Stress perception and the developmental trajectory of smart phone addiction among college students:Based on Parallel Latent Variable Growth Modeling

doi:10.21203/rs.3.rs-4810610/v1

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Research Article

Stress perception and the developmental trajectory of smart phone addiction among college students:Based on Parallel Latent Variable Growth Modeling

https://doi.org/10.21203/rs.3.rs-4810610/v1

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Purpose In recent years, the problem of smart phone addiction among college students has become increasingly serious, which has aroused the attention of colleges and universities at home and abroad. Based on the general stress theory, this study explores the development of stress perception and smart phone addiction among college students over a semester, while further exploring the causal relationship between the two.

Methods A longitudinal study was conducted utilizing a physical education classroom to administer questionnaires on students' stress perception and smart phone addiction levels. The test was administered three times at the beginning, middle, and end of the semester, resulting in 517 valid participants. Data were processed using SPSS and Mplus to explore trends in their stress perception and smart phone addiction using potential growth modeling, as well as causal relationships between the aforementioned variables using cross-lagged modeling.

Results (1) The levels of college students' stress perception and smart phone addiction showed a linear trend of weakening over time; (2)There is a significant positive effect of the intercept of college student stress on the intercept of smart phone addiction and a significant negative effect on the slope of smart phone addiction;(3)The intercept of smart phone addiction among college students has a significant negative impact on the slope of stress perception;(4)The slope of smart phone addiction among college students has a significant positive impact on the slope of stress perception;(5) college students' stress perception and smart phone addiction were causally related to each other.

Conclusion This study reveals the developmental trajectories of stress perception and smart phone addiction among college students over the course of a semester, and explores the causal relationship between the two. These findings may provide insight into how stress perception affects smart phone addictive behaviors, and provide a scientific basis for the development of effective preventive and intervention measures.

Stress perception

smart phone addiction

Longitudinal research

As China enters the Post COVID-19 era, the popularity of information technology and online education is increasing. As an important information technology carrier, smart phone plays an increasingly important role in people's daily life, which greatly facilitates people's online communication, shopping, entertainment, learning and other diversified activities. However, more and more people are facing difficulties in getting rid of their dependence on smart phone. This phenomenon has caused widespread concern in society^[^]. Smart phone addiction is an addictive behavior in which an individual uses a smart phone uncontrollably^[^],thus causing a series of physiological, psychological and social problems with symptoms such as withdrawal and tolerance^[^]. Compared to adults, teenagers are more likely to have smart phone addiction problems^[^]. According to relevant statistics, the smart phone addiction rate of Chinese college students has reached 36.6% in 2022^[^]. Numerous studies have shown that smart phone addiction may lead to physical symptoms such as visual fatigue, hearing loss, arm numbness, wrist swelling, cervical spine pain, etc, which in turn affects academic performance and quality of life^[^]. It can also negatively affect mental health by causing anxiety^[^] and depression^[,^], which in turn affects the quality of sleep^[,^], and in more serious cases, it can lead to a decrease in life satisfaction^[^] and even suicidal tendencies^[^]. Due to its high incidence, rapid growth rate and serious consequences, smart phone addiction has become an important public health problem worldwide^[^]. As the future pillars of society, the health status of college students directly affects the sustainable development of society. Therefore, it is necessary to examine in depth the internal mechanism of smart phone addiction among college students so as to promote the development of protective interventions.

To foster a profound comprehension of smart phone addiction, aiming for its effective prevention and management, we delved into the extant literature. Our exploration revealed a tight correlation between smart phone addiction and inward-facing challenges such as the burdensome weight of information overload^[^], cognitive-behavioral deficits^[^], and stress perception ^[^]. These factors not only compound the problem of smart phone addiction but also necessitate a multifaceted approach to its mitigation.Among the myriad of intricately intertwined risk factors contributing to smart phone addiction, stress perception stands out as a pivotal concern that has garnered considerable attention^[^]. Stress perception, essentially a psychological reaction to stress, originates from an individual's cognitive evaluation of stressful situations, manifesting itself in an array of physical tensions, psychological unease, and discomforts^[^]. Adhering to the overarching framework of general strain theory, it is evident that problematic behaviors often stem from negative experiences stemming from diverse strains and stresses^[^].Initially devised to interpret criminal conduct, general strain theory has since evolved to offer profound insights into addictive behaviors^[,^].With the profound changes in the environment surrounding university students, including changes in teaching methods, diversification of fields of knowledge, and the complexity of interpersonal interactions, coupled with the intensification of the job market, the challenges and pressures they face have greatly increased^[^].These pressures are intricately intertwined with problematic behaviors exhibited by students^[^], a notable example being smart phone addiction. A substantial number of investigations have concurred that there exists a robust correlation between stress perception and the proclivity towards smart phone addiction^[,^]. The present study has shed initial light on the intricate nexus between stress perception and smart phone addiction among university students[].However, the results of existing studies on the mutual predictive relationship between the two are inconsistent and even divergent. This disagreement is reflected not only in the perception of the strength of the relationship, but also in the directional judgment of the relationship. Some scholars believe that stress is a strong predictor of smart phone addiction^[^], and that when college students face stress, they will cope with it by becoming addicted to smart phones^[^], the more stress they perceive, the more serious smart phone addiction will be for college students with poor self-control^[^]. On the other hand, another viewpoint is that smart phone addiction will bring stress to college students^[^], and even the excessive use of smart phones that does not reach the addictive state will make college students experience more stress^[^]. Therefore, it is necessary for us to explore further in order to understand the relationship between the two more accurately. Most of the existing studies have adopted a cross-sectional research design. Although this research method can reveal the relationship between the variables to a certain extent, there are major limitations in exploring the mutual predictive relationship between the variables^[^]. For this reason, the present study will use cross-lagged analysis in order to explore in depth the mutual predictive relationship between stress perception and smart phone addiction among college students.

