Dynamic Structural Equation Research Articles

Investigation of bi-directional relations between pre-sleep electronic media use and sleep: A seven-day dairy study

The current study aimed to examine the bi-directional relationships between pre-sleep electronic media use and sleep, and to assess the relative predictive strength of different types of electronic media use in the evening on subsequent sleep. Eighty-eight young adults (20.57 ± 0.99, 27 males) completed an online intake survey and received notifications to complete daily diaries for seven consecutive days. Results of dynamic structural equation models (DSEM) revealed that the total screen time, sleep onset time, sleep latency, sleep duration, and sleep quality showed significant positive autoregressive parameters. In contrast, the results revealed no statistically significant cross-lagged associations between the total screen time in the evening and sleep outcomes. Inspection of the predictive strength of various types of screen activities at the within-person level revealed that increased active social media use is linked to delayed sleep onset, while internet browsing is associated with shorter sleep latency. At the between-person level, screen time of T.V. watching, video streaming, social media use, and shopping correlated with delayed sleep onset. Shopping was also connected to longer sleep latency. Additionally, more time spent on T.V., video streaming, non-work internet browsing, and shopping was linked to reduced total sleep duration. These findings indicated a screen activity-dependent association between pre-sleep screen time and subsequent sleep. More objective assessments of electronic media use (e.g., app recording screen time) and sleep (e.g., actigraphy) and longitudinal monitoring over a relatively long period (i.e., several weeks or months) are warred to further elucidate (cross-lagged) relationships between electronic media use and sleep.

Exploring the dynamics of virtual value co-creation in tourism: an analysis of social factors, mindful approach, and technological stress over time

AbstractThis research aims to analyze the relationship between social factors (social comparison orientation, loneliness, emotional support, and instrumental support) and the quadratic effects of the mindful approach and technological stress in co-creating virtual value for the tourism sector. Using a dynamic structural equation model, we analyzed data collected from a cohort of 400 tourists who actively participated in virtual tourism services between 2011 and 2022. Using this methodology, we investigate the long-term correlations between different elements and their impact on participants' participation in virtual value co-creation. Our research indicates a distinct correlation between the mindful approach and virtual value co-creation, exhibiting a positive quadratic effect that gradually decreases, implying the necessity of consistent mindfulness practices in the face of technological stress. Interestingly, we also find that technological stress has a positive quadratic role over time. As people become more adept at technology and accustomed to it, its favorable effects on virtual value co-creation diminish. In the current scenario characterized by collaborative innovation and interaction through digital platforms, they are of great importance for companies, especially in adapting to new social dynamics characterized by new technologies. Using the Mindful Approach in the digital context becomes necessary, emphasizing mainly conscious awareness to optimize the level of commitment, increasing the results of interactions. On the other hand, new technologies in value co-creative processes increase concern about technological stresses, especially in exposure to these new environments over time. In this way, achieving more excellent stability between digital interaction and reducing potential stressors becomes a critical business strategy for sustaining collaboration dynamics over time, thus ensuring individuals’ well-being and maximizing the concretion processes’ positive impact at both the individual and social levels.

The dynamics of L2 teacher boredom and their link to creativity: A ban or boon for boredom

AbstractResearch has revealed a prevalence of boredom among L2 teachers, despite efforts to mitigate this negative emotion. The interplay between teacher boredom and creativity, especially their concurrent development, has not been extensively studied longitudinally. Utilizing control‐value theory as its foundation, this study investigates the daily progression of boredom and creativity among L2 teachers, their mutual development, and how control‐value beliefs influence these dynamics. A 5‐day experience sampling method study involving 98 L2 teachers generated 423 observations. Dynamic structural equation modeling (DSEM) was employed at the individual (Level 1) and group (Level 2) levels. DSEM results revealed varied relationships between boredom and creativity changes over a week, influenced by teachers’ control and value beliefs. In innovators, with high perceived control and intrinsic value beliefs and moderate to high extrinsic value beliefs, previous experiences of boredom might positively influence the teacher's creativity the next day. This creativity might, in turn, decrease the teacher's boredom. This suggests a potential positive relationship between boredom and creativity in innovative language teachers. In adaptors, with moderate perceived control and intrinsic value beliefs and medium to low extrinsic value beliefs, previous experiences of boredom did not necessarily influence the teacher's creativity the next day. However, teacher creativity might still decrease teacher boredom. For traditionalists, with medium perceived control and intrinsic value beliefs and moderate to high extrinsic value beliefs, previous experiences of boredom might have decreased the teacher's creativity the next day, while teacher creativity might have decreased the teacher's boredom the same day. Finally, in dissatisfied teachers with low perceived control, intrinsic value, and extrinsic value beliefs, previous experiences of boredom might have decreased the teacher's creativity the next day, while teacher creativity might not necessarily predict the teacher's boredom. Results suggest a reciprocal relationship between boredom and creativity in adaptable and traditionalist teachers. Additionally, Level 2 analysis identified correlations between random effect parameters across four clusters.

