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<ArticleTitle Language="En" OutputMedium="All">The Dynamic Association between Sleep Quality, Suicide Risk, and Perceived Social Support: Based on Social Media Data</ArticleTitle>
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<GivenName>Binyu</GivenName>
<FamilyName>Wang</FamilyName>
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<Email>binyu_wang@mails.ccnu.edu.cn</Email>
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<GivenName>Xiayu</GivenName>
<FamilyName>Du</FamilyName>
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<Email>duxiayu@mails.ccnu.edu.cn</Email>
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<GivenName>Tingshao</GivenName>
<FamilyName>Zhu</FamilyName>
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<Email>tszhu@psych.ac.cn</Email>
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<GivenName>Zongkui</GivenName>
<FamilyName>Zhou</FamilyName>
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<Email>zhouzk@ccnu.edu.cn</Email>
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<GivenName>Xingyun</GivenName>
<FamilyName>Liu</FamilyName>
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<GivenName>Zhihong</GivenName>
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<OrgDivision>Key Laboratory of Adolescent Cyberpsychology and Behavior (CCNU)</OrgDivision>
<OrgName>Ministry of Education</OrgName>
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<OrgDivision>Key Laboratory of Human Development and Mental Health of Hubei Province, School of Psychology</OrgDivision>
<OrgName>Central China Normal University</OrgName>
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<Postcode>430079</Postcode>
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<OrgDivision>CAS Key Laboratory of Behavioral Science, Institute of Psychology</OrgDivision>
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<Postcode>100101</Postcode>
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<Country Code="CN">China</Country>
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<OrgDivision>Department of Psychology</OrgDivision>
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<Para ID="Par1">Binyu Wang<Superscript>1,2</Superscript>, Xiayu Du<Superscript>1,2</Superscript>, Tingshao Zhu<Superscript>3,4</Superscript>, Zongkui Zhou<Superscript>1,2</Superscript>, Xingyun Liu<Superscript>1,2</Superscript>, Zhihong Ren<Superscript>1,2,5</Superscript></Para>
<Para ID="Par2">
<Superscript>1</Superscript>Key Laboratory of Adolescent Cyberpsychology and Behavior (CCNU), Ministry of Education, Wuhan 430079, China</Para>
<Para ID="Par3">
<Superscript>2</Superscript>Key Laboratory of Human Development and Mental Health of Hubei Province, School of Psychology, Central China Normal University, Wuhan 430079, China</Para>
<Para ID="Par4">
<Superscript>3</Superscript>CAS Key Laboratory of Behavioral Science, Institute of Psychology, Beijing 100101, China</Para>
<Para ID="Par5">
<Superscript>4</Superscript>Department of Psychology, University of Chinese Academy of Sciences, Beijing 100049, China</Para>
<Para ID="Par6">
<Superscript>5</Superscript>School of Psychology, Liaoning Normal University, Dalian 116029, China</Para>
<Para ID="Par7">
<Emphasis Type="Bold">Author Email</Emphasis>
</Para>
<Para ID="Par8">Binyu Wang: binyu_wang@mails.ccnu.edu.cn;</Para>
<Para ID="Par9">Xiayu Du: duxiayu@mails.ccnu.edu.cn;</Para>
<Para ID="Par10">Tingshao Zhu: tszhu@psych.ac.cn;</Para>
<Para ID="Par11">Zongkui Zhou: zhouzk@ccnu.edu.cn;</Para>
<Para ID="Par12">Xingyun Liu: liuxingyun@ccnu.edu.cn;</Para>
<Para ID="Par13">Zhihong Ren: ren@ccnu.edu.cn.</Para>
<Para ID="Par14">
<Emphasis Type="Bold">Author ORCID</Emphasis>
</Para>
<Para ID="Par15">Binyu Wang: 0009-0000-8331-4555;</Para>
<Para ID="Par16">Xiayu Du: 0000-0002-1870-9216;</Para>
<Para ID="Par17">Tingshao Zhu: 0000-0003-0020-3812;</Para>
<Para ID="Par18">Zongkui Zhou: 0000-0002-0958-6568;</Para>
<Para ID="Par19">Xingyun Liu: 0000-0001-7118-0465;</Para>
<Para ID="Par20">Zhihong Ren: 0000-0002-3753-6242.</Para>
<Para ID="Par21">
<Emphasis Type="Bold">Correspondence</Emphasis>
</Para>
<Para ID="Par22">Xingyun Liu, School of Psychology, Central China Normal University, Luoyu Road No.152, Hongshan District, Wuhan, 430079, China; Email: liuxingyun@ccnu.edu.cn; Tel: &#x002B;86-15201683001.</Para>
<Para ID="Par23">Zhihong Ren, School of Psychology, Central China Normal University, Luoyu Road No.152, Hongshan District, Wuhan, 430079, China; Email: ren@ccnu.edu.cn; Tel: &#x002B;86-13627131550.</Para>
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<AuthorContribution><Annotation ID="1" RuleID="GoldenMetadataIdentified_01" Status="Neutral" /><Heading>Author Contribution</Heading><SimplePara>Binyu Wang and Xiayu Du contributed equally to this work and should be considered as co-first authors.Binyu Wang: Conceptualization, Formal analysis, Software, Writing &#x2013; original draft; Xiayu Du: Conceptualization, Writing &#x2013; review &#x0026; editing; Tingshao Zhu: Data curation; Zongkui Zhou: Supervision; Xingyun Liu: Data Curation, Writing &#x2013; review &#x0026; editing; Zhihong Ren: Supervision, Writing &#x2013; review &#x0026; editing, Funding Acquisition;</SimplePara></AuthorContribution>
<Para ID="Par24">Binyu Wang: Conceptualization, Formal analysis, Software, Writing &#x2013; original draft;</Para>
<Para ID="Par25">Xiayu Du: Conceptualization, Writing &#x2013; review &#x0026; editing;</Para>
<Para ID="Par26">Tingshao Zhu: Data curation;</Para>
<Para ID="Par27">Zongkui Zhou: Supervision;</Para>
<Para ID="Par28">Xingyun Liu: Data Curation, Writing &#x2013; review &#x0026; editing;</Para>
<Para ID="Par29">Zhihong Ren: Supervision, Writing &#x2013; review &#x0026; editing, Funding Acquisition;</Para>
<FundingInformation><Annotation ID="2" RuleID="IdentifyFundingInformationInArticle_01" Category="Completeness" Status="Neutral" />
<Heading>Funding</Heading>
<SimplePara>This research was supported by the Major Program of the National Social Science Foundation of China (grant No. 22&#x0026;ZD187).</SimplePara>
</FundingInformation>
<Abstract ID="Abs1" Language="En" OutputMedium="All"><Annotation ID="3" RuleID="PrimaryAbstractDiscrepancy_01" Values="6.7%" Category="Discrepancy" Status="Neutral" />
<Heading>Abstract</Heading>
<AbstractSection ID="ASec1">
<Heading>Purpose</Heading>
<Para ID="Par30">Suicide risk and sleep problems are significant public health concerns, with perceived social support acting as a key social determinant of mental health. This study aimed to investigate the dynamic, reciprocal relationships among public sleep quality (SQ), suicide risk (SR), and perceived social support (SS) from a macro-level, epidemiological perspective to understand their systemic interplay over time.</Para>
</AbstractSection>
<AbstractSection ID="ASec2">
<Heading>Methods</Heading>
<Para ID="Par31">We constructed a provincial-level annual panel dataset using public data from Weibo, a major Chinese social media platform, spanning 14 years (2010&#x2013;2023) across 31 provinces. The annual frequencies of keywords related to SQ, SR, and SS were calculated to serve as population-level indicators. Dynamic Structural Equation Modeling (DSEM) was employed to analyze the autoregressive, cross-lagged, and contemporaneous effects among these variables.</Para>
</AbstractSection>
<AbstractSection ID="ASec3">
<Heading>Results</Heading>
<Para ID="Par32">All three variables demonstrated significant temporal continuity. Longitudinally, higher prior SR predicted subsequent declines in both SQ and SS. Paradoxically, however, better prior SQ (i.e., lower scores on the measure) predicted higher subsequent SR, while higher prior SS predicted poorer subsequent SQ. Concurrently, poorer SQ and lower SS were associated with higher SR.</Para>
</AbstractSection>
<AbstractSection ID="ASec4">
<Heading>Conclusions</Heading>
<Para ID="Par33">Utilizing large-scale social media data, this study uncovers the complex feedback loops governing the population-level dynamics of sleep quality, perceived social support, and suicide risk. The findings highlight the necessity of a systemic public health approach for suicide prevention that considers these complex, time-dependent, and sometimes paradoxical interactions, moving beyond simplistic linear risk models.</Para>
</AbstractSection>
</Abstract>
<KeywordGroup Language="En" OutputMedium="All">
<Heading>Keywords:</Heading>
<Keyword>Sleep quality</Keyword>
<Keyword>suicide risk</Keyword>
<Keyword>perceived social support</Keyword>
<Keyword>social media</Keyword>
<Keyword>dynamic structural equation model</Keyword>
</KeywordGroup>
<Para ID="Par34">
<Emphasis Type="Bold">The Dynamic Association between Sleep Quality, Suicide Risk, and Perceived Social Support: Based on Social Media Data</Emphasis>
</Para>
</ArticleHeader>
<Body><Annotation ID="4" RuleID="IdentifyClinicalTrialsKeywordsAndTRN_02" Category="Information" Status="Neutral" />
<Section1 ID="Sec1">
<Heading>1 Introduction</Heading>
<Para ID="Par35">As a global public health challenge causing over 700,000 deaths annually and imposing substantial societal burdens [1], suicide risk (SR) may potentially be mitigated by improving sleep quality (SQ) and perceived social support (SS) [2, 3].</Para>
<Para ID="Par36">The negative link between poor sleep quality and elevated suicide risk is well-established. For instance, a ten-year longitudinal study established that sleep disturbance is a risk factor for suicide, independent of depressive mood [4]. Multiple reviews corroborate this finding, documenting that both objective and subjective sleep disturbances (such as insomnia, nightmares, and poor self-reported sleep quality) can elevate the risk for suicidal ideation, suicide attempts, and death by suicide [2, 5&#x2013;6]. Mechanistically, anxiety and depressive symptoms serially mediate the pathway from poor sleep to suicide risk [7]. However, the effect of suicide risk on sleep quality may be mediated by presleep arousal (PSA), which is defined as a state of excessive arousal at bedtime that is counterproductive to sleep onset and maintenance [8]. Specifically, one study concluded that this association is mediated by presleep cognitive arousal (PSA-C): the degree of mental alertness during attempts to fall asleep that often manifests as rumination and worry, factors strongly associated with suicide risk [9].</Para>