Furthermore, cross-sectional studies usually only observe variable relationships at a particular point in time and fail to reveal trends in these relationships over time. Current research also lacks an exploration of the dynamic trajectory of stress perception and smart phone addiction among college students. Over time, college students' stress perceptions and smart phone addiction tendencies may change, and such changes may be influenced by a variety of factors. Therefore, we need to adopt a more rigorous research design to more accurately explore the dynamic relationship between college students' stress perception and smart phone addiction tendency. The Latent Growth Mixed Model (LGMM), an extension of the latent growth model within the structural equation framework, seems to be an appropriate approach to study changes in specific variables over time^[^]. For this reason, this model will be used in this study to delve into the trends of college students' stress perception and smart phone addiction over time.

In summary, in view of the above literature finding and summarizing, referring to the linear trend and significant level of college students' stress perception and smart phone addiction at the baseline level in previous studies, we consider to reduce the time span research to avoid the loss of subjects and the difficulty of shielding the system^[^]. In this study, we attempted to take a longitudinal tracking study three times a year for six months, and analyzed it with the help of Spss24.0 and Mplus7.0 software, using the unconditional growth model of latent variables, the parallel growth model, and the cross-lagged regression model, to explore the developmental trajectory of the stress perception and smart phone addiction of college students and the relationship of causation and mutual causation. Based on the above literature combing, the following hypotheses are proposed:

Hypothesis 1

The level of stress perception among college students showed a linear decay trend over time;

Hypothesis 2

The level of smart phone addiction among college students showed a linearly weakening trend over time;

Hypothesis 3

The initial level of stress perception among college students positively predicts the initial level of smart phone addiction;

Hypothesis 4

Developmental changes in stress perception among college students positively predicted developmental changes in smart phone addiction;

Hypothesis 5

Initial levels of stress perception among college students negatively predict developmental changes in smart phone addiction;

Hypothesis 6

Initial levels of smart phone addiction in college students negatively predict developmental changes in stress perception;

Hypothesis 7

College students' smart phone addiction and stress perception are causally related to each other.

Participants

Based on the principle of stratified whole group sampling, a total of 600 people from two colleges and universities were selected in Province H, for example. Meanwhile, considering that the physical activity of college students has a certain concentration and continuity during the school period, an eight-week, two-stage tracking survey was conducted in one semester. The first survey Time1(T1) was conducted in March 2024, and a total of 600 questionnaires were collected, with the following characteristics: "missing data on the duration or frequency of physical activity of any intensity", "regularity of filling in the answer", "response rate The criteria for invalid data were "missing data on the duration or frequency of physical activity of any intensity", "regularity of responses", "response rate lower than 3/4", and "omission of questionnaire code (school number)". The second survey (Time2) was conducted in May 2024, and 570 questionnaires were collected, and the third survey (Time3) was conducted in July 2024, and 530 questionnaires were collected. 517 valid questionnaires were retained from the three surveys, using the same screening and inclusion basis as the second survey (T2). The final data were collected from all 517 participants who completed both surveys, of which the average age of the subjects was 18.86 years old, 186 were male and 331 were female; 355 were freshmen and 162 were sophomores; 203 were only children and 314 were non-only children; 246 were from rural areas and 271 were from urban areas. All of these participants attended two large public universities in central China. These students were recruited during compulsory physical education at the beginning of the fall semester. Moreover, there were no significant differences (p > 0.05) between the attrition sample and the active sample in terms of gender, grade level, stress perception score, and smart phone addiction score, and the students were not motivated to participate directly in this study prior to their participation. In order to control for socially desirable responses, the researcher encouraged students to answer the questions as truthfully as possible. The participant defendants ensured that they could withdraw from the study at any time and that their decision would not affect their grades. Permission for this study was obtained from the university's Institutional Review Board and the leadership of the host athletic school, and participant consent was obtained prior to the study. Data were collected through questionnaires distributed in offline classes.

