of this paper and a discussion of future work.

2. Related Work

The Media Agenda-Setting Theory underscores the pivotal function of the media in shaping the public agenda. Research findings indicate that the media exerts influence not only on the issues that resonate with the public but also on their perception of those issues. By shaping the “mimetic environment” of the external world, the media indirectly impact the public’s view of the world. Agenda-Setting Theory has undergone three stages of development: First-Level Agenda Setting, Second-Level Agenda Setting, and Network Agenda Setting. The initial First-Level Agenda Setting, proposed by McCombs and Donald Shaw, posits that the media dictates the agenda of political campaigns by meticulously filtering information and shaping the public’s perception of issues, thereby influencing voter preferences. In contrast, Second-Level Agenda Setting asserts that the media exerts a subtle influence on public perception and response to issues by accentuating particular attributes of those issues (M. McCombs, 2002). Second-Level Agenda Setting posits that the media sifts and reframes information based on morphological awareness and group norms to influence public perceptions, attitudes, and behaviors. Conversely, public agendas can exert a reverse agenda-setting effect on media agendas through the medium of the Internet (M. E. McCombs & Shaw, 1972). Network Agenda Setting (Vu et al., 2014) contends that the media can not only dictate public perceptions and behaviors but also facilitate the integration of disparate information. Network Agenda Setting places emphasis on the cognitive frameworks employed by individuals to interpret social reality, and the manner in which media shapes these connections exerts a significant influence on the public’s comprehension of events (Lang, 2000).

Agenda Synergy Theory posits that interactions and cooperation among media entities influence the formation and dissemination of an agenda (Lewis, 2006; M. McCombs, 2004). Media entities can achieve synergy through various mechanisms, including joint investigations, collaborative reporting, and information exchange. This theory underscores the dynamic process by which media influence each other. The selection of issues by one media entity may consequently prompt coverage by another. This influence is not confined to a single platform; rather, it is characterized by dynamic interactions among traditional and emerging media, which collectively shape and transmit issues (Naik & Raman, 2003; Vonbun et al., 2016). A seminal study by Fabrizio Gilardi et al. examined and categorized the posts of several Swiss newspapers, official accounts of political parties, and politicians (Gilardi et al., 2022), revealing an intricate interplay between traditional media agendas, the social media agendas of political parties, and the social media agendas of politicians. Zhang M et al. studied the social media discussions related to the South Korean presidential election, identified the existence of social bots, and explored the relationship between media agendas, bots’ agendas, and public agendas from the perspective of agenda setting (M. Zhang et al., 2024). Under the perspective of Intermedia Agenda Setting, media interactions and messaging are not only limited to news reporting itself, but also include issue interactions. This influence is frequently multilevel and multichannel, with media actors collaborating and interacting to shape the public agenda. Schmidt expounded on the interactive impact of populism on agenda setting, particularly when populists are outside, elected to public office, or in government, how populist messengers construct debates and how they utilize the media to engage the public (Schmidt, 2025). Cai M et al. employed a combination of topic mining and content analysis to identify issues discussed by government tweets and citizens based on an online agenda-setting model (Cai et al., 2023). Arijeniwa et al. investigated the impact of social media on youth political participation in Nigeria by setting the agenda for public discourse (Arijeniwa & Nwaoboli, 2023). Naik P A et al. explored the effect of media agenda synergy in the field of advertising (Naik & Raman, 2003).

In order to facilitate a more robust examination of agenda-setting networks, researchers frequently employ Granger causality analysis (Granger, 1969) to ascertain whether the agenda-setting of a particular media actor exerts an influence on the agenda of other media actors by examining the causal relationships that exist among them. The models most frequently utilized for Granger causality analysis can be classified into two distinct categories: linear causal models and nonlinear causal models (Lütkepohl, 2013; Shojaie & Fox, 2022). The utilization of Granger causal inference methods based on linear models typically necessitates the presence of linear dependencies between the variables within the system, a condition that is often challenging to fulfill in numerous practical models. Nonlinear Granger causal inference methods, on the other hand, possess the capacity to detect nonlinear dependencies between parameters and can be implemented in various forms. These include nonlinear prediction models based on radial basis functions (Pottmann & Seborg, 1997), nonlinear causal models based on Copula (Kim et al., 2020), methods based on gray correlation analysis, and causal models based on neural networks. Among these, the neural network-based Granger causal inference method (Tank et al., 2021) has demonstrated the capacity to enhance the model’s capability to discern nonlinear systems by integrating neural networks to represent intricate nonlinear interactions between inputs and outputs. HC Baumann et al. employed linear Granger causation to analyze the relationship between political parties and the media in the 2014 Indian general election (Baumann et al., 2018). In another study, L Šķestere et al. employed vector autoregressive modeling to examine agenda-setting dynamics during the course of the COVID-19 pandemic (Šķestere & Darģis, 2022). Additionally, it is important to note that Granger causality—especially in its nonlinear neural implementation—does not establish true causal relationships in the philosophical or experimental sense. Rather, it identifies whether the past behavior of one time series improves the prediction of another, which is suitable for uncovering directional influence patterns in agenda-setting dynamics.