<Para ID="Par37">Similarly, perceived social support is widely recognized as a crucial protective factor against suicide risk. Perceived social support refers to an individual's subjective appraisal of the aid available from various sources, such as family, friends, colleagues, or the community. This support can be emotional, informational, or instrumental (i.e., tangible assistance) [10]. Indeed, the perception of social support seems to be a key factor in mitigating suicidal ideation [11]. Subsequent research has demonstrated that perceived social support moderates the relationship between impulsivity and suicide risk, acting as a buffer for individuals with higher levels of impulsivity [12]. In a similar vein, other studies have found that perceived social support buffers against suicidal ideation by enhancing self-esteem and the utilization of social support [13]. Furthermore, studies using representative samples from the United States and the United Kingdom have associated perceived social support with a reduced likelihood of lifetime suicide attempts, suggesting its role as a cross-cultural protective factor [14]. These findings are echoed in research from China, where psychological autopsy studies of rural youth who died by suicide identified the absence of perceived social support as a critical risk factor, particularly for individuals with psychiatric disorders [15]. Beyond empirical evidence, relevant theories also support this relationship. For instance, individuals who perceive social support are likely to experience a greater sense of belonging. According to the Interpersonal Theory of Suicide, a thwarted sense of belonging increases suicide risk, whereas an established sense of belonging mitigates it [16]. However, the relationship is bidirectional, as suicide risk can also influence perceived social support. For example, according to cognitive theory, individuals with depression and suicide risk exhibit the negative cognitive triad: negative views of the self, the world (including others), and the future [17]. This negative cognitive filter may impair their ability to objectively appraise genuine acts of support, leading to social isolation and a subsequent decline in perceived social support. Furthermore, the stigma surrounding mental illness creates a significant barrier to accessing formal support systems such as mental health services. This barrier to help-seeking arises from both external, anticipated social pressures (public stigma) and internalized feelings of shame and self-devaluation (self-stigma) [18]. This stigma-induced barrier can sever crucial avenues of social support, thereby diminishing an individual's level of perceived social support.</Para>
<Para ID="Par38">A reciprocal relationship is also evident between sleep quality and perceived social support. From a workplace perspective, for instance, improvements in network and emotional support have been shown to lower the risk of sleep disturbances [19]. Similarly, within intimate relationships, supportive partnerships are positively associated with sleep quality, whereas relationships characterized by rejection are predictive of poorer sleep outcomes [20]. From a broader societal perspective, perceived social support exhibits an inverse association with both validated questionnaire scores (e.g., the PSQI) and diary-assessed sleep quality metrics [21]. This association is robust; a meta-analysis demonstrated that higher levels of perceived social support are linked to improved sleep quality, independent of variations in the operationalization of support, study design, or chronic conditions [22]. In the reverse direction, sleep quality also affects the perception of social support. Research has found that sleep-deprived individuals not only report increased feelings of loneliness but also tend to maintain greater social distance from others. Moreover, they are perceived by healthy observers as less socially attractive, thereby reducing the observers' willingness to engage in social interaction [23]. This social withdrawal can ultimately reduce perceived social support.</Para>
<Para ID="Par39">While these dyadic relationships are well-documented, a critical gap remains in understanding how these three factors (sleep quality, suicide risk, and perceived social support) interact dynamically as a system over time, particularly at a collective, societal level. Large-scale social media data offer a unique opportunity to investigate these population-level dynamics. Weibo, a major Chinese social media platform, is a rich data source where users often freely discuss personal topics like sleep and perceived social support [24, 25]. Additionally, Dynamic Structural Equation Modeling (DSEM) provides advanced methods to examine these complex longitudinal relationships. This study applies DSEM to a 14-year Weibo word frequency dataset. We aim to elucidate the annual dynamic relationships among public SQ, SR, and SS in China (2010&#x2013;2023).</Para>
<Para ID="Par40">Based on the literature, we formulated three hypotheses within a dynamic systems framework:</Para>
<FormalPara ID="FPar1" RenderingStyle="Style1">
<Heading>Hypothesis 1</Heading>
<Para ID="Par41">Autoregressive Effects. We hypothesized that each variable would exhibit a significant positive autoregressive effect, reflecting its temporal continuity. That is, the score of each variable at time <Emphasis Type="Italic">t-1</Emphasis> (<InlineEquation ID="IEq1"><EquationSource Format="TEX"><![CDATA[$$\:{SX}_{t-1}$$]]></EquationSource></InlineEquation>&#x200B;) will be positively associated with its score at time <Emphasis Type="Italic">t</Emphasis> (<InlineEquation ID="IEq2"><EquationSource Format="TEX"><![CDATA[$$\:{SX}_{t}$$]]></EquationSource></InlineEquation>&#x200B;) (where SX refers to any of these three variables).</Para>
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<FormalPara ID="FPar2" RenderingStyle="Style1">
<Heading>Hypothesis 2</Heading>
<Para ID="Par42">Cross-Lagged Effects. We posited a series of cross-lagged effects, anticipating that each variable would influence the others over time. Specifically, <InlineEquation ID="IEq3"><EquationSource Format="TEX"><![CDATA[$$\:{SQ}_{t-1}$$]]></EquationSource></InlineEquation>&#x200B; will be positively associated with <InlineEquation ID="IEq4"><EquationSource Format="TEX"><![CDATA[$$\:{SR}_{t}$$]]></EquationSource></InlineEquation> and negatively associated with <InlineEquation ID="IEq5"><EquationSource Format="TEX"><![CDATA[$$\:{SS}_{t}$$]]></EquationSource></InlineEquation>&#x200B;; <InlineEquation ID="IEq6"><EquationSource Format="TEX"><![CDATA[$$\:{SR}_{t-1}$$]]></EquationSource></InlineEquation>&#x200B; &#x200B;will be positively associated with both <InlineEquation ID="IEq7"><EquationSource Format="TEX"><![CDATA[$$\:{SQ}_{t}$$]]></EquationSource></InlineEquation>&#x200B; and <InlineEquation ID="IEq8"><EquationSource Format="TEX"><![CDATA[$$\:{SS}_{t}$$]]></EquationSource></InlineEquation>; and <InlineEquation ID="IEq9"><EquationSource Format="TEX"><![CDATA[$$\:{SS}_{t-1}$$]]></EquationSource></InlineEquation>&#x200B;&#x200B; will be negatively associated with both <InlineEquation ID="IEq10"><EquationSource Format="TEX"><![CDATA[$$\:{SQ}_{t}$$]]></EquationSource></InlineEquation> and <InlineEquation ID="IEq11"><EquationSource Format="TEX"><![CDATA[$$\:{SR}_{t}$$]]></EquationSource></InlineEquation>&#x200B;.</Para>
</FormalPara>
<FormalPara ID="FPar3" RenderingStyle="Style1">
<Heading>Hypothesis 3</Heading>
<Para ID="Par43">Contemporaneous Effects. We hypothesized contemporaneous associations between the variables, reflecting within-year effects on SR. Specifically, <InlineEquation ID="IEq12"><EquationSource Format="TEX"><![CDATA[$$\:{SQ}_{t}$$]]></EquationSource></InlineEquation> will be positively associated with <InlineEquation ID="IEq13"><EquationSource Format="TEX"><![CDATA[$$\:{SR}_{t}$$]]></EquationSource></InlineEquation>&#x200B;, while <InlineEquation ID="IEq14"><EquationSource Format="TEX"><![CDATA[$$\:{SS}_{t}$$]]></EquationSource></InlineEquation> will be negatively associated with <InlineEquation ID="IEq15"><EquationSource Format="TEX"><![CDATA[$$\:{SR}_{t}$$]]></EquationSource></InlineEquation>.</Para>
</FormalPara>
</Section1>
<Section1 ID="Sec2">
<Heading>2 Method</Heading>
<Section2 ID="Sec3">
<Heading>2.1 Data Source and Processing</Heading>
<Para ID="Par44"><Annotation ID="5" RuleID="IdentifyClinicalTrialsTerms_01" Values="Ethics, human, ethical, Consent, registration, Outcome, intervention, interventions" Category="SREP" Status="Neutral" />Text data were sourced via the public Weibo Application Programming Interface (API) from a database covering over 1.16&#x00A0;million active users on Weibo (Sina Weibo), a leading Chinese microblogging platform [26]. The dataset spanned January 1, 2010, to December 31, 2023, consisting of posts from all active users. Following previous research [26, 28], "active users" were defined as those with &#x003E;&#x2009;500 posts since registration and recent activity. To ensure personal perspectives, only posts from private users were retained, excluding institutional accounts (e.g., commercial entities, celebrities, government agencies).</Para>
<Para ID="Par45"><Annotation ID="6" RuleID="IdentifyClinicalTrialsAndSPIRIT_01" Values="protocol" Category="Information" Status="Neutral" />These textual data were then processed using the TextMind system, developed by the Computational Cyberpsychology Lab at the Institute of Psychology, Chinese Academy of Sciences [29]. The system performs an integrated process, from automatic Chinese word segmentation to the calculation of keyword frequencies based on specific dictionaries [26, 30]. For this study, data were aggregated to the provincial level; scores for SQ, SR, and SS were operationalized as the annual frequency of specific keywords within each of the 31 provinces. The research protocol was approved by the Institutional Review Board of the College of Life Sciences at Central China Normal University (Approval No. CCNU-IRB-202504006b).</Para>
</Section2>
<Section2 ID="Sec4">
<Heading>2.2 Dictionary-Based Measures</Heading>
<Para ID="Par46">
<Emphasis Type="Bold">Sleep Quality (SQ).</Emphasis> SQ was measured using a 92-keyword Sleep Quality Dictionary, which was developed by referencing established domestic and international sleep quality questionnaires and has demonstrated good validity [31]. Higher scores on this measure indicate poorer sleep quality.</Para>
<Para ID="Par47">
