3.1 Influence of Physical Exercise on the Depression of All Samples Using Linear Regression
To examine the impact of physical exercise on depression, a basic regression analysis using the least squares method was conducted. To further investigate potential influencing factors, stepwise regression was employed to present baseline regression results (refer to Table 2). In this analysis, only the core independent variable, physical exercise, is included in column (1), revealing a significant negative effect on adolescent depression at the 1% statistical level, with a coefficient estimate of -0.0219 for physical exercise. Subsequently, control variables at the individual, family, and school levels were introduced in columns (2)-(4). The estimation outcomes indicate that physical exercise maintains a significant negative effect on adolescent depression at the 1% statistical level after accounting for individual characteristics, with a coefficient estimate for physical exercise of -0.0128. Upon introducing family characteristics, physical exercise exhibits a significant negative effect on adolescent depression at the 5% statistical level, with a coefficient estimate of -0.00761. After including school characteristics, physical exercise still shows a significant negative effect on adolescent depression at the 1% statistical level, now with a coefficient estimate of -0.00895. In conclusion, even after controlling for individual, family, school-level, and peer characteristic variables, physical exercise significantly and negatively affects adolescent depression, suggesting its efficacy in mitigating depressive symptoms among adolescents. This provides preliminary support for research hypothesis 1 of this paper.
Table 2
Physical exercise and adolescent depression: baseline regression results
VARIABLES | (1) | (2) | (3) | (4) |
Physical exercise | -0.0219*** | -0.0128*** | -0.00761** | -0.00895*** |
| (0.00322) | (0.00335) | (0.00336) | (0.00343) |
personal traits | | control | control | control |
Family characteristics | | | control | control |
School characteristics | | | | control |
Constant | 2.354*** | 2.882*** | 3.319*** | 3.443*** |
| (0.00929) | (0.0284) | (0.0460) | (0.0518) |
Observations | 9, 455 | 8396 | 8, 229 | 7, 902 |
R-squared | 0.006 | 0.065 | 0.105 | 0.109 |
Note:(1)*p < 0.10,**p < 0.05,***p < 0.01.(2)Robust standard errors in parentheses.(3)Control variable regression results are omitted and retained for future reference.the same as below. |
3.2 Endogenous Issues
3.2.1 Propensity Score Matching (PSM)
The examination of the impact of physical exercise on adolescent depression may be subject to confounding factors that influence both variables, leading to sample selection bias and compromising the precision of the estimates.For this reason, this paper uses the propensity score matching method (PSM) to robustly test the results of the benchmark regression.
Adolescents who exercised at least three days a week for 30 minutes or more were considered to be ‘regular participants’ and were categorised as the treatment group.On the contrary, samples with physical exercise levels below this threshold are deemed 'physically inactive,' which is to say, the control group. This reclassification of physical exercise into a dichotomous variable of 0 or 1 meets the fundamental prerequisites for employing the PSM approach.Following the establishment of the treatment and control group samples,the PSM test was carried out in accordance with the steps outlined below.Initially, the conditional probabilities, also known as propensity scores, were computed for the treatment group samples using Logit models that were based on the pertinent control variables listed in column (4) of Table 2.Secondly, to ascertain if there are systematic variations in covariates and propensity scores between the treatment and control groups, this study performs a matching quality assessment by contrasting the kernel density function distribution alterations of the propensity score values pre-and post-matching. Figure 1 displays the alteration in propensity score values for both the treatment and control groups, represented as a function of kernel density matching, contrasting the situations before and after employing nearest neighbor matching with k = 4.As observed in Fig. 1, the probability distribution As observed in Fig. 1, the probability distribution pensity score values exhibited substantial the probability distributions of the two propensity score values exhibited substantial differences prior to matching, either due to inherent patterns in the sample data or the presence of unsuitable confounding variables within the control group.Following the matching process, there was a notable decrease Following the matching process, there was a notable decrease between the kernel density equation curves there was a notable decrease in the disparity between the kernel density equation curves for the treatment and control groups, resulting in more aligned trends.The outcomes of the double t-distribution test for a single covariate and the balance test for the shift in the kernel density function distribution highlight that the employment of the PSM method diminishes the variations between the treatment and control groups concerning the explanatory variables. This aligns with the assumption of conditional independence and effectively reduces the disturbances to the precision of statistical results caused by biases in sample selection.
To precisely gauge the average treatment effect of regular physical exercise on adolescent depression, three prevalent matching techniques were employed: nearest neighbor matching (k = 4), caliper matching (r = 0.01), and kernel matching (using the default kernel function and bandwidth) for estimation purposes.As evidenced by the estimation results presented in Table 3, irrespective of the matching technique employed, the impact of regular physical exercise engagement on adolescent depression consistently exhibits a significant negative correlation. This suggests that consistent involvement in physical exercise substantially decreases the incidence of adolescent depression, with the effects varying between − 0.039 and − 0.036.In comparison to the baseline regression outcomes, the impact In comparison to the baseline regression outcomes, the impact, as estimated using the P the impact of physical exercise on depression, as estimated using the PSM approach, is more substantial. This augmented effect is linked to the criteria for sample grouping that are prerequisite for the application of the PSM method. Consequently, this connection elucidates, to a certain degree, the dependability of the methodology employed in this study for differentiating between the treatment and control groups.Thus,Hypothesis 1 of this paper is fully tested.