Prior research in agenda setting and media interaction suggests that media dynamics are often nonlinear, driven by mechanisms such as agenda competition (where attention to one issue limits attention to others), threshold effects (where influence emerges only after attention crosses a critical level), and agenda substitution (where new topics displace previous ones). These mechanisms create abrupt or feedback-driven shifts in agenda trajectories across media actors. For example, Neuman et al. describe how fragmented and recursive attention dynamics challenge linear assumptions in agenda-setting (Russell Neuman et al., 2014), while Wolfe et al. highlight how bounded attention and institutional friction result in nonlinear agenda transitions in both policy and media environments (Wolfe et al., 2013). This requires us to adopt a nonlinear Granger causality approach to better capture such complex, real-world dependencies among media.

In addition, researchers have employed Hidden Markov Models to examine dynamic interactions in the media context. For instance, Hopp et al. (2020) applied HMMs to model the temporal transactions between news frames and sociopolitical events (Hopp et al., 2020), offering valuable insights into the evolving relationship between media narratives and real-world developments.

The majority of extant studies concentrate on causal analyses of individual events and are still deficient in quantitative modeling of dual-path patterns in cross-media dynamic interaction mechanisms and dynamic identification of heterogeneous media synergy patterns. By constructing a framework of HMM–Granger mixed causal modeling, we reveal the symbiotic mechanism of explicit collaboration and implicit competition in agenda synergy and establish a computational explanatory model for the dynamic evolution of media agenda networks.

3. Materials: Data

3.1. Data Selection

Since most research in the field of agenda setting focuses on single events, few scholars have explored the patterns of agenda setting across a series of similar events. As a result, most research findings cannot be directly applied to guide mainstream media in responding to future public opinion events. Therefore, it is necessary to investigate the agenda-setting patterns of a series of similar news events to better prepare for and respond to similar incidents in the future.

This study selects recent COVID-19-related events within China as the research focus for the following reasons:

First, pandemic-related events offer abundant data sources. In recent years, pandemic-related topics have consistently remained at the forefront of public attention. When an outbreak occurs in a specific region, not only do professional media actors provide comprehensive coverage, but a large number of opinion leaders and members of the public also share their attitudes and viewpoints on related topics.

Second, individual pandemic events tend to span longer periods. Since the process from detecting an outbreak to fully containing it requires time, the dynamics surrounding such events remain continuously updated online for an extended period. Each of the pandemic events selected in this study spans no fewer than 15 days, meeting the temporal requirements for conducting Granger causality tests.

Third, pandemic-related events involve high levels of participation from both the media and the public (W. Zhang et al., 2022). In such events, various media actors engage in reporting, guiding the public to adopt pandemic prevention and control measures. This process not only constitutes an example of media agenda setting targeting the public but also reflects collaboration between media agendas. Thus, relevant tweets related to pandemic events can be collected to study the mechanisms of media agenda collaboration and their influence on the public.

Unlike the approaches proposed by (Trilling & van Hoof, 2020), which define news events using either traditional TF·IDF-based cosine similarity or soft cosine distance based on word embeddings, our study adopts a more pragmatic and data-driven definition of events.

Specifically, we define a news event as a temporally bounded cluster of Weibo posts referring to a specific real-world incident or issue, identified through the co-occurrence of specific keywords and hashtags in post content and temporal proximity, typically within a 48-hour window centered around a peak in post volume.

3.2. Dataset Introduction

This study compiled the Covid19-AgendaFrame dataset by collecting and integrating posts published on Weibo by various media actors during the pandemic period (from 21 May 2021 to 11 November 2021). Following the classification outlined in the “List of Sources for Internet News Information Units” issued by China’s Cyberspace Administration in 2021, mainstream media were categorized into three groups: central media, official media, and regional media. In addition, we divide Weibo users into opinion leaders and the public based on whether they have a Weibo certification, their participation in political and social commentary activities, and their influence on the platform.

As shown in Figure 1, the posts of the general public account for the largest proportion in the Covid19-AgendaFrame dataset, making up 37%, followed by posts from opinion leaders, which account for 27%. This aligns with the reality that the number of ordinary users on the Internet far exceeds that of opinion leaders.

Among the three types of mainstream media, the official media reported COVID-19-related events more frequently than the central media and the regional media, exceeding them by 14 and 19 percentage points, respectively.

The figure below illustrates the temporal changes in the number of posts published by the different actors (the three types of mainstream media, opinion leaders, and the general public) during the time period covered by the dataset.

In the Figure 2, the horizontal axis represents dates, and the vertical axis indicates the number of posts published. Two notable characteristics can be observed in the fluctuations of post counts across the different discourse actors:

The overall trends in post counts among the five types of discourse actors are similar. These trends fluctuate with the progression of the pandemic, with the public showing the most significant fluctuations in post counts. While regional media maintained relatively stable posting patterns, they also exhibited slight fluctuations in response to changes in the posting patterns of other actors. The posting trends of the public and opinion leaders are the most similar. Although the public posted slightly more frequently than opinion leaders, their fluctuations in timing and amplitude were highly aligned.