<Emphasis Type="Bold">Suicide Risk (SR).</Emphasis> SR was assessed using the Chinese Suicide Dictionary, which was specifically designed to detect suicide risk on social media. The dictionary comprises 2,168 words across 13 distinct categories (e.g., suicidal ideation, suicidal behaviors) and has been shown to yield more accurate estimations of suicide risk at both post and user levels compared to general-purpose dictionaries [32]. A higher score represents a greater level of suicide risk.</Para>
<Para ID="Par48">
<Emphasis Type="Bold">Perceived Social Support (SS).</Emphasis> SS was quantified using the 1,312-word Perceived Social Support Dictionary. It incorporates a dynamic corpus-updating mechanism to track the rapid evolution of internet language and has demonstrated good reliability [33]. A higher score corresponds to a greater level of perceived social support.</Para>
</Section2>
<Section2 ID="Sec5">
<Heading>2.3 Data Analysis</Heading>
<Para ID="Par49">We used Dynamic Structural Equation Modeling (DSEM) in Mplus version 8.3 [34] to examine the dynamic relationships among SQ, SR, and SS. This approach tested our hypotheses on autoregressive, cross-lagged, and contemporaneous relationships.</Para>
<Para ID="Par50">The DSEM was specified as a two-level model to account for the nested data structure (i.e., annual observations nested within provinces). Level 1 (within-province) modeled the time-series dynamics, estimating the autoregressive, cross-lagged, and contemporaneous effects for SQ, SR, and SS, as well as their within-province residuals. Level 2 (between-province) modeled the variability across provinces by treating the Level-1 parameters as random effects.</Para>
<Para ID="Par51">DSEM relies on Bayesian analysis via Markov Chain Monte Carlo (MCMC) estimation algorithms, effective for complex models and improving convergence [35]. These algorithms generate a posterior distribution for each parameter. Statistical significance is determined by examining the 95&#x0025; Credible Interval (CI); if the interval (delineated by the 2.5th and 97.5th percentiles of the posterior distribution) does not contain zero, the estimate is considered significant.</Para>
<Para ID="Par52">Model convergence was assessed using the Potential Scale Reduction (PSR) factor, which compares within-chain to between-chain variance; a value approaching 1.0 indicates convergence [36]. A PSR&#x2009;&#x003E;&#x2009;1.05 suggests convergence issues. Our final model (27,000 iterations) achieved adequate convergence with a PSR of 1.038.<Equation ID="Equa"><EquationSource Format="TEX"><![CDATA[$$\:PSR=\sqrt{\frac{W+B}{W}}$$]]></EquationSource></Equation></Para>
<FormalPara ID="FPar4" RenderingStyle="Style1">
<Heading>Note</Heading>
<Para ID="Par53">where <Emphasis Type="Italic">W</Emphasis> is the within-chain variance and <Emphasis Type="Italic">B</Emphasis> is the between-chain variance.</Para>
</FormalPara>
<Para ID="Par54">We used noninformative priors, the default setting in Mplus, which is appropriate for the exploratory nature of this study, as they assume all values are equally likely. All variables were latent, province-mean centered to disentangle within-province from between-province variance. This latent centering approach is superior to observed mean centering as it reduces bias in the estimation of autoregressive and cross-lagged effects. Finally, the TINTERVAL&#x2009;=&#x2009;1 command was used to specify the 1-year interval between each measurement point.</Para>
<Para ID="Par55">As shown in Fig.&#x00A0;<InternalRef RefID="Fig1">1</InternalRef> (for visual clarity, correlations among the random effects are omitted from the diagram), the model specifies parameters at two levels:</Para>
<Para ID="Par56">At Level 1 (Within-Province), the model captures the time-series dynamics within each province (i). These dynamics are composed of several key parameters, including the province-specific intercepts (<InlineEquation ID="IEq16"><EquationSource Format="TEX"><![CDATA[$$\:{\alpha\:}_{1i}$$]]></EquationSource></InlineEquation>, <InlineEquation ID="IEq17"><EquationSource Format="TEX"><![CDATA[$$\:{\alpha\:}_{2i}$$]]></EquationSource></InlineEquation>, and <InlineEquation ID="IEq18"><EquationSource Format="TEX"><![CDATA[$$\:{\alpha\:}_{3i}$$]]></EquationSource></InlineEquation>&#x200B;), which quantify the mean level of each variable for a given province, reflecting its long-term equilibrium across the study period; the autoregressive paths (<InlineEquation ID="IEq19"><EquationSource Format="TEX"><![CDATA[$$\:{\phi\:}_{1i}$$]]></EquationSource></InlineEquation>, <InlineEquation ID="IEq20"><EquationSource Format="TEX"><![CDATA[$$\:{\phi\:}_{2i}$$]]></EquationSource></InlineEquation>, and <InlineEquation ID="IEq21"><EquationSource Format="TEX"><![CDATA[$$\:{\phi\:}_{3i}$$]]></EquationSource></InlineEquation>), which capture the influence of a variable in the previous year on itself in the current year; the cross-lagged paths (<InlineEquation ID="IEq22"><EquationSource Format="TEX"><![CDATA[$$\:{\phi\:}_{4i}$$]]></EquationSource></InlineEquation> through <InlineEquation ID="IEq23"><EquationSource Format="TEX"><![CDATA[$$\:{\phi\:}_{9i}$$]]></EquationSource></InlineEquation>&#x200B;), which capture the influence of one variable in the previous year on a different variable in the current year; and the contemporaneous paths (<InlineEquation ID="IEq24"><EquationSource Format="TEX"><![CDATA[$$\:{\beta\:}_{1i}$$]]></EquationSource></InlineEquation> and <InlineEquation ID="IEq25"><EquationSource Format="TEX"><![CDATA[$$\:{\beta\:}_{2i}$$]]></EquationSource></InlineEquation>&#x200B;), representing the within-year associations of SQ and SS with SR at time t.</Para>
<Para ID="Par57">At Level 2 (Between-Province), the model estimates the population-level means of the Level 1 parameters, which represent the average dynamic effects across all 31 provinces. These are denoted by gamma coefficients (<InlineEquation ID="IEq26"><EquationSource Format="TEX"><![CDATA[$$\:\gamma\:$$]]></EquationSource></InlineEquation>), including the population means for the intercepts (<InlineEquation ID="IEq27"><EquationSource Format="TEX"><![CDATA[$$\:{\gamma\:}_{00}$$]]></EquationSource></InlineEquation>, <InlineEquation ID="IEq28"><EquationSource Format="TEX"><![CDATA[$$\:{\gamma\:}_{10}$$]]></EquationSource></InlineEquation>, and <InlineEquation ID="IEq29"><EquationSource Format="TEX"><![CDATA[$$\:{\gamma\:}_{20}$$]]></EquationSource></InlineEquation>&#x200B;), autoregressive coefficients (<InlineEquation ID="IEq30"><EquationSource Format="TEX"><![CDATA[$$\:{\gamma\:}_{30}$$]]></EquationSource></InlineEquation>, <InlineEquation ID="IEq31"><EquationSource Format="TEX"><![CDATA[$$\:{\gamma\:}_{40}$$]]></EquationSource></InlineEquation>, and <InlineEquation ID="IEq32"><EquationSource Format="TEX"><![CDATA[$$\:{\gamma\:}_{50}$$]]></EquationSource></InlineEquation>&#x200B;), cross-lagged coefficients (<InlineEquation ID="IEq33"><EquationSource Format="TEX"><![CDATA[$$\:{\gamma\:}_{60}$$]]></EquationSource></InlineEquation> through <InlineEquation ID="IEq34"><EquationSource Format="TEX"><![CDATA[$$\:{\gamma\:}_{\text{11,0}}$$]]></EquationSource></InlineEquation>&#x200B;), and contemporaneous coefficients (<InlineEquation ID="IEq35"><EquationSource Format="TEX"><![CDATA[$$\:{\gamma\:}_{\text{12,0}}$$]]></EquationSource></InlineEquation> and <InlineEquation ID="IEq36"><EquationSource Format="TEX"><![CDATA[$$\:{\gamma\:}_{\text{13,0}}$$]]></EquationSource></InlineEquation>&#x200B;).</Para>
<Para ID="Par58">
<Figure Category="Standard" Float="Yes" ID="Fig1">
<Caption Language="En">
<CaptionNumber>Fig. 1</CaptionNumber>
<CaptionContent>
<SimplePara>Path Diagram of the Dynamic Structural Equation Model (DSEM)</SimplePara>
</CaptionContent>
</Caption>
<MediaObject>
<ImageObject FileRef="float_image1.jpeg" Format="JPEG" Color="BlackWhite" Type="Linedraw" Rendition="Print" Width="001" Height="001" Resolution="120" />
<ImageObject FileRef="Online_float_image1.png" Format="PNG" Color="BlackWhite" Type="Linedraw" Rendition="HTML" Width="001" Height="001" Resolution="120" />
</MediaObject>
</Figure>
</Para>
</Section2>
</Section1>
<Section1 ID="Sec6">
<Heading>3 Result</Heading>
<Section2 ID="Sec7">
<Heading>3.1 Descriptive statistics</Heading>
<Para ID="Par59">Table&#x00A0;<InternalRef RefID="Tab1">1</InternalRef> presents descriptive statistics and correlations for the 434 total observations (14 years &#x00D7; 31 provinces). No data were missing for SQ, SR, or SS. Skewness and kurtosis values confirmed the variables' distributions were appropriate for DSEM analysis. Only the correlation between SR and SS was statistically significant, though small (r = -0.042).</Para>
<Para ID="Par60">
<Table Float="Yes" ID="Tab1">
<Caption Language="En">
<CaptionNumber>Table 1</CaptionNumber>
<CaptionContent>
<SimplePara>Descriptive Statistics and Bivariate Correlations Among Variables.</SimplePara>
</CaptionContent>
</Caption>
<tgroup cols="4">
<colspec colnum="1" colname="c1" align="left" />
<colspec colnum="2" colname="c2" align="left" />
<colspec colnum="3" colname="c3" align="left" />
<colspec colnum="4" colname="c4" align="left" />
<thead>
<row>
<entry align="left" colname="c1" />
<entry align="left" colname="c2">
<SimplePara>SQ</SimplePara>
</entry>
<entry align="left" colname="c3">
<SimplePara>SR</SimplePara>
</entry>
<entry align="left" colname="c4">
<SimplePara>SS</SimplePara>
</entry>
</row>
</thead>
<tbody>
<row>
<entry align="left" colname="c1">
<SimplePara>Mean</SimplePara>
</entry>
<entry align="left" colname="c2">
<SimplePara>0.0119</SimplePara>
</entry>
<entry align="left" colname="c3">
<SimplePara>0.0461</SimplePara>
</entry>
<entry align="left" colname="c4">
<SimplePara>0.000104</SimplePara>
</entry>
</row>
<row>
<entry align="left" colname="c1">
<SimplePara>S.D.</SimplePara>
</entry>
<entry align="left" colname="c2">
<SimplePara>0.00128</SimplePara>
</entry>
<entry align="left" colname="c3">
<SimplePara>0.00631</SimplePara>
</entry>
<entry align="left" colname="c4">
<SimplePara>0.000025</SimplePara>
</entry>
</row>
<row>
<entry align="left" colname="c1">
<SimplePara>Min</SimplePara>
</entry>
<entry align="left" colname="c2">
<SimplePara>0.00833</SimplePara>
</entry>
<entry align="left" colname="c3">
<SimplePara>0.0322</SimplePara>
</entry>
<entry align="left" colname="c4">
<SimplePara>0.0000457</SimplePara>
</entry>
</row>
<row>
<entry align="left" colname="c1">
<SimplePara>Max</SimplePara>
</entry>
<entry align="left" colname="c2">
<SimplePara>0.0168</SimplePara>
</entry>
<entry align="left" colname="c3">
<SimplePara>0.0616</SimplePara>
</entry>
<entry align="left" colname="c4">
<SimplePara>0.000192</SimplePara>
</entry>
</row>
<row>
<entry align="left" colname="c1">