For sample size calculations, we used G Power 3.1.9.4 software, in which the parameters to be precisely set covered effect sizes, alpha-type error, test power 1-β, number of groups, number of measurements, intra-group correlation coefficients, and non-spherical correlation. Specifically, for the ANOVA, we set the small, medium, and large effect sizes to 0.1, 0.25, and 0.4^[^], respectively; the alpha error rate was set to 0.05^[^], and the statistical test power 1-β was set to 0.8; the number of groups was determined to be 2, and the number of measurements was 3. Since no pre-study was conducted, we assumed that the intra-group correlation coefficient was 0; the non-spherical correlation was taken as the system default value of 1. Keeping the other parameters constant, we conducted sample size calculations for effect sizes of 0.1, 0.25, and 0.4, which yielded the results of 264, 44, and 20, respectively.However, considering the possibility of subject drift during the actual survey and invalid questionnaires, we assumed an invalid response rate of 15%. Based on this assumption, the number of questionnaires to be distributed to ensure that all the set effect size conditions are met should be 274/(1-0.15) = 322.

Measuring Tools

Stress perception

Stress perception was measured using the Chinese version of the Stress Perception Scale developed by Li Yajie et al^[]. It assess 3 types of stressful situations, namely, daily chores, major events, and changes in stressors. The CPSS consists of 14 items, which 4, 5, 6, 7, 9, 10, and 13 are reverse scored on a 5-point scale from 1 (never) to 5 (a lot), with the total score ranging from 0 to 56, with higher scores indicating higher levels of stress perception.Cronbach's alpha coefficient is 0.878, which indicates a higher reliability.

Smart phone addiction

The short version of the smart phone Addiction Scale (SAS), which consists of 10 items from the SAS that are most closely related to smart phone addiction, was adopted by Xiang Mingqiang et al^[^]. through the expert rating method. The scale has 6 levels of scoring, one dimension, and the scores are "not at all consistent", "mostly not consistent", "somewhat not consistent", " somewhat meets somewhat does not meet," "somewhat meets," and "mostly meets." Students are first asked, "Is there a lack of study programs due to smart phone use?" The Cronbach's alpha coefficients of the questionnaires for the two time periods were 0.848 and 0.871, respectively, showing high reliability.

Statistical analysis

In this study, we used the latest versions of statistical software SPSS 27.0 and Mplus 7.0 for in-depth analysis and processing of the data collected from the questionnaire. These software tools provide us with powerful functions to accomplish various complex statistical analysis tasks. First, we performed a descriptive analysis of the collected data. Through this analysis, we obtained statistical indicators such as the mean, standard deviation, maximum and minimum values of each variable, so as to have a comprehensive understanding of the results of the questionnaire survey. Subsequently, with the help of spearman's correlation coefficient matrix analysis, to determine the degree of significant correlation between stress perception and smart phone addiction on the three time periods (T1, T2, T3). Further, a latent variable growth model LGM of the two variables was developed to observe the trend of the unconditional latent growth model, the trajectory trend of the two during parallel growth, and the causal predictive relationship. Finally, the causal relationship between stress perception and smart phone addiction was further determined by performing a cross-lagged test with three times of data. And model fitting parameter estimation is mainly carried out by drawing on the method of great likelihood MLR^[^].

1. The common method bias

Procedural control method and Harman's one-way test^[^] were used to examine the issue of possible common methodological bias between the two administrations. The procedure-controlled method was chosen from measurement tools that have been used many times by scholars in China and have been proven to have high reliability and validity. When designing the questionnaire, the guiding words were emphasized, bolded, and labeled with the purpose of the survey and the way of confidentiality. Harman's one-way test was used to collect data by filling out the questionnaires online and submitting them as soon as they were answered, and one-way unrotated exploratory factor analysis was conducted on all questions of the two administrations, except demographic variables, and the root factors of T1 and T2 were all extracted from the 5 characteristic root factors of more than 1, and the root factors of T3 had 6 characteristic root factors of more than 1, with the variation rates of the first factor being 31.509% (T1), 28.733% ( T2) and 29.292% (T3), which are all much less than 40%. According to the common method bias^[^].The common method bias of the three administrations was confirmed to be acceptable.

2. Measurement invariance

Table 1

Fit statistics for longitudinal confirmatory factor analysis of smart phone addiction.
Model	X2	DF	CFI	RMSEA90%CI	ΔCFI	ΔRMSEA	BIC
Configural	1669.984	372	0.816	0.082(0.0780.086)			49883.012
Metric	1777.290	390	0.803	0.083(0.0790.087)	-0.013	0.001	49877.852
Scalar	1959.159	430	0.793	0.083(0.0790.087)	-0.010	0.000	49809.800

For the sample data used in this study, we first conducted a test of measurement invariance (Table 1). This test we performed measurement invariance on the short version of the smart phone Addiction Scale to ensure that the observed changes over time were related to real changes and not to structural inequalities over time. We assessed measurement invariance at both time points by means of a morphological equivalence model (constraints on equal factor structure), a unit equivalence model (constraints on equal factor loadings), and a scale equivalence model (constraints on equal observation intercepts). Comparisons between the models showed ΔCFI ≤ 0.01 and ΔRMSEA ≤ 0.015, indicating that the scales had measurement invariance over time^[^].