Beyond one-size-fits-all suicide prediction: Studying idiographic associations of risk factors for suicide in a psychiatric sample using ecological momentary assessment

The Interpersonal Psychological Theory of Suicide (IPTS) states that thwarted belongingness (TB), perceived burdensomeness (PB), and hopelessness are risk factors for suicidal ideation. This ecological momentary assessment (EMA) study aimed to (1) demonstrate that there is substantial between-person variability in the association between IPTS predictors and suicidal ideation, (2) identify clusters of patients for which the predictors differently predict suicidal ideation, and (3) examine whether identified clusters are characterized by specific patient characteristics. EMA data were collected ten times per day for six days in 74 psychiatric inpatients and was analyzed with dynamic structural equation modelling. Idiographic associations were obtained and clustered using k-means clustering. We found substantial between-person variability in associations between IPTS predictors and suicidal ideation. Four distinct clusters were identified and different risk factors were relevant for different clusters. In the largest cluster (n = 36), none of the IPTS predictors predicted suicidal ideation. Clusters in which associations between IPTS variables and suicidal ideation were stronger showed higher suicidal ideation, depression, and lower positive affect. These findings suggest that a one-size-fits-all model may not adequately reflect idiosyncratic processes leading to suicidal ideation. A promising avenue might be to use idiographic approaches to personalize prediction and interventions.

Evidence for a vicious socioemotional cycle of negative emotions and interpersonal conflict.

Four samples of adults (Sample 1, N = 145; Sample 2, N = 160; Sample 3, N = 297; Sample 4 = 89 dyads, 178 individuals) completed ecological momentary assessment protocols focused on a variety of interpersonal and emotional experiences. Samples were enriched for aggressive and self-harming behavior (Sample 1), trait hostility (Sample 2), interpersonal problems (Sample 3), and personality disorder features (Sample 4). Using multilevel dynamic structural equation modeling, we investigated how emotions and interpersonal functioning operate over brief timescales in daily life. We found evidence for a vicious socioemotional cycle across all four samples, whereby negative emotions related to interpersonal conflict (i.e., perceptions of and enacting cold, antagonistic, or quarrelsome behavior; components that contribute to the interpersonal situation from the perspective of CIIT) which in turn related to increased negative emotions. Although individuals differed in the strength of this process, it was unrelated to trait negative affectivity. Viewing these results through the lens of CIIT, we discuss multiple intervention points highlighted by these dynamic results whereby the vicious cycle might be changed. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Protocol and preregistration for the CODEC project: measuring, modelling and mechanistically understanding the nature of cognitive variability in early childhood

BackgroundChildren’s cognitive performance fluctuates across multiple timescales. However, fluctuations have often been neglected in favour of research into average cognitive performance, limiting the unique insights into cognitive abilities and development that cognitive variability may afford. Preliminary evidence suggests that greater variability is associated with increased symptoms of neurodevelopmental disorders, and differences in behavioural and neural functioning. The relative dearth of empirical work on variability, historically limited due to a lack of suitable data and quantitative methodology, has left crucial questions unanswered, which the CODEC (COgnitive Dynamics in Early Childhood) study aims to address.MethodThe CODEC cohort is an accelerated 3-year longitudinal study which encompasses 600 7-to-10-year-old children. Each year includes a ‘burst’ week (3 times per day, 5 days per week) of cognitive measurements on five cognitive domains (reasoning, working memory, processing speed, vocabulary, exploration), conducted both in classrooms and at home through experience sampling assessments. We also measure academic outcomes and external factors hypothesised to predict cognitive variability, including sleep, mood, motivation and background noise. A subset of 200 children (CODEC-MRI) are invited for two deep phenotyping sessions (in year 1 and year 3 of the study), including structural and functional magnetic resonance imaging, eye-tracking, parental measurements and questionnaire-based demographic and psychosocial measures. We will quantify developmental differences and changes in variability using Dynamic Structural Equation Modelling, allowing us to simultaneously capture variability and the multilevel structure of trials nested in sessions, days, children and classrooms.DiscussionCODEC’s unique design allows us to measure variability across a range of different cognitive domains, ages, and temporal resolutions. The deep-phenotyping arm allows us to test hypotheses concerning variability, including the role of mind wandering, strategy exploration, mood, sleep, and brain structure. Due to CODEC’s longitudinal nature, we are able to quantify which measures of variability at baseline predict long-term outcomes. In summary, the CODEC study is a unique longitudinal study combining experience sampling, an accelerated longitudinal ‘burst’ design, deep phenotyping, and cutting-edge statistical methodologies to better understand the nature, causes, and consequences of cognitive variability in children.Trial registrationClinicalTrials.gov - NCT06330090