<SimplePara>Skewness</SimplePara>
</entry>
<entry align="left" colname="c2">
<SimplePara>0.747</SimplePara>
</entry>
<entry align="left" colname="c3">
<SimplePara>0.468</SimplePara>
</entry>
<entry align="left" colname="c4">
<SimplePara>-0.080</SimplePara>
</entry>
</row>
<row>
<entry align="left" colname="c1">
<SimplePara>Kurtosis</SimplePara>
</entry>
<entry align="left" colname="c2">
<SimplePara>-0.069</SimplePara>
</entry>
<entry align="left" colname="c3">
<SimplePara>-0.664</SimplePara>
</entry>
<entry align="left" colname="c4">
<SimplePara>-0.471</SimplePara>
</entry>
</row>
<row>
<entry align="left" colname="c1">
<SimplePara>SQ</SimplePara>
</entry>
<entry align="left" colname="c2">
<SimplePara>-</SimplePara>
</entry>
<entry align="left" colname="c3" />
<entry align="left" colname="c4" />
</row>
<row>
<entry align="left" colname="c1">
<SimplePara>SR</SimplePara>
</entry>
<entry align="left" colname="c2">
<SimplePara>0.031</SimplePara>
</entry>
<entry align="left" colname="c3">
<SimplePara>-</SimplePara>
</entry>
<entry align="left" colname="c4" />
</row>
<row>
<entry align="left" colname="c1">
<SimplePara>SS</SimplePara>
</entry>
<entry align="left" colname="c2">
<SimplePara>-0.025</SimplePara>
</entry>
<entry align="left" colname="c3">
<SimplePara>-0.042*</SimplePara>
</entry>
<entry align="left" colname="c4">
<SimplePara>-</SimplePara>
</entry>
</row>
</tbody>
</tgroup>
<tfooter>
<SimplePara><Emphasis Type="Italic">Note</Emphasis>. * &#x003C; 0.05</SimplePara>
</tfooter>
</Table>
</Para>
</Section2>
<Section2 ID="Sec8">
<Heading>3.2 DSEM results</Heading>
<Para ID="Par61">DSEM results are summarized in Fig.&#x00A0;<InternalRef RefID="Fig2">2</InternalRef> and detailed in Table&#x00A0;<InternalRef RefID="Tab2">2</InternalRef>; all variables were standardized (z-scored) before analysis. The population-level mean intercepts were not significant for SQ, but were significant for both SR (Median = -0.875, 95&#x0025; CI [-1.151, -0.649]) and SS (Median&#x2009;=&#x2009;0.926, 95&#x0025; CI [0.704, 1.179]). Significant random intercept variances for SQ (0.015), SR (0.002), and SS (0.002) indicated substantial between-province heterogeneity.</Para>
<Para ID="Par62">
<Figure Category="Standard" Float="Yes" ID="Fig2">
<Caption Language="En">
<CaptionNumber>Fig. 2</CaptionNumber>
<CaptionContent>
<SimplePara>Path Diagram of the DSEM results</SimplePara>
</CaptionContent>
</Caption>
<MediaObject>
<ImageObject FileRef="float_image2.jpeg" Format="JPEG" Color="BlackWhite" Type="Linedraw" Rendition="Print" Width="001" Height="001" Resolution="120" />
<ImageObject FileRef="Online_float_image2.png" Format="PNG" Color="BlackWhite" Type="Linedraw" Rendition="HTML" Width="001" Height="001" Resolution="120" />
</MediaObject>
</Figure>
</Para>
<Para ID="Par63">
<Table Float="Yes" ID="Tab2">
<Caption Language="En">
<CaptionNumber>Table 2</CaptionNumber>
<CaptionContent>
<SimplePara>DSEM Results for Path Coefficients and Variance Components.</SimplePara>
</CaptionContent>
</Caption>
<tgroup cols="7">
<colspec colnum="1" colname="c1" align="left" />
<colspec colnum="2" colname="c2" align="left" />
<colspec colnum="3" colname="c3" align="left" />
<colspec colnum="4" colname="c4" align="left" />
<colspec colnum="5" colname="c5" align="left" />
<colspec colnum="6" colname="c6" align="left" />
<colspec colnum="7" colname="c7" align="left" />
<thead>
<row>
<entry align="left" namest="c1" nameend="c7">
<SimplePara>Intercept</SimplePara>
</entry>
</row>
</thead>
<tbody>
<row>
<entry align="left" colname="c1">
<SimplePara>Effect</SimplePara>
</entry>
<entry align="left" namest="c2" nameend="c3" />
<entry align="left" colname="c4">
<SimplePara>Notation</SimplePara>
</entry>
<entry align="left" colname="c5">
<SimplePara>Posterior median</SimplePara>
</entry>
<entry align="left" namest="c6" nameend="c7">
<SimplePara>95&#x0025; credible interval</SimplePara>
</entry>
</row>
<row>
<entry align="left" namest="c1" nameend="c2">
<SimplePara>Int(SQ, <InlineEquation ID="IEq37"><EquationSource Format="TEX"><![CDATA[$$\:{\alpha\:}_{1i}$$]]></EquationSource></InlineEquation>)</SimplePara>
</entry>
<entry align="left" colname="c3" />
<entry align="left" colname="c4">
<SimplePara><InlineEquation ID="IEq38"><EquationSource Format="TEX"><![CDATA[$$\:{\gamma\:}_{00}$$]]></EquationSource></InlineEquation></SimplePara>
</entry>
<entry align="left" colname="c5">
<SimplePara>-0.068</SimplePara>
</entry>
<entry align="left" namest="c6" nameend="c7">
<SimplePara>[-0.361,0.215]</SimplePara>
</entry>
</row>
<row>
<entry align="left" namest="c1" nameend="c2">
<SimplePara>Int(SR, <InlineEquation ID="IEq39"><EquationSource Format="TEX"><![CDATA[$$\:{\alpha\:}_{2i}$$]]></EquationSource></InlineEquation>)</SimplePara>
</entry>
<entry align="left" colname="c3" />
<entry align="left" colname="c4">
<SimplePara><InlineEquation ID="IEq40"><EquationSource Format="TEX"><![CDATA[$$\:{\gamma\:}_{10}$$]]></EquationSource></InlineEquation></SimplePara>
</entry>
<entry align="left" colname="c5">
<SimplePara><Emphasis Type="Bold">-0.875</Emphasis></SimplePara>
</entry>
<entry align="left" namest="c6" nameend="c7">
<SimplePara>[-1.151,-0.649]</SimplePara>
</entry>
</row>
<row>
<entry align="left" namest="c1" nameend="c2">
<SimplePara>Int(SS, <InlineEquation ID="IEq41"><EquationSource Format="TEX"><![CDATA[$$\:{\alpha\:}_{3i}$$]]></EquationSource></InlineEquation>)</SimplePara>
</entry>
<entry align="left" colname="c3" />
<entry align="left" colname="c4">
<SimplePara><InlineEquation ID="IEq42"><EquationSource Format="TEX"><![CDATA[$$\:{\gamma\:}_{20}$$]]></EquationSource></InlineEquation></SimplePara>
</entry>
<entry align="left" colname="c5">
<SimplePara><Emphasis Type="Bold">0.926</Emphasis></SimplePara>
</entry>
<entry align="left" namest="c6" nameend="c7">
<SimplePara>[0.704,1.179]</SimplePara>
</entry>
</row>
<row>
<entry align="left" namest="c1" nameend="c2">
<SimplePara>Ln(Var[SQ], <InlineEquation ID="IEq43"><EquationSource Format="TEX"><![CDATA[$$\:{\sigma\:}_{2i}^{2}$$]]></EquationSource></InlineEquation>)</SimplePara>
</entry>
<entry align="left" colname="c3" />
<entry align="left" colname="c4">
<SimplePara><InlineEquation ID="IEq44"><EquationSource Format="TEX"><![CDATA[$$\:{w}_{00}$$]]></EquationSource></InlineEquation></SimplePara>
</entry>
<entry align="left" colname="c5">
<SimplePara><Emphasis Type="Bold">-1.652</Emphasis></SimplePara>
</entry>
<entry align="left" namest="c6" nameend="c7">
<SimplePara>[-1.898,-1.406]</SimplePara>
</entry>
</row>
<row>
<entry align="left" namest="c1" nameend="c2">
<SimplePara>Ln(Var[SR], <InlineEquation ID="IEq45"><EquationSource Format="TEX"><![CDATA[$$\:{\sigma\:}_{2i}^{2}$$]]></EquationSource></InlineEquation>)</SimplePara>
</entry>
<entry align="left" colname="c3" />
<entry align="left" colname="c4">
<SimplePara><InlineEquation ID="IEq46"><EquationSource Format="TEX"><![CDATA[$$\:{w}_{10}$$]]></EquationSource></InlineEquation></SimplePara>
</entry>
<entry align="left" colname="c5">
<SimplePara><Emphasis Type="Bold">-2.859</Emphasis></SimplePara>
</entry>
<entry align="left" namest="c6" nameend="c7">
<SimplePara>[-3.137,-2.587]</SimplePara>
</entry>
</row>
<row>
<entry align="left" namest="c1" nameend="c2">
<SimplePara>Ln(Var[SS], <InlineEquation ID="IEq47"><EquationSource Format="TEX"><![CDATA[$$\:{\sigma\:}_{3i}^{2}$$]]></EquationSource></InlineEquation>)</SimplePara>
</entry>
<entry align="left" colname="c3" />
<entry align="left" colname="c4">
<SimplePara><InlineEquation ID="IEq48"><EquationSource Format="TEX"><![CDATA[$$\:{w}_{20}$$]]></EquationSource></InlineEquation></SimplePara>
</entry>
<entry align="left" colname="c5">
<SimplePara><Emphasis Type="Bold">-1.259</Emphasis></SimplePara>
</entry>
<entry align="left" namest="c6" nameend="c7">
<SimplePara>[-1.510,-1.015]</SimplePara>
</entry>
</row>
<row>
<entry align="left" namest="c1" nameend="c7">
<SimplePara>Path coefficient</SimplePara>
</entry>
</row>
<row>
<entry align="left" colname="c1">
<SimplePara>Predictor</SimplePara>
</entry>
<entry align="left" namest="c2" nameend="c3">
<SimplePara>Outcome</SimplePara>
</entry>
<entry align="left" colname="c4">
<SimplePara>Notation</SimplePara>
</entry>
<entry align="left" colname="c5">
<SimplePara>Posterior median</SimplePara>
</entry>
<entry align="left" namest="c6" nameend="c7">
<SimplePara>95&#x0025; credible interval</SimplePara>
</entry>
</row>
<row>
<entry align="left" colname="c1">
<SimplePara>SQ at t-1</SimplePara>
</entry>
<entry align="left" namest="c2" nameend="c3">
<SimplePara>SQ at t(<InlineEquation ID="IEq49"><EquationSource Format="TEX"><![CDATA[$$\:{\phi\:}_{1i}$$]]></EquationSource></InlineEquation>)</SimplePara>
</entry>
<entry align="left" colname="c4">
<SimplePara><InlineEquation ID="IEq50"><EquationSource Format="TEX"><![CDATA[$$\:{\gamma\:}_{30}$$]]></EquationSource></InlineEquation></SimplePara>
</entry>
<entry align="left" colname="c5">
<SimplePara><Emphasis Type="Bold">0.768</Emphasis></SimplePara>
</entry>
<entry align="left" namest="c6" nameend="c7">
<SimplePara>[0.687,0.858]</SimplePara>
</entry>
</row>
<row>
<entry align="left" colname="c1">
<SimplePara>SR at t-1</SimplePara>
</entry>
<entry align="left" namest="c2" nameend="c3">
<SimplePara>SR at t(<InlineEquation ID="IEq51"><EquationSource Format="TEX"><![CDATA[$$\:{\phi\:}_{2i}$$]]></EquationSource></InlineEquation>)</SimplePara>
</entry>
<entry align="left" colname="c4">
<SimplePara><InlineEquation ID="IEq52"><EquationSource Format="TEX"><![CDATA[$$\:{\gamma\:}_{40}$$]]></EquationSource></InlineEquation></SimplePara>
</entry>
<entry align="left" colname="c5">
<SimplePara><Emphasis Type="Bold">0.699</Emphasis></SimplePara>
</entry>
<entry align="left" namest="c6" nameend="c7">
<SimplePara>[0.635,0.761]</SimplePara>
</entry>
</row>
<row>
<entry align="left" colname="c1">
<SimplePara>SS at t-1</SimplePara>
</entry>
<entry align="left" namest="c2" nameend="c3">
<SimplePara>SS at t(<InlineEquation ID="IEq53"><EquationSource Format="TEX"><![CDATA[$$\:{\phi\:}_{3i}$$]]></EquationSource></InlineEquation>)</SimplePara>
</entry>
<entry align="left" colname="c4">
<SimplePara><InlineEquation ID="IEq54"><EquationSource Format="TEX"><![CDATA[$$\:{\gamma\:}_{50}$$]]></EquationSource></InlineEquation></SimplePara>
</entry>
<entry align="left" colname="c5">
<SimplePara><Emphasis Type="Bold">0.130</Emphasis></SimplePara>
</entry>
<entry align="left" namest="c6" nameend="c7">
<SimplePara>[0.045,0.210]</SimplePara>
</entry>
</row>
<row>
<entry align="left" colname="c1">
<SimplePara>SR at t-1</SimplePara>
</entry>
<entry align="left" namest="c2" nameend="c3">