3.Descriptive analysis

Table 2

Statistics of Pearson Correlation Coefficient
Variable	M	SD	1	2	3	4	5	6	7	8
1.gender	1.64	0.480	1
2.Age	18.86	0.860	0.354^**	1
3.T1SP	2.926	0.649	0.035	-0.064	1
4.T2SP	2.932	0.522	0.030	0.016	0.384^**	1
5.T3SP	2.854	0.501	-0.013	-0.009	0.126^**	0.206^**	1
6.T1SMA	3.475	0.960	0.101^*	0.035	0.506^**	0.303^**	0.134^**	1
7.T2SMA	3.502	0.967	0.073	0.008	0.271^**	0.516^**	0.205^**	0.439^**	1
8.T3SMA	3.354	0.985	0.030	-0.018	0.143^**	0.200^**	0.520^**	0.242^**	0.204^**	1

Note: T1 = Time1, T2 = Time2, T3 = Time3,SP = stress perception, SMA = smart phone addiction,**p < 0.01, *p < 0.05,.

Further, we examined the relationship between smart phone addiction and stress perception at different time points. From the results of descriptive statistics and correlation analysis, the results are shown in Table 2. First, the effects of gender and age on smart phone addiction (SMA) and stress perception (SP) were not significant. This means that students in our sample faced similar smart phone addiction and stress perception problems regardless of gender and age. By calculating the Pearson correlation coefficient, we obtained the correlation between the variables. In the correlation analysis, we found that there was a significant positive correlation between smart phone addiction and stress perception at different time points. Specifically, there was a strong positive correlation between smart phone addiction (T1SMA) at T1 time and stress perception (T1SP) at T1 time (r = 0.506**, p < 0.01), while smart phone addiction (T2SMA) at T2 time and stress perception (T2SP) at T2 time also showed a significant positive correlation (r = 0.516**, p < 0.01), and smart phone addiction at T3 (T3SMA) also showed a significant positive correlation with stress perception at T3 (T3SP) (r = 0.520**, p < 0.01), and furthermore, we observed a certain continuity between smart phone addiction and stress perception across time. Specifically, there was a positive correlation between T1SMA and T2SMA and T3SMA (r = 0.303**, 0.516**, 0.200**, p < 0.01), and similarly between T1SP and T2SP and T3SP (r = 0.384**, 0.126**, 0.500**, p < 0.01).

4. developmental trajectories of smart phone addiction and stress perception among college students

4.1 unconditional linear latent variable growth model of stress perception

As shown in Fig. 1, the unconditional linear latent variable growth model of college students' stress perception was constructed, and the unconditional linear latent variable growth model only required the estimation of intercept (α) and slope (β), where the intercept represented the starting level of stress perception trend and all factor loadings were fixed at 1.0. The intercept represents the starting level of the stress perception trend, with all factor loadings fixed at 1.0, and the slope represents the rate of change in the stress perception trend, with factor loadings set at 1.0, 2.0, and 3.0. The equation for the first level of the horizontal model is: Y = \alpha + \beta \ Time + \xi), where Y is the observed value of stress perception, and (\alpha) is the intercept, which represents the initial level of pressure perception. (\beta) is the slope, indicating the rate of change in pressure perception. (Time) is the time variable. (\xi) is the residual term, which represents the influences other than the intercept and slope. Examine the trend of overall pressure perception. The fitting index X2/df = 4.31, P < 0.01, CFI = 0.977, TLI = 0.932, RMSEA = 0.080, SRMR = 0.027, the overall fitting index of the model is up to the standard, and the parameters of the model are shown in Table 3. The initial level of college students' smart phone addiction in the linear unconditional growth model is 3.490, and the trend of college students' stress perception is declining. This result is consistent with hypothesis 1. The correlation coefficients of the final intercept and slope were significant (r=-0.-177, P < 0.001), i.e., the group with a high initial level of college students' stress perception, the slower the rise of stress perception in the subsequent three observations.

Note: SP = stress perception,** P < 0.01, * P < 0.05

4.2 unconditional linear latent variable growth model of smart phone addiction

As shown in Fig. 2, an unconditional linear latent variable growth model of smart phone addiction among college students was constructed to test the trend of overall smart phone addiction. The fitting index X2/df = 3.11, P < 0.01, CFI = 0.980, TLI = 0.939, RMSEA = 0.064, SRMR = 0.022, the overall fitting index of the model is up to the standard, and the parameters of the model are shown in Table 3. The initial level of college students' smart phone addiction in the linear unconditional growth model is 2.941, and the college students' smart phone addiction is in a downward trend. This result is consistent with hypothesis 2. The correlation coefficients of the final intercept and slope were significant (r=-0.-177, P < 0.001), i.e., the group with a high initial level of college students' smart phone addiction, the slower the rise of smart phone addiction was in the subsequent three observations.