Applying dynamic structural equation modeling (DSEM) to examine the dynamics of students’ affect and learning goal achievement

Affect is a critical factor impacting students’ goal setting and goal achievement in learning. While existing studies have demonstrated the vital role of affect in learning and goal achievement, the day-to-day fluctuations of affect and their impact on learning have rarely been examined. This study explored the dynamic relationships between positive affect (PA), negative affect (NA), and daily learning goal achievement (LGA) in 72 college students ahead of a high-stakes test, analyzing 32 days of survey responses totaling 2111 observations. We employed dynamic structural equation modeling (DSEM) to assess the stability, variability, and potential reciprocal relationships of PA, NA, and LGA. Additionally, we investigated the effects of depression, age, and the number of semesters studied on these variables. Results indicated that PA, NA, and LGA remained stable over the observation period, with no systematic changes or trajectories, yet exhibited significant fluctuations within and between participants. All autoregressive effects for PA, NA, and LGA were significant. Both PA and NA were significantly related to concurrent measures of LGA, although no significant cross-lagged relationships between PA and NA were found. Variability in PA, NA, and LGA was significantly explained by students’ age, number of semesters studied, and level of depressive symptoms. Further findings and implications of the study are discussed.

Connecting the Dots of Creativity and Curiosity: A Weekly Diary Examination Using Dynamic Structural Equation Modeling

ABSTRACTIn the last decade, research on the connection between curiosity and creativity has surged revealing a positive correlation. However, these findings are primarily based on cross‐sectional studies, which do not establish the direction of the relationship between creativity and curiosity. Is curiosity the driving force behind creativity, or does creativity spark curiosity? The present study addresses this question by examining the potential reciprocal associations between creativity and curiosity within‐persons using state‐of‐the‐art methodology and statistics. Self‐reported data were collected on a weekly basis from a sample of Greek entrepreneurs (N = 195, 49% female) over a 10‐week period. We used the dynamic structural equation modeling (DSEM) framework for data analyses. Results supported the positive relationship between creativity and curiosity within and between individuals. At the within‐person level, creativity and curiosity exhibited significant carry‐over effects from 1 week to the next. However, we did not find consistent evidence for cross‐lagged effects, meaning that curiosity and creativity did not directly cause changes in each other within a 1‐week period. We also found significant random effects underscoring the role of curiosity as a catalyst for creativity, particularly when individuals do not have a strong tendency for their creative levels to persist but do have a strong tendency for their curiosity levels to persist. In such cases, curiosity seems to have a more pronounced impact on shaping creative endeavors. We discuss the implications of our findings for theory and practice and suggest directions for future research.

Phase-Transitions in Disgust During Self-Initiated Eating Among Adolescents With Anorexia Nervosa and Related Low-Weight Eating Disorders and Matched Controls.

Understanding the emotional context of feeding behavior may help identify causal mechanisms of food avoidance among individuals with anorexia nervosa. Although predominant food avoidance models assume fear of fat drives feeding behavior, disgust may be more theoretically and proximally relevant to moment-to-moment experiences of feeding. This study, therefore, aimed to examine affect and food avoidance using automated affect analysis from facial response by measuring time-specific transitions in disgust during a laboratory eating paradigm. We hypothesized that phase transitions in disgust would distinguish temporally self-initiated eating from food avoidance. Sixty-three adolescents with anorexia nervosa or another low-weight eating disorder (LWED) and 27 age- and sex-matched controls were recruited as part of a larger study; 45 patients and 22 controls provided data on autonomous eating and facial affect during a laboratory meal. Dynamic structural equation models quantified moment-to-moment relationships between disgust and feeding behavior. Self-initiated eating was associated with greater increases in disgust, but not fear, intensity among those with LWED relative to control participants and greater disgust intensity predicted lower likelihood of self-initiated eating. Phasic transitions in disgust provide moment-to-moment evidence of affective influence on self-initiated eating and lend credibility to the hypothesis that disgust contributes to food avoidance and initiation in individuals with LWED.