<SimplePara>SQ at t(<InlineEquation ID="IEq55"><EquationSource Format="TEX"><![CDATA[$$\:{\phi\:}_{4i}$$]]></EquationSource></InlineEquation>)</SimplePara>
</entry>
<entry align="left" colname="c4">
<SimplePara><InlineEquation ID="IEq56"><EquationSource Format="TEX"><![CDATA[$$\:{\gamma\:}_{60}$$]]></EquationSource></InlineEquation></SimplePara>
</entry>
<entry align="left" colname="c5">
<SimplePara><Emphasis Type="Bold">0.099</Emphasis></SimplePara>
</entry>
<entry align="left" namest="c6" nameend="c7">
<SimplePara>[0.026,0.207]</SimplePara>
</entry>
</row>
<row>
<entry align="left" colname="c1">
<SimplePara>SS at t-1</SimplePara>
</entry>
<entry align="left" namest="c2" nameend="c3">
<SimplePara>SQ at t(<InlineEquation ID="IEq57"><EquationSource Format="TEX"><![CDATA[$$\:{\phi\:}_{5i}$$]]></EquationSource></InlineEquation>)</SimplePara>
</entry>
<entry align="left" colname="c4">
<SimplePara><InlineEquation ID="IEq58"><EquationSource Format="TEX"><![CDATA[$$\:{\gamma\:}_{70}$$]]></EquationSource></InlineEquation></SimplePara>
</entry>
<entry align="left" colname="c5">
<SimplePara><Emphasis Type="Bold">0.154</Emphasis></SimplePara>
</entry>
<entry align="left" namest="c6" nameend="c7">
<SimplePara>[0.093,0.236]</SimplePara>
</entry>
</row>
<row>
<entry align="left" colname="c1">
<SimplePara>SQ at t-1</SimplePara>
</entry>
<entry align="left" namest="c2" nameend="c3">
<SimplePara>SR at t(<InlineEquation ID="IEq59"><EquationSource Format="TEX"><![CDATA[$$\:{\phi\:}_{6i}$$]]></EquationSource></InlineEquation>)</SimplePara>
</entry>
<entry align="left" colname="c4">
<SimplePara><InlineEquation ID="IEq60"><EquationSource Format="TEX"><![CDATA[$$\:{\gamma\:}_{80}$$]]></EquationSource></InlineEquation></SimplePara>
</entry>
<entry align="left" colname="c5">
<SimplePara><Emphasis Type="Bold">-0.121</Emphasis></SimplePara>
</entry>
<entry align="left" namest="c6" nameend="c7">
<SimplePara>[-0.197,-0.035]</SimplePara>
</entry>
</row>
<row>
<entry align="left" colname="c1">
<SimplePara>SS at t-1</SimplePara>
</entry>
<entry align="left" namest="c2" nameend="c3">
<SimplePara>SR at t(<InlineEquation ID="IEq61"><EquationSource Format="TEX"><![CDATA[$$\:{\phi\:}_{7i}$$]]></EquationSource></InlineEquation>)</SimplePara>
</entry>
<entry align="left" colname="c4">
<SimplePara><InlineEquation ID="IEq62"><EquationSource Format="TEX"><![CDATA[$$\:{\gamma\:}_{90}$$]]></EquationSource></InlineEquation></SimplePara>
</entry>
<entry align="left" colname="c5">
<SimplePara>0.024</SimplePara>
</entry>
<entry align="left" namest="c6" nameend="c7">
<SimplePara>[-0.029,0.076]</SimplePara>
</entry>
</row>
<row>
<entry align="left" colname="c1">
<SimplePara>SQ at t-1</SimplePara>
</entry>
<entry align="left" namest="c2" nameend="c3">
<SimplePara>SS at t(<InlineEquation ID="IEq63"><EquationSource Format="TEX"><![CDATA[$$\:{\phi\:}_{8i}$$]]></EquationSource></InlineEquation>)</SimplePara>
</entry>
<entry align="left" colname="c4">
<SimplePara><InlineEquation ID="IEq64"><EquationSource Format="TEX"><![CDATA[$$\:{\gamma\:}_{10,0}$$]]></EquationSource></InlineEquation></SimplePara>
</entry>
<entry align="left" colname="c5">
<SimplePara>0.000</SimplePara>
</entry>
<entry align="left" namest="c6" nameend="c7">
<SimplePara>[-0.085,0.089]</SimplePara>
</entry>
</row>
<row>
<entry align="left" colname="c1">
<SimplePara>SR at t-1</SimplePara>
</entry>
<entry align="left" namest="c2" nameend="c3">
<SimplePara>SS at t(<InlineEquation ID="IEq65"><EquationSource Format="TEX"><![CDATA[$$\:{\phi\:}_{9i}$$]]></EquationSource></InlineEquation>)</SimplePara>
</entry>
<entry align="left" colname="c4">
<SimplePara><InlineEquation ID="IEq66"><EquationSource Format="TEX"><![CDATA[$$\:{\gamma\:}_{11,0}$$]]></EquationSource></InlineEquation></SimplePara>
</entry>
<entry align="left" colname="c5">
<SimplePara><Emphasis Type="Bold">-0.626</Emphasis></SimplePara>
</entry>
<entry align="left" namest="c6" nameend="c7">
<SimplePara>[-0.724,-0.530]</SimplePara>
</entry>
</row>
<row>
<entry align="left" colname="c1">
<SimplePara>SQ at t</SimplePara>
</entry>
<entry align="left" namest="c2" nameend="c3">
<SimplePara>SR at t(<InlineEquation ID="IEq67"><EquationSource Format="TEX"><![CDATA[$$\:{\beta\:}_{1i}$$]]></EquationSource></InlineEquation>)</SimplePara>
</entry>
<entry align="left" colname="c4">
<SimplePara><InlineEquation ID="IEq68"><EquationSource Format="TEX"><![CDATA[$$\:{\gamma\:}_{12,0}$$]]></EquationSource></InlineEquation></SimplePara>
</entry>
<entry align="left" colname="c5">
<SimplePara><Emphasis Type="Bold">0.263</Emphasis></SimplePara>
</entry>
<entry align="left" namest="c6" nameend="c7">
<SimplePara>[0.200,0.338]</SimplePara>
</entry>
</row>
<row>
<entry align="left" colname="c1">
<SimplePara>SS at t</SimplePara>
</entry>
<entry align="left" namest="c2" nameend="c3">
<SimplePara>SR at t (<InlineEquation ID="IEq69"><EquationSource Format="TEX"><![CDATA[$$\:{\beta\:}_{2i}$$]]></EquationSource></InlineEquation>)</SimplePara>
</entry>
<entry align="left" colname="c4">
<SimplePara><InlineEquation ID="IEq70"><EquationSource Format="TEX"><![CDATA[$$\:{\gamma\:}_{\text{13,0}}$$]]></EquationSource></InlineEquation></SimplePara>
</entry>
<entry align="left" colname="c5">
<SimplePara><Emphasis Type="Bold">-0.170</Emphasis></SimplePara>
</entry>
<entry align="left" namest="c6" nameend="c7">
<SimplePara>[-0.256,-0.097]</SimplePara>
</entry>
</row>
<row>
<entry align="left" namest="c1" nameend="c7">
<SimplePara>Between-level residual variance</SimplePara>
</entry>
</row>
<row>
<entry align="left" colname="c1">
<SimplePara>Effect</SimplePara>
</entry>
<entry align="left" namest="c2" nameend="c3" />
<entry align="left" colname="c4">
<SimplePara>Notation</SimplePara>
</entry>
<entry align="left" namest="c5" nameend="c6">
<SimplePara>Posterior median</SimplePara>
</entry>
<entry align="left" colname="c7" />
</row>
<row>
<entry align="left" colname="c1">
<SimplePara>Var(<InlineEquation ID="IEq71"><EquationSource Format="TEX"><![CDATA[$$\:{u}_{0i}$$]]></EquationSource></InlineEquation>)</SimplePara>
</entry>
<entry align="left" namest="c2" nameend="c3" />
<entry align="left" colname="c4">
<SimplePara><InlineEquation ID="IEq72"><EquationSource Format="TEX"><![CDATA[$$\:{\tau\:}_{00}$$]]></EquationSource></InlineEquation></SimplePara>
</entry>
<entry align="left" namest="c5" nameend="c6">
<SimplePara><Emphasis Type="Bold">0.015</Emphasis></SimplePara>
</entry>
<entry align="left" colname="c7" />
</row>
<row>
<entry align="left" colname="c1">
<SimplePara>Var(<InlineEquation ID="IEq73"><EquationSource Format="TEX"><![CDATA[$$\:{u}_{1i}$$]]></EquationSource></InlineEquation>)</SimplePara>
</entry>
<entry align="left" namest="c2" nameend="c3" />
<entry align="left" colname="c4">
<SimplePara><InlineEquation ID="IEq74"><EquationSource Format="TEX"><![CDATA[$$\:{\tau\:}_{11}$$]]></EquationSource></InlineEquation></SimplePara>
</entry>
<entry align="left" namest="c5" nameend="c6">
<SimplePara><Emphasis Type="Bold">0.002</Emphasis></SimplePara>
</entry>
<entry align="left" colname="c7" />
</row>
<row>
<entry align="left" colname="c1">
<SimplePara>Var(<InlineEquation ID="IEq75"><EquationSource Format="TEX"><![CDATA[$$\:{u}_{2i}$$]]></EquationSource></InlineEquation>)</SimplePara>
</entry>
<entry align="left" namest="c2" nameend="c3" />
<entry align="left" colname="c4">
<SimplePara><InlineEquation ID="IEq76"><EquationSource Format="TEX"><![CDATA[$$\:{\tau\:}_{22}$$]]></EquationSource></InlineEquation></SimplePara>
</entry>
<entry align="left" namest="c5" nameend="c6">
<SimplePara><Emphasis Type="Bold">0.002</Emphasis></SimplePara>
</entry>
<entry align="left" colname="c7" />
</row>
<row>
<entry align="left" colname="c1">
<SimplePara>Var(<InlineEquation ID="IEq77"><EquationSource Format="TEX"><![CDATA[$$\:{u}_{3i}$$]]></EquationSource></InlineEquation>)</SimplePara>
</entry>
<entry align="left" namest="c2" nameend="c3" />
<entry align="left" colname="c4">
<SimplePara><InlineEquation ID="IEq78"><EquationSource Format="TEX"><![CDATA[$$\:{\tau\:}_{33}$$]]></EquationSource></InlineEquation></SimplePara>
</entry>
<entry align="left" namest="c5" nameend="c6">
<SimplePara><Emphasis Type="Bold">0.003</Emphasis></SimplePara>
</entry>
<entry align="left" colname="c7" />
</row>
<row>
<entry align="left" colname="c1">
<SimplePara>Var(<InlineEquation ID="IEq79"><EquationSource Format="TEX"><![CDATA[$$\:{u}_{4i}$$]]></EquationSource></InlineEquation>)</SimplePara>
</entry>
<entry align="left" namest="c2" nameend="c3" />
<entry align="left" colname="c4">
<SimplePara><InlineEquation ID="IEq80"><EquationSource Format="TEX"><![CDATA[$$\:{\tau\:}_{44}$$]]></EquationSource></InlineEquation></SimplePara>
</entry>
<entry align="left" namest="c5" nameend="c6">
<SimplePara><Emphasis Type="Bold">0.001</Emphasis></SimplePara>
</entry>
<entry align="left" colname="c7" />
</row>
<row>
<entry align="left" colname="c1">
<SimplePara>Var(<InlineEquation ID="IEq81"><EquationSource Format="TEX"><![CDATA[$$\:{u}_{5i}$$]]></EquationSource></InlineEquation>)</SimplePara>
</entry>
<entry align="left" namest="c2" nameend="c3" />
<entry align="left" colname="c4">
<SimplePara><InlineEquation ID="IEq82"><EquationSource Format="TEX"><![CDATA[$$\:{\tau\:}_{55}$$]]></EquationSource></InlineEquation></SimplePara>
</entry>
<entry align="left" namest="c5" nameend="c6">
<SimplePara><Emphasis Type="Bold">0.002</Emphasis></SimplePara>
</entry>
<entry align="left" colname="c7" />
</row>
<row>
<entry align="left" colname="c1">
<SimplePara>Var(<InlineEquation ID="IEq83"><EquationSource Format="TEX"><![CDATA[$$\:{u}_{6i}$$]]></EquationSource></InlineEquation>)</SimplePara>
</entry>
<entry align="left" namest="c2" nameend="c3" />
<entry align="left" colname="c4">
<SimplePara><InlineEquation ID="IEq84"><EquationSource Format="TEX"><![CDATA[$$\:{\tau\:}_{66}$$]]></EquationSource></InlineEquation></SimplePara>
</entry>
<entry align="left" namest="c5" nameend="c6">
<SimplePara><Emphasis Type="Bold">0.002</Emphasis></SimplePara>
</entry>
<entry align="left" colname="c7" />
</row>
<row>
<entry align="left" colname="c1">
<SimplePara>Var(<InlineEquation ID="IEq85"><EquationSource Format="TEX"><![CDATA[$$\:{u}_{7i}$$]]></EquationSource></InlineEquation>)</SimplePara>
</entry>
<entry align="left" namest="c2" nameend="c3" />
<entry align="left" colname="c4">
<SimplePara><InlineEquation ID="IEq86"><EquationSource Format="TEX"><![CDATA[$$\:{\tau\:}_{77}$$]]></EquationSource></InlineEquation></SimplePara>
</entry>
<entry align="left" namest="c5" nameend="c6">
<SimplePara><Emphasis Type="Bold">0.002</Emphasis></SimplePara>
</entry>
<entry align="left" colname="c7" />
</row>
<row>