Note: SMA = smart phone addiction,** P < 0.01, * P < 0.05

Table 3

Unconditional potential growth model fit indices with intercepts and slopes for the main study variables
	X²	df	CFI	TLI	RMSEA	SRMR	mean		oblique related
	X²	df	CFI	TLI	RMSEA	SRMR	slope intercept		oblique related
SP	4.31	1	0.977	0.932	0.080	0.027	3.490**	-0.049	-0.177**
SMA	3.11	1	0.980	0.939	0.064	0.022	2.941**	-0.036**	-0.088**

Note:SP = stress perception, SMA = smart phone addiction

4.3 Parallel Growth Model of Stress Perception and College Students' smart phone Addiction

In order to further explore the association between stress perception and smart phone addiction, an attempt was made to construct a parallel growth model while simultaneously examining the overall profile of the slope and intercept term of the two variables over time. The intercept term and slope of college students' stress perception were used to predict the linear growth trend of smart phone addiction, and the results are shown in Fig. 3. In the latent variable parallel growth model of college students' stress perception refining and smart phone addiction, the intercept regression coefficient of college students' stress perception intercept on college students' smart phone addiction was significant, β = 0.309, P < 0.001, indicating that the higher the initial level of college students' stress perception, the higher the initial level of college students' smart phone addiction, which was in line with the result of the research hypothesis 3. It was also found that the intercept of college students' stress perception negatively predicted the slope of college students' smart phone addiction, β=-0.234, P < 0.001, indicating that the lower the initial level of college students' stress perception, the faster the college students' smart phone addiction developed in subsequent time, and the results were consistent with research hypothesis 4. It was also found that the slope of college students' stress perception positively predicted the slope of college students' smart phone addiction, β = 0.061, P < 0.001, indicating that with the fluctuation of time, college students' stress perception decayed, and the rate of growth of smart phone addiction slowed down, and the results were consistent with research hypothesis 5. Finally the initial level of college students' smart phone addiction also negatively predicted the rate of stress perception development, β=-0.550, P < 0.001, indicating that the lower the level of smart phone addiction, the faster the subsequent stress growth.

Note:SP = stress perception, SMA = smart phone addiction,** P < 0.01, * P < 0.05

5. Cross-lagged test of stress perception and college students' smart phone addiction

The latent variable model can further observe the dynamic trajectory of the variables. In order to further clarify the sequential causal relationship between college students' stress perception and smart phone addiction over time, and to broaden the intrinsic mechanism between the two variables, based on Martens and Haase's proposal^[^]. Three instances of longitudinal data were selected to conduct cross-lagged regression analyses of stress perception and smart phone addiction among college students. Because it was a saturated model, there was no need to report the fit indices. The output of the saturated model is shown in Table 4, the autoregressive pathways of stress perception T1→T2 (β = 0.408, SE = 0.050, P < 0.001), T2→T3 ( β = 0.074, SE = 0.053,P > 0.05) and T1→T3 (β = 0.172, SE = 0.049, P < 0.01) except for T2→T3 were all statistical significance. The autoregressive pathways of smart phone addiction T1→T2(β = 0.249, SE = 0.040, P < 0.001), T2→T3(β = 0.116, SE = 0.056,P < 0.05) and T1→T3(β = 0.036, SE = 0.031, P > 0.05) were statistically significant. 0.031, P > 0.05) were statistically significant except for the autoregressive pathway of T1→T3. This indicates that smart phone addiction in T1 affects smart phone addiction in T2, and smart phone addiction in T2 affects smart phone addiction in T3, but smart phone addiction in T1 does not affect smart phone addiction in T3; the cross-lagged pathways from stress perception to the tendency of smart phone addiction in T1→T2 (β = 0.080, SE = 0.027, P < 0.01) and T2→T3 (β = 0.067, SE = 0.067, P < 0.05) were statistically significant. 0.067, SE = 0.026, P < 0.01) were statistically significant, suggesting that stress perception in the previous measurement positively predicted smart phone addiction in the later measurement; whereas in the cross-lagged path from smart phone addiction to stress perception, T1→T2 (β = 0.099, SE = 0.071, P > 0.05), this pathway was not statistically significance, indicating that smart phone addiction in the first measurement could not predict stress perception in the second measurement; however, since the path of T2→T3 (β = 0.210, SE = 0.100, P < 0.05) held, this implied that smart phone addiction in the second measurement could predict stress perception in the third measurement see Fig. 4.