4. The HMM–Granger Hybrid Modeling Framework for Media Agenda Synergy

The HMM–Granger Media Agenda Synergy hybrid modeling framework combines Granger causal inference methods with Hidden Markov Models to provide new perspectives on the analysis of agenda setting and media communication paths, and The HMM–Granger hybrid modeling framework is shown in Figure 3 below.

(1)

Data preprocessing: We processed the series of events from Weibo and counted and calculated the corresponding epidemic news time series (HeatSeq) of various media.

The resulting series are sequences of hourly aggregated post counts, categorized by media type (e.g., central media, opinion leaders, and the public). These sequences serve as the foundation for both the Granger causality matrix and the Hidden Markov Model.

(2)

Construct the Granger causality matrix of media agendas: We utilize the long- and short-term memory network model to construct multiple neural network models for the time series of different media, so as to obtain the causal relationship between different media and between the media and the public.

(3)

Collaborative agenda prediction based on Hidden Markov Chain: In order to further explain the synergistic effect between media agendas and their impacts, we introduce the Hidden Markov Chain. The introduction of the Hidden Markov Model allows us to analyze the dynamic changes of agenda setting at a higher level, and we represent the transfer probability between different media agendas through the state transfer probability matrix. This can help us reveal the agenda collaboration patterns among media. Especially in complex environments involving multiple media interactions, capturing the state transfer relationship between different media through HMM provides a new control mechanism and strategy for media agenda collaboration and optimizes the media’s ability to cooperate and guide in the process of information dissemination.

5. Intermedia Agenda-Setting Matrix Based on Granger Causality Analysis

Agenda-setting relationships can be manifested through causality, and Granger causality analysis is by far the most widely used causal inference method in the field of agenda-setting analysis. However, most of the Granger causal inference methods are based on the assumption of linear time series dynamics, and the VAR model used does not test the nonlinear dependence problem and fails to capture important nonlinear interactions among predictors (Shojaie & Fox, 2022). To address this limitation, this paper proposes a novel approach: the training of multi-group LSTM network models for the agenda-setting analysis. The proposed method involves the construction of multi-group LSTM neural networks, which are then utilized to conduct Granger causality tests on time series data comprising the number of media reports or public comments. The objective is to extract the agenda-setting direction and attribute the agenda-setting direction in the epidemic event, respectively. This chapter will introduce the time series of epidemic news, the modeling process, and the experimental results of the model used for agenda-setting analysis.

5.1. Create a Time Series of Epidemic News

The Covid19-FrameSeries used in this chapter is constructed as follows: the sum of the number of Weibo posts of each media in the Covid19-AgendaFrame dataset in each day is composed of its heat time series of that day, and each media corresponds to a heat time series, and a total of five heat time series are obtained.

5.2. Extracting Hidden Relationships in Time Series

By using the prediction function of neural networks, the Neural Granger Causality model based on neural networks can continuously optimize the causal relationship between variables in iterations (Tank et al., 2021).

The basic formula of Neural Granger Causality (NGC) based on neural network is as follows:

$$\begin{array}{c}{x}_{ti}=g_i\left(x_{<t1},\dots ,x_{<tp}\right)+e_{t_i}\end{array}$$

(1)

where $g_i$ is a neural network function that maps all variables from the past t − 1 time steps to the current moment. $x_{<ti}$ denotes the past of sequence i, and $e_t$ denotes the average noise. In this context, if the value of the function $g_i$ does not depend on $x_{<tj}$, it means that there is no Granger causality between sequences j and i.

In order to effectively extract the agenda-setting relationship, i.e., the influence relationship between the media or the public opinion field, implicit in the multivariate nonlinear time series consisting of the number of reports or comments, this paper proposes a Granger causality test for inter-media agendas using a multi-group LSTM (Greff et al., 2016; Sherstinsky, 2020) neural network model.

We obtain and quantify Granger causality by training multi-group LSTM neural network models and comparing the model differences, and our algorithm flow is shown in Figure 4 below.

Here, we give an example to illustrate the flow of the algorithm: If there exists a set of time series as $x_{<ti}$, $x_{<tj}$, they can form a set of time series group {$x_{<ti}$:$x_{<ti}$, $x_{<ti}$:$x_{<tj}$}, where “:” means sequence concatenation. By constructing an LSTM neural network model, the model is trained by taking the time series consisting of $x_{<ti}$:$x_{<ti}$ as the input and $x_{ti}$ as the predicted value to obtain model i. Then, the model is trained by taking the time series consisting of $x_{<ti}$:$x_{<tj}$ as the input and $x_{ti}$ as the predicted value to obtain model j.