<entry align="left" colname="c1">
<SimplePara>Var(<InlineEquation ID="IEq87"><EquationSource Format="TEX"><![CDATA[$$\:{u}_{8i}$$]]></EquationSource></InlineEquation>)</SimplePara>
</entry>
<entry align="left" namest="c2" nameend="c3" />
<entry align="left" colname="c4">
<SimplePara><InlineEquation ID="IEq88"><EquationSource Format="TEX"><![CDATA[$$\:{\tau\:}_{88}$$]]></EquationSource></InlineEquation></SimplePara>
</entry>
<entry align="left" namest="c5" nameend="c6">
<SimplePara><Emphasis Type="Bold">0.002</Emphasis></SimplePara>
</entry>
<entry align="left" colname="c7" />
</row>
<row>
<entry align="left" colname="c1">
<SimplePara>Var(<InlineEquation ID="IEq89"><EquationSource Format="TEX"><![CDATA[$$\:{u}_{9i}$$]]></EquationSource></InlineEquation>)</SimplePara>
</entry>
<entry align="left" namest="c2" nameend="c3" />
<entry align="left" colname="c4">
<SimplePara><InlineEquation ID="IEq90"><EquationSource Format="TEX"><![CDATA[$$\:{\tau\:}_{99}$$]]></EquationSource></InlineEquation></SimplePara>
</entry>
<entry align="left" namest="c5" nameend="c6">
<SimplePara><Emphasis Type="Bold">0.001</Emphasis></SimplePara>
</entry>
<entry align="left" colname="c7" />
</row>
<row>
<entry align="left" colname="c1">
<SimplePara>Var(<InlineEquation ID="IEq91"><EquationSource Format="TEX"><![CDATA[$$\:{u}_{10i}$$]]></EquationSource></InlineEquation>)</SimplePara>
</entry>
<entry align="left" namest="c2" nameend="c3" />
<entry align="left" colname="c4">
<SimplePara><InlineEquation ID="IEq92"><EquationSource Format="TEX"><![CDATA[$$\:{\tau\:}_{\text{10,10}}$$]]></EquationSource></InlineEquation></SimplePara>
</entry>
<entry align="left" namest="c5" nameend="c6">
<SimplePara><Emphasis Type="Bold">0.014</Emphasis></SimplePara>
</entry>
<entry align="left" colname="c7" />
</row>
<row>
<entry align="left" colname="c1">
<SimplePara>Var(<InlineEquation ID="IEq93"><EquationSource Format="TEX"><![CDATA[$$\:{u}_{11i}$$]]></EquationSource></InlineEquation>)</SimplePara>
</entry>
<entry align="left" namest="c2" nameend="c3" />
<entry align="left" colname="c4">
<SimplePara><InlineEquation ID="IEq94"><EquationSource Format="TEX"><![CDATA[$$\:{\tau\:}_{\text{11,11}}$$]]></EquationSource></InlineEquation></SimplePara>
</entry>
<entry align="left" namest="c5" nameend="c6">
<SimplePara><Emphasis Type="Bold">0.002</Emphasis></SimplePara>
</entry>
<entry align="left" colname="c7" />
</row>
<row>
<entry align="left" colname="c1">
<SimplePara>Var(<InlineEquation ID="IEq95"><EquationSource Format="TEX"><![CDATA[$$\:{u}_{12i}$$]]></EquationSource></InlineEquation>)</SimplePara>
</entry>
<entry align="left" namest="c2" nameend="c3" />
<entry align="left" colname="c4">
<SimplePara><InlineEquation ID="IEq96"><EquationSource Format="TEX"><![CDATA[$$\:{\tau\:}_{\text{12,12}}$$]]></EquationSource></InlineEquation></SimplePara>
</entry>
<entry align="left" namest="c5" nameend="c6">
<SimplePara><Emphasis Type="Bold">0.001</Emphasis></SimplePara>
</entry>
<entry align="left" colname="c7" />
</row>
<row>
<entry align="left" colname="c1">
<SimplePara>Var(<InlineEquation ID="IEq97"><EquationSource Format="TEX"><![CDATA[$$\:{u}_{13i}$$]]></EquationSource></InlineEquation>)</SimplePara>
</entry>
<entry align="left" namest="c2" nameend="c3" />
<entry align="left" colname="c4">
<SimplePara><InlineEquation ID="IEq98"><EquationSource Format="TEX"><![CDATA[$$\:{\tau\:}_{\text{13,13}}$$]]></EquationSource></InlineEquation></SimplePara>
</entry>
<entry align="left" namest="c5" nameend="c6">
<SimplePara><Emphasis Type="Bold">0.007</Emphasis></SimplePara>
</entry>
<entry align="left" colname="c7" />
</row>
<row>
<entry align="left" colname="c1">
<SimplePara>Var(<InlineEquation ID="IEq99"><EquationSource Format="TEX"><![CDATA[$$\:{u}_{14i}$$]]></EquationSource></InlineEquation>)</SimplePara>
</entry>
<entry align="left" namest="c2" nameend="c3" />
<entry align="left" colname="c4">
<SimplePara><InlineEquation ID="IEq100"><EquationSource Format="TEX"><![CDATA[$$\:{\tau\:}_{\text{14,14}}$$]]></EquationSource></InlineEquation></SimplePara>
</entry>
<entry align="left" namest="c5" nameend="c6">
<SimplePara><Emphasis Type="Bold">0.275</Emphasis></SimplePara>
</entry>
<entry align="left" colname="c7" />
</row>
<row>
<entry align="left" colname="c1">
<SimplePara>Var(<InlineEquation ID="IEq101"><EquationSource Format="TEX"><![CDATA[$$\:{u}_{15i}$$]]></EquationSource></InlineEquation>)</SimplePara>
</entry>
<entry align="left" namest="c2" nameend="c3" />
<entry align="left" colname="c4">
<SimplePara><InlineEquation ID="IEq102"><EquationSource Format="TEX"><![CDATA[$$\:{\tau\:}_{\text{15,15}}$$]]></EquationSource></InlineEquation></SimplePara>
</entry>
<entry align="left" namest="c5" nameend="c6">
<SimplePara><Emphasis Type="Bold">0.371</Emphasis></SimplePara>
</entry>
<entry align="left" colname="c7" />
</row>
<row>
<entry align="left" colname="c1">
<SimplePara>Var(<InlineEquation ID="IEq103"><EquationSource Format="TEX"><![CDATA[$$\:{u}_{16i}$$]]></EquationSource></InlineEquation>)</SimplePara>
</entry>
<entry align="left" namest="c2" nameend="c3" />
<entry align="left" colname="c4">
<SimplePara><InlineEquation ID="IEq104"><EquationSource Format="TEX"><![CDATA[$$\:{\tau\:}_{\text{16,16}}$$]]></EquationSource></InlineEquation></SimplePara>
</entry>
<entry align="left" namest="c5" nameend="c6">
<SimplePara><Emphasis Type="Bold">0.281</Emphasis></SimplePara>
</entry>
<entry align="left" colname="c7" />
</row>
</tbody>
</tgroup>
<tfooter>
<SimplePara><Emphasis Type="Italic">Note</Emphasis>. Boldface indicates that the 95&#x0025; Credible Interval does not contain zero.</SimplePara>
</tfooter>
</Table>
</Para>
<Para ID="Par64">First, all three variables demonstrated significant positive autoregressive effects, indicating temporal continuity. The standardized coefficients were significant for SQ (<InlineEquation ID="IEq105"><EquationSource Format="TEX"><![CDATA[$$\:{\gamma\:}_{30}$$]]></EquationSource></InlineEquation> = 0.768, 95&#x0025; CI [0.687, 0.858]), SR (<InlineEquation ID="IEq106"><EquationSource Format="TEX"><![CDATA[$$\:{\gamma\:}_{40}$$]]></EquationSource></InlineEquation> = 0.699, 95&#x0025; CI [0.635, 0.761]), and SS (<InlineEquation ID="IEq107"><EquationSource Format="TEX"><![CDATA[$$\:{\gamma\:}_{50}$$]]></EquationSource></InlineEquation> = 0.130, 95&#x0025; CI [0.045, 0.210]). All coefficients were between &#x2212;&#x2009;1 and 1, confirming time series stationarity [37].</Para>
<Para ID="Par65">Next, we examined the cross-lagged effects between the variables. Four of the six possible pathways were found to be significant:</Para>
<Para ID="Par66">Higher prior suicide risk (<InlineEquation ID="IEq108"><EquationSource Format="TEX"><![CDATA[$$\:{SR}_{t-1}$$]]></EquationSource></InlineEquation>) predicted poorer subsequent sleep quality (<InlineEquation ID="IEq109"><EquationSource Format="TEX"><![CDATA[$$\:{SQ}_{t}$$]]></EquationSource></InlineEquation>, <InlineEquation ID="IEq110"><EquationSource Format="TEX"><![CDATA[$$\:{\gamma\:}_{60}$$]]></EquationSource></InlineEquation> = 0.099, 95&#x0025; CI [0.026, 0.207]) (i.e., a higher <InlineEquation ID="IEq111"><EquationSource Format="TEX"><![CDATA[$$\:{SQ}_{t}$$]]></EquationSource></InlineEquation> score).</Para>
<Para ID="Par67">Higher prior perceived social support (<InlineEquation ID="IEq112"><EquationSource Format="TEX"><![CDATA[$$\:{SS}_{t-1}$$]]></EquationSource></InlineEquation>) also predicted poorer subsequent sleep quality (<InlineEquation ID="IEq113"><EquationSource Format="TEX"><![CDATA[$$\:{SQ}_{t}$$]]></EquationSource></InlineEquation>, <InlineEquation ID="IEq114"><EquationSource Format="TEX"><![CDATA[$$\:{\gamma\:}_{70}$$]]></EquationSource></InlineEquation> = 0.154, 95&#x0025; CI [0.093, 0.236]) (i.e., a higher <InlineEquation ID="IEq115"><EquationSource Format="TEX"><![CDATA[$$\:{SQ}_{t}$$]]></EquationSource></InlineEquation> score).</Para>
<Para ID="Par68">Higher prior sleep quality (<InlineEquation ID="IEq116"><EquationSource Format="TEX"><![CDATA[$$\:{SQ}_{t-1}$$]]></EquationSource></InlineEquation>) (i.e., a lower <InlineEquation ID="IEq117"><EquationSource Format="TEX"><![CDATA[$$\:{SQ}_{t}$$]]></EquationSource></InlineEquation> score) predicted large subsequent suicide risk (<InlineEquation ID="IEq118"><EquationSource Format="TEX"><![CDATA[$$\:{SR}_{t}$$]]></EquationSource></InlineEquation>, <InlineEquation ID="IEq119"><EquationSource Format="TEX"><![CDATA[$$\:{\gamma\:}_{80}$$]]></EquationSource></InlineEquation> = -0.121, 95&#x0025; CI [-0.197, -0.035]).</Para>
<Para ID="Par69">Higher prior suicide risk (<InlineEquation ID="IEq120"><EquationSource Format="TEX"><![CDATA[$$\:{SR}_{t-1}$$]]></EquationSource></InlineEquation>) predicted a large decrease in subsequent perceived social support (<InlineEquation ID="IEq121"><EquationSource Format="TEX"><![CDATA[$$\:{SS}_{t}$$]]></EquationSource></InlineEquation>) (<InlineEquation ID="IEq122"><EquationSource Format="TEX"><![CDATA[$$\:{\gamma\:}_{11,0}$$]]></EquationSource></InlineEquation> = -0.626, 95&#x0025; CI [-0.724, -0.530]).</Para>
<Para ID="Par70">The effect of prior suicide risk on subsequent social support was notably large in magnitude, whereas the other cross-lagged effects were relatively small.</Para>
<Para ID="Par71">Contemporaneously, both sleep quality and social support significantly predicted suicide risk. Specifically, within the same year, poorer sleep quality (<InlineEquation ID="IEq123"><EquationSource Format="TEX"><![CDATA[$$\:{SQ}_{t}$$]]></EquationSource></InlineEquation>) was associated with higher suicide risk (<InlineEquation ID="IEq124"><EquationSource Format="TEX"><![CDATA[$$\:{SR}_{t}$$]]></EquationSource></InlineEquation>, <InlineEquation ID="IEq125"><EquationSource Format="TEX"><![CDATA[$$\:{\gamma\:}_{12,0}$$]]></EquationSource></InlineEquation> = 0.263, 95&#x0025; CI [0.200, 0.338]), while higher perceived social support (<InlineEquation ID="IEq126"><EquationSource Format="TEX"><![CDATA[$$\:{SS}_{t}$$]]></EquationSource></InlineEquation>) was associated with lower suicide risk (<InlineEquation ID="IEq127"><EquationSource Format="TEX"><![CDATA[$$\:{SR}_{t}$$]]></EquationSource></InlineEquation>, <InlineEquation ID="IEq128"><EquationSource Format="TEX"><![CDATA[$$\:{\gamma\:}_{13,0}$$]]></EquationSource></InlineEquation> = -0.170, 95&#x0025; CI [-0.256, -0.097]). The variances for both contemporaneous effects were also significant, indicating notable between-province variability in the strength of these within-year relationships.</Para>