Table 4

Results of cross-lagged analysis of stress perception and smart phone addiction tendency
Path	β	SE	P
T1SP→T2SP	0.408	0.050	0.000
T1SMA→T2SP	0.099	0.071	0.165
T1SP→T2SMA	0.080	0.027	0.003
T1SMA→T2SMA	0.249	0.040	0.000
T2SP→T3SP	0.074	0.053	0.160
T2SMA→T3SP	0.210	0.100	0.037
T1SP→T3SP	0.172	0.049	0.000
T2SP→T3SMA	0.070	0.026	0.008
T2SMA→T3SMA	0.116	0.056	0.038
T1SMA→T3SMA	0.036	0.031	0.250
T1SP↔T1SMA	0.315	0.035	0.000
T2SP↔T2SMA	0.185	0.023	0.000
T3SP↔T3SMA	0.226	0.030	0.000

Note: T1 = Time1, T2 = Time2, T3 = Time3,SP = stress perception, SMA = smart phone addiction

Note:SP = stress perception, SMA = smart phone addiction,** P < 0.01, * P < 0.05

1. Developmental trajectories of stress perception and smart phone addiction among college students and their dynamic relationship

1.1 Trends in the development of stress perception profiles among college students

The purpose of this research study is intended to investigate the developmental trajectory of college students' stress perception, and the results of the study indicate that college students' stress perception shows a downward trend over time. From the model parameters, the slope is non-significantly negative, indicating that the level of college students' stress perception tends to decline during the test period, but this trend is not significant. This result verifies hypothesis 1. This is consistent with the results of previous studies^[^]. Stress coping theory^[^] suggests that individuals adopt a series of psychological and behavioral responses to adapt to stress when facing stress. These responses involve emotional regulation, thought pattern adjustment, and behavioral changes. According to the theory, stress coping strategies can be categorized into positive coping strategies, avoidance coping strategies and compromise coping strategies^[^]. During a semester, college students will constantly encounter various stressors, such as exams, assignments, and relationships. Over time, they will adopt some appropriate ways or means to deal with and cope with the frustrating events and frustrating situations they face under the synergistic effect of internal regulation and external resources^[^], and learn to cope more effectively, thereby reducing stress perceptions As the semester progresses, the college student population tends to experience significant shifts in personal growth and mindset. During this process, they tend to be more rational in their evaluation of stimuli, less likely to perceive such events as a source of stress, and more confident in their ability to deal with situations successfully^[^].

1.2 Trends of smart phone addiction among college students

This study found that smart phone addiction among college students shows a downward trend over time. According to the model parameters, the slope is significantly negative, indicating that the level of smart phone addiction among college students shows a significant downward trend during the test period. This is consistent with previous research^[^]and validates hypothesis 2. According to self-control theory^[^], individuals demonstrate superior self-regulation to ensure that their behavior is highly consistent with their personal value system and social expectations. This ability demonstrates its importance in a variety of contexts, including, but not limited to, suppressing impulses, resisting temptation, delaying gratification of immediate needs, and adopting appropriate behaviors based on social contexts. As college students become more mentally mature, they tend to strengthen their self-management and self-restraint ^[^], especially in the control of smart phone use time. Given that the subjects of this study are schools with relatively high standards in central China, these students generally have a high degree of purposefulness and self-control, so they are more inclined to take exams as their primary goal during critical periods such as midterms and finals, and thus take the initiative to reduce smart phone use.

In addition, this study also found that the initial level (intercept) of smart phone addiction among college students was significantly negatively correlated with the late growth rate (slope) (β = -0.088, P < 0.001), which further indicates that the rate of late weakening will be slower in the group of college students with higher levels of smart phone addiction, and vice versa in the group with lower initial levels. This may be due to the fact that with the improvement of health awareness, college students gradually begin to realize the adverse effects of excessive use of smart phones on physical and mental health^[^], such as vision loss, reduced sleep quality^[^], and so on. As a result, they may take the initiative to reduce their smart phone usage time to maintain their health. Meanwhile, we also found those groups with lower initial levels of smart phone addiction. These groups may have greater self-control and rational thinking^[^], and they are able to better manage their time and the way they use their smart phones. When they find themselves overly dependent on their smart phones, they may be more likely to take proactive steps to reduce their use, which could lead to a faster attenuation of the addictive state.

1.3 The influence of college students' stress perception on the developmental changes of smart phone addiction

This study also found that the initial level of stress perception among college students positively predicted the initial level of smart phone addiction, which validated Hypothesis 3. This implies that students with high initial stress perception would have deep smart phone addiction, which is consistent with previous cross-sectional studies^[,^]At the university level, students are generally challenged by environmental adaptation, academic pressure, interpersonal interactions, romantic relationships, and family responsibilities ^[^]. Based on coping theory^[^], individuals may adopt coping strategies such as seeking help or escaping when facing these pressures. In this process, smart phones, as an important tool, can effectively assist individuals in implementing these strategies. At the same time, the satisfaction that an individual obtains from the use of the medium will further increase his or her frequency of using the medium. Therefore, when individuals face stress and seek coping strategies, the convenience of the smart phone will motivate them to increase their use of the smart phone.