$$\begin{array}{c}{Model}_i=LSTM\left(x_{<ti}:x_{<ti}\right),{Model}_j=LSTM\left(x_{<ti}:x_{<tj}\right)\hfill \\ {MSE}_i=Test\left({Model}_i\right),MS{E}_j=Test\left({Model}_j\right)\hfill \end{array}$$

(2)

Subsequent to the initial evaluation, a comparison of the performance of models i and j on the test set is conducted, resulting in the determination of the respective mean square errors ($MS{E}_i$ and $MS{E}_j$). Thereafter, a comparison of the performance of the models on the test set is necessary. If the model effect has been significantly improved, the inclusion of another time series is considered beneficial to the prediction of the original time series. That is to say, the other time series is considered to have a Granger influence on the original time series. In order to quantify the extent of this Granger influence, this paper will use the Error Reduction Ratio (ERR) to assess the Granger causality, hereinafter referred to as the Granger Causal Weight. The ERR quantifies the reduction in the prediction error by incorporating additional variables, and its calculation is outlined as follows:

$$\begin{array}{c}{ERR}_{i,j}={\displaystyle \frac{{MSE}_i-{MSE}_j}{{MSE}_i}}\end{array}$$

(3)

where ${MSE}_i$ is the mean square error of model i (using only the sequence $x_{<ti}$). ${MSE}_j$ is the mean square error of model j (using sequences $x_{<ti}$ and $x_{<tj}$), and ERR denotes the relative improvement in prediction performance after the introduction of $x_{<tj}$, with larger values indicating a stronger Granger causality of $x_{<tj}$ on $x_{<ti}$.

5.3. Constructing the Granger Causality Matrix

$$\begin{array}{c}{C}_{i,j}=ER{R}_{i,j}={\displaystyle \frac{MS{E}_i-MS{E}_j}{MS{E}_i}}i\ne j,i,j\in \{1,2,3,4,5\}\hfill \end{array}$$

(4)

We will obtain the five heat time series for each media actors, denoted by $O_1$, $O_2$, $O_3$, $O_4$, $O_5$. Subsequently, we will construct a multi-group long and short-term memory network through the training of 5.2, and then, according to The formula (4) will yield the Granger Causal Weight matrix for each media actors, where the degree of influence between the same media actors is recorded as 1. The results of the matrix are as follows in Figure 5:

Through the above experimental design, we conducted an in-depth analysis of Granger causality among the five types of media. The results show that central media has a strong causal relationship on the agenda setting of key opinion leaders. This suggests that central media has a significant influence on opinion leaders in shaping public issues, and changes in the heat of key opinion leaders are more affected by the agenda setting of central media.

Regional media has a weaker influence on the agenda setting of local media, but the response of local media to regional media is more sensitive, showing the responsive nature of local media to the agenda of regional media. The causal relationship between different types of media shows a significant hierarchy. The causal relationship between central media and other media is generally stronger, with stronger guiding ability in agenda setting, reflecting the dominant role of central media in the media agenda, a result that is also consistent with the traditional view (A. J. Luo, 2015), while the causal relationship between key opinion leaders and other media is more balanced, suggesting that their agenda setting is more dependent on public interactions and communication channels.

Through the quantitative Granger causality analysis, we further reveal the complex interaction mechanism among media agendas, which provides the basis for the introduction of Hidden Markov Chains in the following section.

6. Agenda Synergy Prediction Based on Hidden Markov Chain

A Markov chain is a stochastic process with a distinguishing characteristic of “memorylessness” or “Markovianity,” signifying that the present state is solely dependent on the preceding state and exhibits independence from prior states (Chung, 1967). Hidden Markov models represent a progression from Markov chains, predominantly employed to characterize systems where the state remains unobserved, yet its hidden state is derived from a sequence of observable output signals (observations) (Eddy, 1996). To intuitively explain its relevance, consider the problem of identifying the season of the year. The season itself is not directly visible—it’s a “hidden” state. However, we can observe indirect indicators, such as the temperature, people’s clothing, or the presence of flowers and snow. By analyzing these observable cues over time, we can infer whether it is spring, summer, autumn, or winter. This is the essence of HMM: using a sequence of observations to infer a corresponding sequence of unobserved states. Such framing is particularly helpful in analyzing agenda-setting patterns, where media roles shift dynamically and are not always directly visible but can be inferred from publishing behavior and response patterns (Hopp et al., 2020; Vermeer & Trilling, 2020).

In the HMM–Granger Hybrid Modeling Framework of this paper, each hidden state in the HMM corresponds to a specific media actor type, such as central media, regional media, opinion leaders, or the public. These states are latent and cannot be directly observed, but can be inferred from the observable signals over time (e.g., the heat of discussion in social media, the amount of news coverage, etc.) By maximizing the joint probability of state transfer, the most likely state path—that is to say, the media release sequence—can be inferred.

Agenda setting is widely recognized as a cumulative and path-dependent process that unfolds through nonlinear, temporally extended interactions, particularly during protracted public events. As Downs’ issue–attention cycle suggests (Downs, 2016), the salience of public issues often develops through cumulative trajectories rather than single-step transitions. We fully acknowledge that the first-order Markov assumption—where the current state depends only on the immediately preceding state—appears theoretically limiting in this broader context.