<Para ID="Par72">Finally, the model accounted for a substantial portion of the variance in all three variables, demonstrating considerable explanatory power. The <InlineEquation ID="IEq129"><EquationSource Format="TEX"><![CDATA[$$\:{R}^{2}$$]]></EquationSource></InlineEquation> values were 62.8&#x0025; (95&#x0025; CI [54.4&#x0025;, 74.0&#x0025;]) for SQ, 80.8&#x0025; (95&#x0025; CI [76.3&#x0025;, 84.8&#x0025;]) for SR, and 55.7&#x0025; (95&#x0025; CI [47.8&#x0025;, 63.1&#x0025;]) for SS.</Para>
</Section2>
</Section1>
<Section1 ID="Sec9">
<Heading>4 Discussion</Heading>
<Para ID="Par73">This study used DSEM and a large-scale Weibo dataset to investigate the dynamic relationships among sleep quality, suicide risk, and perceived social support. While some findings were expected, several key cross-lagged effects emerged as counterintuitive. These paradoxical results challenge conventional assumptions and require deeper interpretation.</Para>
<Section2 ID="Sec10">
<Heading>4.1 Continuity of Sleep Quality, Suicide Risk, and Perceived Social Support</Heading>
<Para ID="Par74">As hypothesized, sleep quality showed strong continuity. This finding resonates with research by Pierson-Bartel and Ujma [38], who found moderate to high correlations between objective measures of sleep quality (such as sleep macrostructure and quantitative EEG indicators as measured by mobile EEG devices) and subjective measures (such as self-reports). This consistency reinforces the stability of sleep quality.</Para>
<Para ID="Par75">Likewise, suicide risk showed high continuity, as hypothesized. This finding echoes the work of Preti and Lentini [39], who demonstrated that historical suicide time-series data can predict future trends, thus corroborating the strong autoregressive effect observed in our study. The high autoregressive coefficient suggests a societal-level "memory effect," where major events have lingering impacts on suicide risk. Its effects may dissipate over months or years. One potential mechanism for this societal memory may be related to the phenomenon of suicide contagion. In their systematic review, Cheng et al. [40] outlined four mechanisms for the formation of suicide clusters: transmission, imitation, contextual influences, and group affiliation. Among these, imitation is considered the mechanism with the most heuristic utility.</Para>
<Para ID="Par76">In contrast to the stability of the other two variables, perceived social support showed only weak positive continuity, a finding that was also consistent with our hypothesis. This suggests that perceived social support is a more volatile construct, with year-to-year fluctuations that are difficult to predict at the regional level. This phenomenon can be explained through the lens of the Conservation of Resources (COR) theory, which conceptualizes social support as a valuable resource. COR theory posits that individuals are fundamentally motivated to obtain, retain, protect, and accumulate valued resources [41]. The theory explains resource dynamics through "loss spirals" and "gain spirals," wherein the loss or gain of one resource can trigger a cycle of further gains or losses. Because this process is sensitive to cultural and social contexts, the interplay of these resource spirals with societal events makes perceived social support difficult to maintain and, consequently, hard to predict. This macro-level instability mirrors findings at the micro-level; for instance, a daily diary study by Coppersmith et al. [42] found high day-to-day variability in perceived social support within individuals.</Para>
</Section2>
<Section2 ID="Sec11">
<Heading>4.2 The relationship between sleep quality and suicide risk</Heading>
<Para ID="Par77">As hypothesized, higher prior suicide risk predicted poorer subsequent sleep quality. This is likely because suicide risk is often comorbid with psychiatric disorders like depression, anxiety, or PTSD. The core symptoms of these conditions, including rumination and psychomotor agitation, can directly disrupt sleep architecture, leading to difficulty initiating sleep, sleep fragmentation, or early morning awakening.</Para>
<Para ID="Par78">The most striking finding, however, was the paradoxical effect of sleep on later suicide risk. Contrary to our hypothesis, better prior sleep quality predicted an increase in subsequent suicide risk. This phenomenon is conceptually analogous to "paradoxical suicidality," a term describing the emergence or worsening of suicidal ideation or behaviors in patients initiating antidepressant treatment, despite these medications being intended to alleviate, rather than exacerbate, such risk. Explanations for this effect include the possibility that medication increases energy and agitation before mood improves, providing the capacity to act on pre-existing suicidal impulses [43] or that it enhances the cognitive capacity for suicidal ideation [44]. Applying this logic, we propose that the paradoxical effect in our study operates via a similar mechanism: improved sleep may restore the physical energy and cognitive resources required for an at-risk individual to plan and act on suicidal impulses, thus leading to an observable increase in suicide risk.</Para>
<Para ID="Par79">At the contemporaneous level, and consistent with our hypothesis, poorer sleep quality was associated with higher suicide risk within the same year. This macro-level, within-year association is consistent with micro-level, high-frequency findings from Ecological Momentary Assessment (EMA) studies, which show that poor sleep can significantly predict suicidal ideation on the following day [45]. This finding underscores the importance of addressing immediate sleep problems as a potential strategy for mitigating suicide risk.</Para>
</Section2>
<Section2 ID="Sec12">
<Heading>4.3 The relationship between suicide risk and perceived social support</Heading>
<Para ID="Par80">Our analysis of the lagged relationships between perceived social support and suicide risk yielded a noteworthy asymmetry. Contrary to our hypothesis, prior perceived social support did not significantly predict a change in subsequent suicide risk. Conversely, and also contrary to our hypothesis, a strong negative cross-lagged relationship emerged in the opposite direction: higher prior suicide risk was a powerful predictor of a decline in subsequent perceived social support. This erosion of social support can be understood from the perspectives of both the support recipient and the provider.</Para>
<Para ID="Par81">From the recipient's perspective, psychological mechanisms may lead to social withdrawal. For instance, Joiner's Interpersonal Theory of Suicide posits that perceived burdensomeness and thwarted belongingness are significant correlates of suicide risk, a finding robustly validated by meta-analysis [46]. Individuals with high suicide risk may internalize a sense of being a burden, which, combined with feelings of thwarted belongingness, can foster social withdrawal and thus reduce perceived support. Moreover, individuals at high risk for suicide may exhibit an attentional bias toward negative stimuli [47], causing them to overlook supportive cues from their environment and further diminishing their perception of available support. From the provider's perspective, social-psychological phenomena can inhibit supportive action. The diffusion of responsibility, for example, may lead potential supporters to assume others will intervene in a crisis, thereby reducing their own supportive expressions [48]. Furthermore, a provider's self-efficacy is crucial. Research shows a significant positive correlation between one's self-efficacy and their willingness to intervene in a suicide crisis [49]. A lack of knowledge or skills can lead supporters to feel a low sense of self-efficacy and anticipate that their intervention would be futile, prompting them to refrain from offering support.</Para>
<Para ID="Par82">In contrast to the lagged findings, the contemporaneous relationship was consistent with our hypothesis: higher perceived social support was associated with lower concurrent suicide risk. This macro-level, within-year association mirrors findings from micro-level daily diary studies, which have also found a significant negative correlation between perceived social support and same-day suicidal ideation [42]. This finding reinforces the role of perceived social support as both a crucial protective factor and a viable target for intervention. Indeed, higher levels of perceived social support have been linked to a reduced likelihood of lifetime suicide attempts in representative national samples [13]. As an intervention target, a meta-analysis by Hou et al. [3] concluded that while social support interventions may not always reduce suicide attempts, they are a valuable component of broader suicide prevention strategies.</Para>
</Section2>
<Section2 ID="Sec13">
<Heading>4.4 The relationship between sleep quality and perceived social support</Heading>
<Para ID="Par83"><Annotation ID="7" RuleID="IdentifyCAMTerms_01" Values="harmony" Category="SREP" Status="Neutral" />The dynamic between sleep and social support was also unexpectedly asymmetric. While prior sleep quality did not significantly predict subsequent social support, higher prior social support paradoxically predicted a decline in subsequent sleep quality, contrary to our hypothesis. This result runs counter to the general consensus from meta-analytic evidence, which indicates that higher social support is typically associated with better sleep quality [22]. However, our paradoxical finding aligns with a smaller body of literature that has reported similar negative associations [e.g., 50, 51]. A compelling explanation for this paradox, suggested by Kent et al. [22], lies in the crucial distinction between perceived and received social support. While the perception of available support is beneficial, the act of receiving support can sometimes be harmful. When received support is either mismatched with an individual's needs or exceeds their coping abilities, it can become a stressor that creates a psychological burden and disrupts sleep [52]. Our findings, situated in the collectivist context of China, may be particularly illuminated by this distinction. Here, a cultural emphasis on interpersonal harmony may compel individuals to accept unwanted or unhelpful support to avoid relational friction. This compelled acceptance, rather than genuine utilization of support, could increase psychological burden and, in turn, disrupt sleep.</Para>
</Section2>
<Section2 ID="Sec14">
<Heading>4.5 Implications for Research and Practice</Heading>