Enhancing energy harvesting capability through analysis of flow-induced vibrations in double sprung circular cylinders exposed to turbulent flow: Influence of incidence angle

The current study explores the potential for energy harvesting arising from vortex-induced and wake-induced vibrations of two circular cylinders. These cylinders are elastically mounted and exposed to turbulent flow, allowing them to undergo free oscillations. Their relative orientation, determined by the incidence angle, ranges from zero to ninety degrees. To analyze this phenomenon, we employ a finite volume methodology for computational analysis to calculate the Reynolds-averaged governing equations. Additionally, we use the explicit integration method to solve the structural dynamics equations. Our numerical analysis reveals that the upstream cylinder uniquely demonstrates vortex-induced vibration, while the downstream cylinder experiences wake-induced vibration, especially at lower incidence angles. Interestingly, as the incidence angles increase, the wake-induced vibration in the downstream cylinder diminishes, and its vibration response aligns with that of the upstream cylinder. Furthermore, the power profile of the upstream cylinder corresponds to the progression of displacement amplitude. In contrast, for the downstream cylinder, at lower incidence angles, the maximum power increases with rising reduced velocity. However, at higher angles, the power behavior resembles that of the upstream cylinder. We determine that the optimal incidence angle for maximizing harvested power is θ=30°, resulting in a total root mean square (RMS) of 5.83W. This represents a substantial increase of 548% compared to the combined power of two separate cylinders. The second most effective angle is θ=15°, yielding a total RMS of 4.75W and a 375% increase, while θ=0° occupies the third position, providing a total RMS of 3.53W and a 293% increase.

What does the customer incivility tell me about my worth? A diary study on the short-term effects of customer incivility on self-esteem and job satisfaction

ABSTRACT This study aims to clarify what are the short-term effects of customer incivility on targeted employees’ self-esteem and job satisfaction. We hypothesised that daily customer incivility reported at the end of the previous workday would predict decreases in next-day morning employees’ self-esteem. In turn, lowered self-esteem would be related to lower job satisfaction levels at the end of the same workday. Additionally, we predicted that the link between lowered self-esteem and lowered job satisfaction would be weaker for employees who engaged more in deep acting. To test our hypotheses, we conducted a daily study on 144 customer-contact employees. Participants completed online questionnaires for 31 days reporting their morning self-esteem levels, together with evening customer incivility and job satisfaction levels. The data were analysed using dynamic structural equation models that allow examining intra-person time series trends, on a day-to-day level, while estimating individual differences therein. Consistent with our predictions, the results provided evidence for the short-term detrimental effects of customer incivility on next-day job satisfaction through lowered self-esteem and for the buffering role of deep acting. Service employees could benefit from training aimed at strengthening their self-esteem and skills on how to handle misbehaving customers effectively.

Irregular ANCF model and experimental investigations of the irregular membrane structures with variable cross-section

The membrane spacecraft structures are widely used for deep space exploration and on-orbit operation, but the dynamic responses of them is more complex. To advance the state of membrane structures, in this paper, a new ANCF membrane element is established to model dynamic equations of the membrane structure precisely and efficiently. Firstly, the irregular ANCF membrane element is studied by considering anomalistic boundary and variable cross-section. The mapping relations between the sub-ANCF element and the parent-ANCF element are illuminated by the Jacobian matrix, which makes the strain of each irregular element accurately calculated with the same shape functions. It is helpful to improve the description accuracy of inherent attributes and reduce the element number of dynamic systems. Further, the nonlinear dynamic model for membrane spacecraft system is established by the virtual work principle. Finally, the numerical examples and experiments are analyzed to verify the correctness of the proposed method and discuss the influence of nonlinear geometry and distortion on the dynamic behaviors. The results from the time domain and frequency domain analyses demonstrate that the distinct irregular geometric boundary of the irregular spacecraft can be more accurately modeled using the presented method. However, the difference becomes more pronounced when the distortion is too large. The research outcomes of this paper can provide theoretical guidance for the irregular spacecraft system, which is of great significance and urgently needs to be studied.

Friend Emotional Support and Dynamics of Adolescent Socioemotional Problems.