Instead, the model serves as a simplified approximation that highlights short-term probabilistic transitions between media actors during discrete events. Our intention is not to present the Hidden Markov Model as a comprehensive representation of the cognitive or sociopolitical mechanisms of agenda-setting, but rather as a tractable framework for capturing immediate intermedia influence patterns. While the Markovian “memoryless” property necessarily abstracts away from long-term dynamics, we address part of this limitation by incorporating a Granger Causal Weight matrix, which reflects directional influence accumulated over time and provides the model with a degree of historical sensitivity. In this sense, the framework should be interpreted as a tool for identifying short-term agenda leadership dynamics—that is, temporary dominance of certain media actors in initiating or amplifying event-related discourse—rather than as a full model of cumulative agenda-setting processes.

In this way, our approach approximates localized agenda shifts and media dominance transitions while maintaining computational tractability. We believe this modeling choice is appropriate for detecting interpretable patterns in large-scale, time-ordered communication data.

6.1. Methodology

How can we observe the sequence of public behavior to infer the publishing behavior of each media behind? We can use a Hidden Markov Model to solve this problem. Suppose we observe a sequence of signals $O_1,O_2,O_3$, …, which represent the public’s behavior or reaction (e.g., retweets, discussions, etc.)

Based on these observed signals, we can infer the behavioral sequences $S_1,S_2,S_3$, …, i.e., the news release order of various types of media (e.g., central media, regional media, key opinion leaders, etc.) of the corresponding senders (media). We speculate the most likely media release sequence by maximizing the joint probability:

$$\begin{array}{c}{S}_1,S_2,S_3,\dots =arg{max}_{\mathrm{all}S}P\left(S_1,S_2,S_3,\dots \mid O_1,O_2,O_3,\dots \right)\end{array}$$

(5)

Hidden Markov Modeling, as a probabilistic inference framework, allows us to reconstruct the latent structure of agenda-setting dynamics among different media actors. It helps reveal how various types of media influence each other—not only through their own content, but also through mutual responses, feedback loops, and indirect attention flows. As a result, a complex and evolving intermedia communication network emerges over time.

In our implementation, the initial state of the HMM is determined based on the dominant media actor in the early hours of each event. The state transition probability matrix is derived from the Granger causality matrix generated in Section 5.3, which reflects the directional influence strength between media types. To convert this influence matrix into a usable transition probability matrix, we normalize each row so that the probabilities sum to one. To prevent numerical instability during decoding (e.g., state paths being entirely excluded), we further apply additive smoothing by replacing any zero entries with a small constant (0.1). In agenda-setting contexts, even rarely connected media types may occasionally influence one another, so assigning a minimal non-zero probability acknowledges these latent connections while maintaining model completeness.

Once the HMM is fully specified, we apply the Viterbi algorithm (Forney, 1973) to infer the most probable sequence of hidden states, i.e., the dominant media types at each of the 24 hourly time steps in an event. The Viterbi algorithm is a dynamic programming method that efficiently computes the most likely path of hidden states given a sequence of observations and a trained Hidden Markov Model. In our context, it helps reconstruct how agenda-setting leadership transitions across different media actor types during an event.The output sequence captures how agenda-setting roles shift across different media actors throughout the lifecycle of a public issue.

The calculation allows us to obtain the most probable media news release order and dissemination path for a given dissemination effect. The algorithm is listed in Algorithm 1, and the state transfer graph is depicted in Figure 6.

Algorithm 1 Media publication sequence generation

1: Input: Media State Transition Matrix T  2: Input: Initial State Distribution D  3: Output: Media Publication Sequence O  4: Normalize the state transition matrix T and set values at 0 to 0.1  5: Extract the public transition probabilities matrix P from T  6: Set the corresponding discrete observation signal sequence O  7: for each observation signal $O_i$ do  8:     Calculate the probability of the previous state using matrix P, denoted as $P\left(O_i\right|S_j)$  9: end for 10: Set the initial state distribution to D 11: Use the Viterbi algorithm to backtrack and obtain the publication sequence S

6.2. Experimental Analyses

In this paper, public issues (climate change, social equity, and public health) were selected for experimental analysis in the same time period (Figure 7), namely, Weibo posts during the epidemic period with the themes of “Beijing Winter Olympics Epidemic Prevention and Control Policy Announced”, “Shanghai Disney Stopped Tourists from Entering”, “1 Case of COVID-19 Positive Found in Jiangxi”, and “Fosun Pharmaceuticals to Supply COVID-19 Pandemic Vaccine to Taiwan”; and Weibo posts during the time period of November 2024, comparing and contrasting Weibo posts with the themes such as “Google’s Fines by Russia Totaled to 35 Digits”, “Sanya rainstorm”, “Qingdao Notified of Surrogate Pregnancy Incident”, and “Qinhuangdao air odor incident”.