In addition to this the present study also found that college students' stress-only perception trends positively predicted changes in the development of smart phone addiction only, which verified hypothesis 4. In short, the faster the rate of decline in college students' stress perceptions, the faster the rate of decline in their smart phone addiction. This may be due to the fact that may be they gradually adapted to a new study environment, lifestyle or successfully coped with certain stressors and found healthier ways to cope with stress, such as exercise, social activities or participation in interest groups. These positive changes may help to reduce their smart phone usage time, which in turn reduces the risk of smart phone addiction.

Finally this study found that the initial level of stress perception among college students negatively affects the rate of developmental shaping of smart phone addiction, which validates hypothesis 5. This means that college students who are in a high stressful time at the beginning of the semester, this may be because the smart phone has become a tool for escapism. In a high-pressure environment, college students may feel anxious and helpless, and smart phones provide a relatively safe and controlled haven. They may divert their attention by browsing social media, playing games, watching videos, etc. to temporarily forget the reality of their worries. While this escapist behavior briefly relieves stress, this slows down the rate of decline in the level of smart phone addiction.

And the initial level of smart phone addiction among college students likewise negatively affects the rate of development of stress perception. This also verified hypothesis 6. Similarly, college students who were at a high level of smart phone addiction at the beginning of the semester had a low rate of decline in their stress perception. This may be due to the fact that over-addiction to smart phones can take up a lot of time and energy of college students, resulting in their inability to effectively cope with the stress in their lives. At the same time, the social and entertainment functions in smart phones may allow college students to temporarily escape from real-life stress, but this escape is only temporary and cannot really solve the problem; instead, it may worsen the stress problem.

2. The mutual predictive relationship between stress perception and smart phone addiction among college students

By constructing a cross-lagged regression model, this study found that stress perception positively predicted college students' smart phone addiction in all three measurements, and smart phone addiction in the second time positively predicted stress perception in the third time, which verified hypothesis 7. This is not consistent with the results of previous studies^[^]. The inconsistency with the study of Wang Yake. may be due to the fact that the female students in their study accounted for 85% of the total sample size. And cell phone addiction has a significant difference in gender ^[^].The results of this study indicate that the higher the stress perception, the higher their future smart phone addiction, and the general stress theory suggests that stress increases the likelihood of an individual's negative emotions, which in turn trigger undesirable behaviors, which in turn are a way of relieving stress ^[^], based on the fact that stress is the main influencing factor of smart phone addiction. The stronger the individual's perception of stress, the greater the likelihood of cell phone addiction ^[^]. Therefore, college students will involuntarily develop the undesirable behavior of cell phone addiction when facing stress. On the other hand, we found that college students' level of smart phone addiction at the beginning of the semester did not significantly predict their perception of stress in the middle of the semester. It is worth noting that the beginning of the semester tends to be a relatively relaxing time for college students. At this stage, they have just returned to campus from vacation and have not yet faced the pressure of heavy coursework. Compared with the intense preparation for exams at the end of the semester, they have more free time and leisure to organize their lives at this time. In view of this, they may be inclined to spend more time on campus activities such as ball games and excursions with their roommates and peers in order to fully enjoy the pleasures of campus life. This change in lifestyle will undoubtedly have a significant impact on smart phone usage habits. In a relaxed and energetic atmosphere, college students may become less reliant on their phones, reduce their aimless browsing and screen time, and engage in more authentic and interesting social and recreational activities. Such behavioral patterns naturally help to reduce smart phone addiction to some extent. Over time, however, mid-semester cell phone addiction then significantly predicted end-of-semester stress perceptions, possibly because individuals are likely to become addicted to their phones when cell phone users experience more stress^[^]. According to the theory of psychological defense mechanisms, college students may adopt immature psychological defense mechanisms (e.g., attempting to resort to entertainment such as cell phone surfing) for self-protection and escapism, or catharsis through substance abuse and addiction to dissipate stress when faced with stress or negative emotions^[^]. In summary, college students' stress perceptions significantly and positively predicted smart phone addiction tendencies, and smart phone addiction positively predicted stress perceptions at the end of the semester in the middle of the semester.

1. The level of stress perception among college students showed a linear decay trend over time;

2. The level of smart phone addiction among college students showed a linearly weakening trend over time;

3.The initial level of college students' stress perception positively predicts the initial level of smart phone addiction;

4.Developmental changes in college students' stress perception positively predicted developmental changes in smart phone addiction.

5.The initial level of stress perception of college students negatively predicts the developmental changes of smart phone addiction;

6.The initial levels of smart phone addiction in college students negatively predict developmental changes in stress perception;

7. Smart phone addiction and stress perception are causally related to each other among college students.

Innovations and Implications

This study applies the potential growth model to the study of college students' smart phone addiction and stress perception. Compared with traditional statistical analysis methods, the potential growth model can more comprehensively consider the time factor and individual differences in the data, thus more accurately describing the development trend of smart phone addiction and stress perception among college students. In addition, this study further verified the mutual influence relationship between smart phone addiction and stress perception through cross-lagged analysis, which provides an important theoretical basis for future interventions.