Emotional support from friends is a crucial source of social support for adolescents, significantly influencing their psychological development. However, previous research has primarily focused on how this support correlates with general levels of socioemotional problems among adolescents, neglecting the significance of daily fluctuations in these problems. The aim of this study was to explore the relationship between friend emotional support and both the average and dynamic indicators of daily emotional and peer problems in adolescents. These dynamic indicators include within-domain dynamics-such as inertia, which reflects the temporal dependence of experiences, and volatility, which indicates within-person variance-and cross-domain dynamics, such as transactional effects, which measure the strength of concurrent or lagged associations between daily emotional and peer problems. Participants were 315 seventh-grade Chinese adolescents (Mage = 13.05 years, SD = 0.77 years; 48.3% girls). Adolescents reported on their friends' emotional support at baseline and then completed measures of daily emotion and peer problems over a 10-day period. Using dynamic structural equation models, the results revealed that higher levels of friend emotional support were associated with fewer daily socioemotional problems. This was evident both in terms of average levels and dynamic aspects, characterized by lower mean levels of daily emotional and peer problems, reduced inertia and volatility of these problems, and a weaker spillover effect from daily emotional issues to peer problems. These findings highlight the significant role of friend-emotional support in mitigating adolescents' daily socioemotional challenges.

A tripartite model of the psychotherapy relationship: Interrelations among its components and their unfolding across sessions.

The tripartite model of the therapy relationship, which includes the working alliance, real relationship, and transference-countertransference configuration, has been a useful way to conceptualize the complexity of the connection between a therapist and a client. However, little research has focused on the interrelationships between these three components over time. This study sought to replicate the findings of Bhatia and Gelso (2018) by examining the between-person relationships among each of the three elements averaged across all sessions. Additionally, we extended earlier work by examining the within-person relationship between the working alliance, the real relationship, and transference-countertransference with themselves as well as with each of the other elements across sessions. Using 5,931 sessions across 142 clients and 36 therapists, we examined time-ordered associations among the cocreated working alliance, cocreated real relationship, and the therapist-rated transference-countertransference configuration using latent variable dynamic structural equation modeling. Results replicated the findings of Bhatia and Gelso (2018), demonstrating that in one session, the working alliance and the real relationship were positively related, and both the working alliance and the real relationship were negatively related to the transference-countertransference configuration. Regarding the interrelations over time, the findings revealed that the working alliance in the previous session had a significant and positive relationship with real relationship in the current session, and the real relationship in the previous session was related to reduced transference-countertransference in the current session. These findings provide support for complex interrelations among the components over time. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Loneliness in the Digital World: protocol for a co-produced ecological momentary assessment study in adolescents

IntroductionLoneliness has been identified as an important public health issue, peaking during adolescence. Previous research has suggested that social interaction is a key factor in loneliness, and positive social interaction...

Emotion regulation difficulties in depression and anxiety: Evidence from the dynamics of strategy use and daily affect

Anxiety and depression are believed to be associated with increased use of maladaptive emotion regulation (ER) strategies and decreased use of adaptive strategies; nonetheless, most work on this topic has been approached using static perspectives on measuring ER, which may overlook the dynamic interplay between ER and emotional experiences. We combined ecological momentary assessment and dynamic structural equation modeling in two independent college-student samples (N1 = 202; N2 = 213) to investigate bidirectional relationships between ER and daily affect. In Study 1, we examined reciprocal associations between negative affect and two ER strategies characterized by repetitive negative thinking (rumination and worry), while in Study 2, we explored reciprocal relationships between both negative and positive affect and two context-dependent and cognitively demanding ER strategies (reappraisal and distraction). We then explored associations of these reciprocal relations with laboratory questionnaires of anxiety and depression. Results indicated both anxiety and depression were associated with greater average negative affect in daily life, greater use of worry, and greater variability in positive affect. However, anxiety was related specifically to difficulties in maintenance of distraction, whereas depression showed unique associations with negative affect inertia, average use of rumination, and difficulties in maintenance of cognitive reappraisal. Findings collectively reveal commonalities and differences in dynamics of ER and daily affect experience related to depression and anxiety. These insights can inform future research into targeted interventions for these negative emotions.

Idiographic bidirectional associations of stressfulness of events and negative affect in daily life as indicators for mental health: An experience sampling study.