<Para ID="Par84">This study holds several key research and practical implications. Methodologically, it demonstrates the utility of social media data for population-level mental health monitoring. Theoretically, it provides ecological validation for the Interpersonal Theory of Suicide. Practically, it offers a new macro-level perspective on SR dynamics, informing public health policy.</Para>
<Para ID="Par85">At the individual level, long-term sleep management, monitored via wearables or diaries, is a critical intervention point. When poor sleep is detected, interventions like CBT-I can be used to improve sleep and potentially reduce downstream suicide risk. Crucially, the paradoxical finding that improved sleep can precede higher suicide risk underscores the need for enhanced monitoring during this apparent recovery phase.</Para>
<Para ID="Par86">At the societal level, culturally tailored programs are needed to disseminate knowledge of suicide intervention, foster responsibility, promote effective support, and enhance public awareness. Given the societal "memory effect," government agencies should consider longitudinal models to monitor suicide risk after major events. Concurrently, suicide-related information must be carefully managed to prevent contagion.</Para>
</Section2>
<Section2 ID="Sec15">
<Heading>4.6 Limitations and future directions</Heading>
<Para ID="Par87">This study has several limitations.</Para>
<Para ID="Par88">First, our Weibo data are susceptible to demographic biases, likely skewed towards younger, urban, and educated users. This limits generalizability to rural, elderly, and non-Internet-using groups. Additionally, our self-report variables are subject to social desirability, recall, and expressive biases.</Para>
<Para ID="Par89">Second, word frequency analysis remains subject to expressive biases. Social stigma, for instance, might lead to under-reporting due to users avoiding sensitive terms, potentially resulting in an underestimation of true risk. Conversely, the use of metaphor, sarcasm, and evolving slang presents misclassification risks, as static dictionaries might fail to capture the true sentiment of nuanced expressions. Additionally, the tendency for exaggerated expressions of emotion and behavior on social media could introduce noise into the frequency counts, potentially resulting in an overestimation of the true risk.</Para>
<Para ID="Par90">Third, methodological limitations exist within our model. DSEM assumes linear relationships and fixed time lags, while actual psychological processes might be non-linear or involve heterogeneous delays (e.g., effects manifesting over weeks versus years). Moreover, using annual data precludes capturing short-term dynamics, and excluding potential covariates limits the model's explanatory power.</Para>
<Para ID="Par91">Finally, limited generalizability may exist outside China's unique socio-cultural context (e.g., mental health stigma, collectivist pressures, censorship), potentially limiting direct extrapolation to individualistic cultures. Indeed, measuring these constructs within a collectivist context may require more culturally-attuned instruments to capture unique influencing factors.</Para>
<Para ID="Par92">Despite these limitations, this study holds significant value. Its application of DSEM to large-scale, longitudinal social media data yielded novel population-level insights into the interplay of sleep quality, perceived social support, and suicide risk. Building upon this foundation, future research should aim to utilize more granular data (e.g., monthly) for analyzing finer-grained dynamics; incorporate validated scales as covariates for specific populations; and test the generalizability of these in findings within individualistic cultures, exploring culture's moderating role.</Para>
</Section2>
</Section1>
<Section1 ID="Sec16">
<Heading>5 Conclusion</Heading>
<Para ID="Par93">Using a 14-year provincial Weibo dataset, this study applied DSEM to examine the dynamics of public sleep quality, suicide risk, and perceived social support in China.</Para>
<Para ID="Par94">Our findings revealed a system of complex and reciprocal influences. Specifically, the results revealed that all three variables demonstrated significant temporal continuity. The cross-lagged analysis uncovered several key predictive relationships. As expected, higher prior suicide risk predicted a subsequent decline in sleep quality. However, three findings were contrary to our hypotheses: higher prior suicide risk also predicted a decline in subsequent perceived social support; poorer prior sleep quality predicted a decrease in future suicide risk; and higher prior social support predicted a decline in future sleep quality. At the contemporaneous level, both poor sleep quality and low perceived social support were strongly associated with higher suicide risk within the same year.</Para>
<Para ID="Par95">Taken together, these findings reveal that the relationships among sleep quality, perceived social support, and suicide risk are not static or unidirectional. Rather, they constitute a dynamic system with nuanced, time-dependent feedback mechanisms. This underscores the necessity for public health interventions to move beyond simple, linear models and instead account for these complex interactions to effectively mitigate both present and future suicide risk.</Para>
</Section1>
</Body>

<ArticleBackmatter>
<Ethics>
<Heading>
<Emphasis Type="Bold">Statements and Declarations</Emphasis>
</Heading>
<FormalPara ID="FPar5" RenderingStyle="Style1">
<Heading>Funding</Heading>
<Para ID="Par96">This research was supported by the Major Program of the National Social Science Foundation of China (grant No. 22&#x0026;ZD187).</Para>
</FormalPara>
</Ethics>
<Ethics>
<FormalPara ID="FPar6" RenderingStyle="Style1">
<Heading>Competing interests</Heading>
<Para ID="Par97">The authors declare that they have no conflict of interest.</Para>
</FormalPara>
<FormalPara ID="FPar7" RenderingStyle="Style1">
<Heading>Ethics approval</Heading>
<Para ID="Par98">All procedures performed in this study involving human data were in accordance with the ethical standards of the institutional and/or national research committee and with the 1964 Declaration of Helsinki and its later amendments or comparable ethical standards. Specifically, this study strictly adheres to the principles of the Declaration regarding the protection of research participants' privacy and the confidentiality of their personal information (Article 24). As the research is based on publicly available, anonymized social media data, it did not involve the direct recruitment of human participants. The research protocol was reviewed and approved by the Institutional Review Board of the College of Life Sciences at Central China Normal University (Approval No. CCNU-IRB-202504006b).</Para>
</FormalPara>
<FormalPara ID="FPar8" RenderingStyle="Style1">
<Heading>Consent to participate</Heading>
<Para ID="Par99">Informed consent to participate was not required as this study is based on publicly available, anonymized social media data and does not contain clinical studies or individual patient data.</Para>
</FormalPara>
</Ethics>
<DataAvailability><Annotation ID="8" RuleID="GoldenMetadataIdentified_01" Status="Neutral" /><Heading>Data Availability</Heading><SimplePara>Data sets generated during the current study are available from the corresponding author on reasonable request.</SimplePara></DataAvailability>
<Ethics>
<FormalPara ID="FPar9" RenderingStyle="Style1">
<Heading>Authors' contributions</Heading>
<Para ID="Par100">Binyu Wang and Xiayu Du contributed equally to this work and should be considered as co-first authors.</Para>
<Para ID="Par101">Binyu Wang: Conceptualization, Formal analysis, Software, Writing &#x2013; original draft;</Para>
<Para ID="Par102">Xiayu Du: Conceptualization, Writing &#x2013; review &#x0026; editing;</Para>
<Para ID="Par103">Tingshao Zhu: Data curation;</Para>
<Para ID="Par104">Zongkui Zhou: Supervision;</Para>
<Para ID="Par105">Xingyun Liu: Data Curation, Writing &#x2013; review &#x0026; editing;</Para>
<Para ID="Par106">Zhihong Ren: Supervision, Writing &#x2013; review &#x0026; editing, Funding Acquisition;</Para>
</FormalPara>
</Ethics>
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</ArticleBackmatter><submission-metadata><Submission-Metadata Rules="ArticleTitle Abstract " /><RoleBasedAnnotationDisplay DynamicView="True" /><Submission-Metadata-Present>Yes</Submission-Metadata-Present><Abstract ID="Abs1" Language="EN" OutputMedium="All"><Heading>Abstract</Heading><SectionHeadings><SectionHeading><Paragraphs><Para ID="Par1">Abstract Purpose: Suicide risk and sleep problems are significant public health concerns, with perceived social support acting as a key social determinant of mental health. This study aimed to investigate the dynamic, reciprocal relationships among public sleep quality (SQ), suicide risk (SR), and perceived social support (SS) from a macro-level, epidemiological perspective to understand their systemic interplay over time. Methods: We constructed a provincial-level annual panel dataset using public data from Weibo, a major Chinese social media platform, spanning 14 years (2010&#x2013;2023) across 31 provinces. The annual frequencies of keywords related to SQ, SR, and SS were calculated to serve as population-level indicators. Dynamic Structural Equation Modeling (DSEM) was employed to analyze the autoregressive, cross-lagged, and contemporaneous effects among these variables. Results: All three variables demonstrated significant temporal continuity. Longitudinally, higher prior SR predicted subsequent declines in both SQ and SS. Paradoxically, however, better prior SQ (i.e., lower scores on the measure) predicted higher subsequent SR, while higher prior SS predicted poorer subsequent SQ. Concurrently, poorer SQ and lower SS were associated with higher SR. Conclusions: Utilizing large-scale social media data, this study uncovers the complex feedback loops governing the population-level dynamics of sleep quality, perceived social support, and suicide risk. The findings highlight the necessity of a systemic public health approach for suicide prevention that considers these complex, time-dependent, and sometimes paradoxical interactions, moving beyond simplistic linear risk models. Keywords: Sleep quality; suicide risk; perceived social support; social media; dynamic structural equation model.</Para></Paragraphs></SectionHeading></SectionHeadings></Abstract></submission-metadata>
</Article>