These data were collected via the Weibo open API using a set of event-related keywords, within a defined temporal window surrounding each selected event. Basic preprocessing steps included duplicate removal, filtering for Chinese-language content, and identification of verified account types.

We divided the Weibo posts into central media, official media, regional media, opinion leaders, and the public, and analyzed the causal relationship between the media and online agenda setting.

We use hourly time granularity to model the media release sequence in specific events (Figure 8). The original intention of this setting is that a finer time resolution helps to depict the rhythm of the agenda interaction of different media entities in the short time scale during the development of events. Although the Granger causality analysis in the previous article uses daily granularity data to depict the overall impact trend over a longer period of time, this granularity is not enough to reflect the changes in agenda dominance at the micro level.

Hourly data can more clearly reveal the alternation of media agenda dominance during the event process, especially for crisis events or sudden public opinion scenarios.

To construct the media sequence required by the Hidden Markov Model, we transformed the raw time series of Weibo posts into a discrete sequence of media states. Each event was divided into 24 one-hour time slots. For each hour, we identified the media type (e.g., central media, regional media, opinion leaders, or the public) that contributed the largest number of posts related to the event.

This dominant media type was then assigned as the representative “state” for that hour. The resulting sequence consists of 24 ordered media states, each representing the most active agenda-setting agent at that time point.

For example, if, in a given event, central media dominated the first 3 h, opinion leaders took over during hours 4–8, and the public became most active in hours 9–15, then the state sequence would be as follows: [central, central, central, opinion, opinion, …, public, public, …].

We take the heat of each hour as a discrete observation signal to build a communication effect sequence O with a length of 24, and take the media with the largest proportion of each hour as the publisher to construct a media real release sequence ST with a length of 24. We take the accuracy of the predicted release sequence S compared with ST, ACC, as an evaluation index.

According to Granger causality coefficient matrix (

Table 1. Granger causality coefficient matrix of each media actors.

	Central Media	Key Opinion Leaders	Official Media	Regional Media	The Public
Central Media	1	0.013	0.080	0	0.014
Key Opinion Leaders	0.756	1	0.284	0.494	0.324
Official Media	0.003	0.120	1	0.001	0.095
Regional Media	0	0.003	0.043	1	0.036
The Public	0.627	0.645	0.461	0.704	1

), the corresponding media release sequence can be obtained according to the algorithm solution process. We conducted evaluation experiments on the news of the above topics and got the results shown in the table below.

The experimental results demonstrate that the dissemination pattern of different thematic events and the manner of media participation exert a substantial influence on the accuracy of the media release sequence predicted by the model. A thorough analysis of the experimental results yielded the following conclusions:

(1)

To evaluate validity, we compared the sequences predicted by the model with observed media release sequences. As reported in

Table 2. Predicted accuracy of the obtained media release order sequence.

Event Threads	ACC
Beijing Winter Olympics Epidemic Prevention and Control Policy Announced	0.833
Shanghai Disney Stopped Tourists from Entering	0.792
1 Case of COVID-19 Positive Found in Jiangxi	0.708
Fosun Pharmaceuticals to Supply COVID-19 Pandemic Vaccine to Taiwan	0.750
Google’s Fines by Russia Totaled to 35 Digits	0.458
Sanya Rainstorm	0.625
Qingdao Notified of Surrogate Pregnancy Incident	0.833
Qinhuangdao Air Odor Incident	0.583

, predictive accuracies consistently exceed chance levels (0.200), indicating that the model reliably captures the dynamics of agenda leadership, even if it does not represent the entire cumulative process of agenda setting.

(2)

The role of different types of media in agenda setting is an area of study that has been the focus of many academic inquiries. Mainstream media has been shown to play a leading role in agenda setting, while some domain-specific or niche media (e.g., specialized media, community media) have been found to influence the agendas of specific groups.

(3)

The communication pathways of these events exhibit notable variations, underscoring the pivotal role that intermedia agenda-setting processes play in shaping public opinion. A case in point is the “Beijing Winter Olympics Epidemic Prevention and Control Policy Announced” event, which has a model prediction accuracy of 0.833. This event is predominantly influenced by mainstream media, particularly central media or official media, and its trajectory is characterized by a high degree of centralization and stability. In such instances, central media’s reporting frequently serves as a catalyst for subsequent coverage by regional media and social media actors, thereby establishing a continuous positive feedback loop that reinforces the agenda’s dissemination through continuous interaction among media entities. However, the dissemination of local events, such as the “Sanya Rainstorm” and the “Qinhuangdao Air Odor Incident,” presents a more intricate scenario. These events exhibit lower levels of predictability, with prediction accuracies of 0.625 and 0.583, respectively. The dissemination of local events is influenced by a variety of factors, including geographic, cultural, and territorial considerations. This complexity leads to more variable agenda interactions among media actors, resulting in fragmented dissemination paths and increasing the difficulty of model prediction (Liu et al., 2018).

(4)

The Granger causality matrix, trained on data from the epidemic, exhibited higher subject event accuracy during the epidemic period compared to the time period around November 2024, which indicates that the propagation law remains relatively stable within a certain time period. This also suggests that the model is capable of capturing the pattern of the media actors’s publishing behavior in the short term to a certain extent.