Evidence suggests that complex micro-dynamics occurring in daily life underly the development of mental distress. We aimed to (1) study the cross-lagged association between stressful events and negative affect (NA), (2) show that there is substantial between-person variability in idiographic associations and (3) show that idiographic associations are indicative of mental health. Experience sampling study assessing perceived stressfulness of events (PSE) and NA four times per day for 2weeks in a non-clinical convenience sample (N=70, mean age=22.9, 61% female, 69% German). Bivariate vector autoregressive model implemented in dynamic structural equation modelling to model the associations between stressful events and NA and obtain idiographic associations. Stressfulness of events and NA were significantly reciprocally associated. Autocorrelations and cross-lagged associations from PSE to NA showed substantial variability and were significantly related with trait measures of depression, anxiety, well-being, and perceived stress. Contrary to expectations, cross-lagged associations from NA to stressfulness of events were not related to trait mental health. The approach outlined in this article is useful for studying idiographic dynamics in daily life. The findings increase our understanding of micro-dynamics underlying mental health and individual differences in these processes.

Location-scale modeling as an integrative approach to symptom dynamics during psychotherapy: An illustration with depressive symptoms.

Depressive symptom dynamics, including change trajectories and symptom variability, have been related to therapy outcomes. However, such dynamics have often been examined separately and related to outcomes of interest using two-step analyses, which are characterized by several limitations. Here, we show how to overcome these limitations using location-scale models in a dynamic structural equation modeling framework. We introduce location-scale modeling in an accessible manner to pave the way for its use in research integrating within-person dynamics and intervention-related change in psychopathology, and we illustrate this modeling approach in a large-scale internet-based intervention for depression (N = 1,656). Using eight data points sampled across about 8 weeks, we predicted improvement across the intervention (50% symptom reduction) as a function of early change and symptom variability. Early symptom change was associated with a more likely improvement across therapy. Variability of symptoms beyond change trajectories during the intervention was associated with less likely improvement. Location-scale models, and dynamic structural equation modeling more generally, are well suited to modeling how patterns of symptom change during psychotherapy are related to important (e.g., therapy) outcomes. Our illustrative application of location-scale modeling showed that symptom variability was associated with less overall improvement in depressive symptoms. However, this finding requires replication with more intensive sampling of symptoms before final conclusions can be drawn on when and how to distinguish maladaptive from adaptive variability during psychotherapy. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

A Daily Diary Study of the Reciprocal Relation between Parental Psychological Aggression and Adolescent Anxiety in China.

The daily reciprocal relations between parental psychological aggression and adolescent anxiety and the heterogeneity, i.e., whether these relations vary across different adolescents, remain unclear. This study examined this issue with a 15-day daily diary study among 326 Chinese adolescents (Mage = 14.53 years, SD = 0.60, 47.2% girls). Dynamic structural equation models revealed that parental psychological aggression co-fluctuated with adolescent anxiety within a day. For lagged associations, only father-driven effects were supported but not mother-driven effects, whereas child-driven effects were supported for both parents. These within-person associations were heterogeneous across adolescents. Moreover, adolescents with more parental psychological aggression reported higher anxiety. This study revealed the reciprocal relations between parental psychological aggression and adolescent anxiety at the micro timescale and also highlighted that the within-person associations were heterogeneous across different adolescents.

Time-frequency analysis of nonlinear structures under nonstationary excitation by directly solving structural dynamic equation through absolute displacement

The time-frequency evolution of seismic ground motion energy under strong earthquakes, which can be described by the evolutionary power spectral density (EPSD) matrix, will amplify the most unfavorable responses of members in nonlinear structural systems. However, the existing general finite element software fails to reduce the dimension of the EPSD matrix and then decouple time from frequency in frequency domain analysis. This failure greatly limits the simulation and calculation of multi-dimensional nonlinear structures with multiple degrees of freedom by the stochastic vibration theory. In this study, the pseudo excitation method (PEM), which can direct solve structural dynamic equations using absolute displacement, is used to derive the self-spectral and cross-spectral densities of seismic ground motions in one-dimensional and multi-dimensional cases. In MATLAB, the EPSD matrix is transformed into a four-dimensional uniform modulation excitation matrix independent of the time variable. Nonlinear iteration is conducted and the precise integration method (PIM) is employed through a transient analysis module. Furthermore, a simple one-dimensional example is presented to verify the correctness of the proposed algorithm herein. Finally, as an example, we select important parameters of the coherence model at different supports of a half-through three-span concrete-filled steel tubular (CFST) tied-arch bridge in view of real engineering conditions, and calculate the time-varying power spectrum and variance of the responses of arch ribs, arch feet and the bridge deck system. The results show that the theoretical derivation and the algorithm constructed in this paper can simulate the time-delay effect of the nonlinear structural system. This proves the feasibility of general finite element software in solving and analyzing random responses to multi-dimensional and multi-support non-stationary excitation of nonlinear structures.