In terms of revelation, the results of this study indicate that there is an interactive relationship between smart phone addiction and stress perception among college students. Therefore, when intervening in college students' smart phone addiction, we need to comprehensively consider the individual's psychological condition and life environment and take comprehensive intervention measures. For example, we can help college students reduce stress and improve their ability to cope with stress by providing mental health education, social support, and increased physical exercise, thus reducing their dependence on cell phones. In addition, we need to strengthen the supervision and guidance of college students' smart phone use to help them establish the correct concept of cell phone use and form healthy living habits. Meanwhile, the results of this study also remind us that the developmental changes of smart phone addiction and stress perception among college students are a long-term process that requires continuous attention and intervention. Therefore, in future studies, we need to use longer-term tracking studies to more comprehensively understand the developmental trends of college students' smart phone addiction and stress perception, and to provide a more accurate and effective basis for intervention.

In conclusion, the findings of this study yield profound implications for both college administration and familial educational practices. Institutions of higher learning must prioritize and augment their focus on fostering mental wellbeing among students, offering comprehensive psychological support and counseling services tailored to their needs. Additionally, it is imperative for colleges and universities to intensify their oversight and guidance in regards to students' smart phone usage, facilitating the cultivation of salutary habits. Regarding familial education, parents are encouraged to be vigilant of their offspring's psychological state and mobile device usage, steering them towards responsible phone usage patterns, while evading excessive dependence that could potentially hinder their academic pursuits and quality of life.

Limitations and Future Research

This study examined the developmental trajectory of stress perception and smart phone addiction among college students and the causal relationship between them through a six-month follow-up study. There are still some shortcomings and areas to be improved and remedied in this study. First of all, the subjects' methods of using variables in this study were all questionnaire filling methods. Although the objectivity and fairness of the subjects who fill in the questionnaire entries are strictly controlled during the scheduling of the subjects' work in the early stage, the subjectivity of individual filling in the questionnaire as well as the bias in the understanding of knowledge cannot be guaranteed, which will inevitably result in the formation of systematic bias due to the formation of individual differences. In subsequent studies, neuroscientific instruments such as fnirs can be used to obtain more objective and informative experimental data. In the current study, the subjects were selected from institutions with high school rankings, a choice that does not cover the variability of multilevel schools. In order to ensure the comprehensiveness and depth of the study, the follow-up work will adopt the multilevel linear regression method in order to explore in depth the influence of different levels of schools on the phenomenon of college students' cell phone addiction, as well as the variability among individual students. Through this method, we expect to have a more comprehensive understanding of the current situation of college students' cell phone addiction, and to provide a more solid basis for related research and interventions.

Finally, future research could further focus on interventions for smart phone addiction. Although we have proposed some comprehensive interventions, how to apply them effectively in practice is still a problem to be solved. Future research could focus on the effectiveness, feasibility, and sustainability of the interventions, with a view to providing more operational guidance for the intervention of smart phone addiction among college students.

Ethics approval and consent to participate

All methods were performed in accordance with the relevant guidelines and regulations. The study protocol was approved by the ethics committee of Wuhan University of Science and Technology School of Physical Education and Sport. Before formal investigation and testing, the researchers received the informed consent of the subjects involved in this study.

Consent for publication

Not applicable.

Funding

No funding was obtained for this study

Availability of data and materials

The raw data supporting the conclusions of this article can be made available by the authors Zicong Ye([email protected]), without undue reservation.

Competing interests

The authors declare no conflict of interest.

Authors' contributions

Conceptualization, Data curation, Funding acquisition, Investigation, Methodology, Writing—original draft,Zicong Ye;T Zhang; Formal analysis, Supervision, Xiantao Huang,Ying Peng, Wei Rao and Jie Yao. All authors have read and agreed to the published version of the manuscript.

Acknowledgments

We are grateful to the participants and their universities for the cooperation and participation in this study.

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Stress perception and the developmental trajectory of smart phone addiction among college students:Based on Parallel Latent Variable Growth Modeling

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Abstract

Figures

Background

Materials and Methods

Participants

Measuring Tools

Stress perception

Smart phone addiction

Statistical analysis

Results

1. The common method bias

2. Measurement invariance

4. developmental trajectories of smart phone addiction and stress perception among college students

4.1 unconditional linear latent variable growth model of stress perception

Note: SP = stress perception,** P < 0.01, * P < 0.05

Note: SMA = smart phone addiction,** P < 0.01, * P < 0.05

Note:SP = stress perception, SMA = smart phone addiction

4.3 Parallel Growth Model of Stress Perception and College Students' smart phone Addiction

Note:SP = stress perception, SMA = smart phone addiction,** P < 0.01, * P < 0.05

5. Cross-lagged test of stress perception and college students' smart phone addiction

Discussion

1.1 Trends in the development of stress perception profiles among college students

1.2 Trends of smart phone addiction among college students

2. The mutual predictive relationship between stress perception and smart phone addiction among college students

Conclusion

Innovations and Implications

Limitations and Future Research

Declarations

References

Additional Declarations

Status:

Version 1