6.3. Propagation Effect Control Through Media Release Sequences

In the contemporary context of information dissemination, the media assume a dual responsibility: to disseminate information and to shape public perception and behavior. The formation and dissemination of public opinion is a multilevel, multidimensional, and complex process influenced by numerous factors (Page et al., 1987). For governments, a central issue in public opinion control is how to arrange the media to release information at the appropriate time to achieve the desired communication effect (Graber & Graber, 2007). In the preceding section, we demonstrated the efficacy of a model that predicted media release sequences based on communication effect sequences. This suggests that by manipulating the media release sequence, we can influence the communication effect sequence and, consequently, steer public opinion. Our model offers decision-makers a framework to optimize information release strategies, thereby mitigating the propagation of negative public opinion and fostering the development of positive public opinion.

By exercising reasonable control over a serious negative event and mitigating its propagation, the heat curve is expected to exhibit a distinct shape compared to its natural outbreak state. This is primarily characterized by a rapid initial rise in heat, followed by a shorter duration and a more rapid subsequent decline (Xie et al., 2023). Such heat curves typically demonstrate more precipitous rises and sharp declines compared to natural outbreaks of negative events, resulting in an overall lower level, devoid of prolonged periods of high consolidation.

Based on the heat curve, we used an algorithm to calculate a relatively reasonable media release sequence: central media–official media–regional media–opinion leaders–central media–opinion leaders–official media–regional media. The incident of “A man in Zhuhai drives into crowd, causing 35 deaths” is selected to demonstrate the efficacy of regulating the media release sequence in influencing public opinion to a certain extent.

“A man in Zhuhai drives into crowd, causing 35 deaths” is a typical negative breaking-news incident involving a large number of casualties and is highly newsworthy (Figure 9). The graph about the trends in event is shown in Figure 10, the incident’s gravity immediately attracted media attention upon its occurrence, swiftly entering the public eye. Regional media, typically the primary conduit for breaking news, was the first to report on the incident. In the early stages, regional media expedited the incident’s entry into the public consciousness by disseminating comprehensive information about the case. However, as the coverage of such incidents typically attracts widespread attention, it can be readily superseded by higher or more authoritative media actors (e.g., central media), thereby establishing a more pronounced opinion leadership. In the aftermath of the incident, central media expeditiously intervened, effectively shaping the agenda. This observation suggests that the incident transcended the boundaries of a mere local public safety event, but rather, it possessed a national dimension. Central media swiftly intensified the discourse surrounding the incident through enhanced frequency and comprehensive coverage. The intervention of central media was able to transform the coverage of the incident from a single regional media story to a nationwide topic of discussion, influencing the direction of public opinion and public perception (Y. Luo, 2014).

In the following context, we analyze the theoretical validity of the media release order sequence that we have developed and which is applicable to negative events in the context of communication theory.

As a national-level information publisher, the central media debut exerts considerable authority and wields significant influence, swiftly capturing public attention in the nascent stage of public opinion and establishing the foundation for subsequent public opinion orientation (T. Zhang et al., 2017). Its debut ensures the extensive dissemination and effective coverage of information.

The official media’s role in the dissemination of information following the release of content by the central media is twofold. Firstly, it provides detailed information with credible and rational content, guiding the public to understand governmental decisions, policy backgrounds, and so on. Secondly, it helps avoid polarization of public opinion, conducts effective rational channeling, and reduces emotional reactions. The release of information by regional media is instrumental in garnering attention at the local level, thereby facilitating a balanced perspective that encompasses localized emotions and contexts. This approach ensures that the focus of public attention does not become confined to a particular region or group, thereby mitigating the unwarranted proliferation of information (Guo & Zhang, 2020). The role of key opinion leaders in fostering rational discussion and emotional channeling through their public image and professional background is noteworthy. Their published content has the potential to reduce public anxiety by offering a diversified perspective that circumvents the bias inherent in a single narrative (Stockmann & Luo, 2017).

In the process of fading public opinion, the re-release of central media can reaffirm the original position and further calm the heat, ensuring that the whole topic gradually fades. Its authority helps to maintain a moderate level of attention, as public opinion tends to subside. Key opinion leaders intervene again, bringing more personal and emotionally resonant voices, and this level of guidance helps to calm public opinion and reduce emotional reactions. The re-released official media content is designed to facilitate a rational discussion of the information, offering policy-level support and reducing public anxiety through the official voice. The final regional media release aims to ensure that public concern diminishes at the local level, guiding public opinion toward its conclusion through localized content. Additionally, regional media can provide updates on developments in specific cases or events, thereby bringing the message to a close.

7. Results and Discussion

This study innovatively proposes an HMM–Granger Hybrid Modeling Framework for Media Agenda Synergy, which reveals the “explicit collaboration” and “implicit competition” in Media Agenda Synergy, and confirms the feasibility and effectiveness of utilizing communication effect sequences to predict media release sequences by comparing the model prediction results with the real media release sequences.

A Granger causality analysis was conducted on the time series data from various media sources to derive a causality matrix, which revealed the unique roles of different media types in the agenda-setting process for major events. The analysis demonstrated that mainstream media, regional media, and key opinion leaders have a distinct influence on the communication of various issues. This finding indicates that the collaboration among media agendas is not a unidirectional influence, but rather a multifaceted process, in which various types of media frequently collaborate to influence public opinion in the process of agenda-setting.

In the training results of the Hidden Markov Model, the state transfer probability matrices of different media show the complex pattern of agenda interaction among media. The analysis of the state transfer probability matrix shows that the Hidden Markov Model effectively captures the agenda collaboration mechanism among the media, and reveals the agenda switching frequency and collaboration pattern among different types of media, such as central media, official media, and key opinion leaders, at different stages of the event, i.e., the central media’s guiding effect on other media and the agenda interaction between official media and key opinion leaders at the early stage of the event. Central media guided other media’s attention through stable agenda setting, while regional media and key opinion leaders supplemented the communication effect of mainstream media at different stages of events through more flexible agenda-setting strategies. This collaborative mechanism allows the media agenda to form an overall synergy and guide public opinion more effectively during major events. The results of the study show that the media agenda undergoes a process of transferring to different states in hot social events, which is characterized by cyclicality and diversity. The agenda of central media remains stable and is less influenced by other media. Key opinion leaders, on the other hand, have more frequent changes in their agendas and are more susceptible to the agendas of external media, reflecting their flexibility and adaptability in the dissemination of issues.

Finally, the communication effect is controlled through the media release sequence, and a media release sequence for negative public opinion is obtained. The validity and rationality of the sequence are discussed in terms of factual data as well as theory. This provides a reference for the media to enhance the communication effect of public issues. In addition, it provides data-driven decision support for optimizing public opinion guidance strategies and promoting public participation.

The results of this study reveal the importance of media agenda collaboration in the modern information society. From a theoretical perspective, this paper builds the HMM–Granger Hybrid Modeling Framework for Media Agenda Synergy by introducing Hidden Markov Model and Granger Causality Analysis, which extends the traditional Agenda-Setting Theory and enables it to better adapt to the complex multimedia communication environment. In particular, the state transfer probability matrix provided by the Hidden Markov Model (HMM) provides a new approach to understand the dynamics of media agendas and collaboration patterns. The application of this model enriches the research on Agenda Synergy Theory and helps to build a more comprehensive theoretical framework for media communication.

From a practical point of view, the results of the study provide guidance for the media’s public opinion guidance strategy during major events. The agenda synergy between mainstream media and social media during major events can generate the Multiplier Effect, which can significantly increase the intensity of the public agenda. By analyzing the collaboration mechanism of different media, it can help the media plan and guide the sustainable development issues more effectively and improve the communication effect of sustainable development issues. With the help of the model and methodology provided by this study, the media can optimize their collaboration strategies to form a synergy in the coverage of public issues. For media managers, the results of this study provide a reference path to improve the effectiveness of media agenda setting and issue enhancement and help the media to deal with the complex public opinion environment more effectively.

8. Limitations and Future Work

While this study presents a novel approach to modeling agenda-setting dynamics using Hidden Markov Models and Granger causality, several limitations should be acknowledged.

First, the dataset is derived exclusively from the Chinese social media platform Weibo, within a distinct political and media environment. As a result, the observed agenda-setting patterns may reflect characteristics specific to China’s centralized media system. Future research could test the applicability of our framework in more decentralized or cross-national media contexts.

Second, the effectiveness of the HMM depends on the quality and structure of the Granger causality matrix, which in turn relies on assumptions such as normalization and smoothing. The model does not account for latent variables beyond observable media behavior.

Third, each event is modeled independently. Longitudinal modeling across overlapping or evolving events may offer additional insights into sustained media interactions. In our framework, agenda leadership is defined as the temporary dominance of one type of media actor in initiating or amplifying discourse, modeled as short-term probabilistic transitions rather than strict causal chains. While the integration of the Granger Causal Weight matrix introduces some historical sensitivity, the approach remains constrained by the memoryless assumption of the Hidden Markov Model. As such, it cannot fully capture the long-term, path-dependent processes emphasized in agenda-setting theory. Moreover, our validity check is limited to comparing predicted sequences with observed sequences, which demonstrates predictive reliability but does not equate to comprehensive causal validation. Future research could address these limitations by combining HMM-based methods with approaches explicitly designed to incorporate recursive dependencies, feedback loops, and long-term dynamics.

Fourth, our analysis does not fully capture the semantic diversity of discourse. Future work could integrate deeper semantic modeling, such as stance detection or narrative trajectory tracking.

Finally, we did not apply explicit bot detection. While some automated accounts exhibit human-like behavior and exert measurable influence, their presence may introduce bias. Incorporating bot filtering could enhance actor classification granularity in future implementations.