Table 3
Physical exercise and adolescent depression: results of PSM estimation
Matching method | T | C | ATT | Std. Dev. |
Nearest neighbor matching | 2.253 | 2.294 | − .040*** | 0.011 |
caliper matching | 2.253 | 2.297 | − .044*** | 0.010 |
kernel matching | 2.253 | 2.302 | − .048*** | 0.010 |
Note: The data in the table are the results obtained after 500 repeated runs using the Bootstrap method. |
3.3 Mediation Effect Test Results
3.3.1 Analysis of the Mediating Effects of Parent-Child Interactions and Peer Relationships between Physical Exercise and Depression
To investigate the mechanisms governing the interplay between physical exercise and depression, this study incorporated two mediating variables: parent-child interaction and peer relationships. The objective was to analyze their mediating influences on the relationship between physical exercise and depression.
Upon establishing the mediation model, which includes Upon establishing the mediation model, which includes along with added control variables which includes parent-child interaction (along with added control variables), as illustrated in Fig. 2, the total effect value of physical exercise on depressive symptoms was found to be -0.009, while the direct effect value was − 0.008. The consistency in the signs of ab and c' indicates a partial mediating role of parent-child interaction in the relationship between physical exercise and depressive symptoms.The application of the same modeling approach to peer relationship mediation revealed that the direct effect value of physical exercise on depressive symptoms was − 0.007. Moreover, the congruence in the signs of ab and c' implies that parent-child interaction partially mediated the influence between physical exercise and depressive symptoms.
The findings, after the incorporation of control variables, demonstrated that physical exercise exerted an influence on parent-child interaction, peer relationships, and depressive symptoms. Specifically, the c value was t = 0.00304 with a significance level of P < 0.001, indicating the effect of physical exercise on depressive symptoms. Additionally, the a value for parent-child interaction was t = 0.0435, P < 0.001, and the a value for peer relationships was t = 0.0206, P < 0.001.Upon the introduction of the mediator variable, physical exercise, parent-child interaction, and peer relationships were all found to have an impact on depression. Specifically, the c' value for parent-child interaction was t = 0.00324 with a significance level of p < 0.05, indicating the effect of parent-child interaction on depression. The b value for parent-child interaction was t = 0.000870, P < 0.001. Similarly, the c' value for peer relationship was t = 0.00309, P < 0.05, showing the effect of peer relationships on depression. The b value for peer relationship was t = 0.00171, P < 0.001. These results are presented in Table 4.In this study, three tests of significance are conducted during the Sgmediation command test, namely the Sobel, Goodman1, and Goodman2 tests. All these tests yielded significant results, thereby supporting hypotheses H2 and H3.
Table 4
Mediation effect test results
VARIABLES | (1) depression | Mediating variable : parent-child interaction | Mediating variable : peer relationship |
(2) | (3) | (4) | (5) |
parent-child interaction | depression | peer relationship | depression |
Mediating variable | | | -0.00239*** | | -0.0129*** |
| | | (0.000870) | | (0.00171) |
Physical exercise | -0.00895*** | 0.419*** | -0.00772** | 0.131*** | -0.00719** |
| (0.00304) | (0.0435) | (0.00324) | (0.0206) | (0.00309) |
personal traits | control | control | control | control | control |
Family characteristics | control | control | control | control | control |
School characteristics | control | control | control | control | control |
Constant | 3.334*** | 11.89*** | 3.398*** | 6.696*** | 3.416*** |
| (0.0433) | (0.611) | (0.0464) | (0.292) | (0.0452) |
Observations | 7, 902 | 7, 262 | 7, 262 | 7, 668 | 7, 668 |
R-squared | 0.109 | 0.323 | 0.114 | 0.108 | 0.115 |
Sobel | -0.001***(z= -2.645 ) | -0.002***(z= -4.858 ) |
Goodman 1 | -0.001***(z= -2.632 ) | -0.002***(z= -4.833) |
Goodman 2 | -0.001***(z= -2.658 ) | -0.002***(z= -4.883 ) |
Indirect effect | -0.001***(z= -2.645 ) | -0.002***(z= -4.858 ) |
Direct effect | -0.008**(z= -2.382 ) | -0.007**(z= -2.327 ) |
Total effect | -0.009***(z= -2.707 ) | -0.0088***(z= -2.869 ) |
Proportion of total effect | 0.1150 | 0.1899 |
Note: (1) physical exercise predicts depression. (2) physical exercise predicts parent-child interaction. (3) hysical Exercise and Parent-Child Interaction Together Predict Depression. (4) peer relationships predict depression. (5) Physical exercise and peer relationships jointly predict depression.***、**、* represents passing the test of significance at the 1 per cent, 5 per cent and 10 per cent levels, respectively, with test t-values in parentheses. |
3.4 Bootstrap Mediation Effect Tests for Parent-Child Interaction, Peer Relationships Between Physical Exercise and Depression in Adolescents
The hypothesis testing for the mediating effects of parent-child interactions and peer relationships in the relationship between physical exercise and adolescent depression was conducted using the nonparametric percentile Bootstrap test. By setting the Bootstrap method to randomly sample 500 times, it was shown that none of the Bootstrap confidence intervals included zero, suggesting that certain mediating effects of parent-child interactions and peer relationships in the influence of pro-adolescent physical exercise on depression were statistically significant, as presented in Table 5.
Table 5
Bootstrap mediation effect test for ADL between diabetes, depressive symptoms in older adults
| Observed coefficient | Boot Std.Err. | Normal-based [95% conf. interval] | Efficacy as a percentage of |
Lower | Upper |
Mediating effects of parent-child interactions | − .0010 | 0.0004 | − .0018 | − .0002 | 11.50% |
Direct effect | − .0078 | 0.0035 | − .0144 | − .0010 | 88.50% |
Total effect | − .0087 | 0.0035 | − .0156 | − .0019 | |
Mediating effects of peer relationships | − .0017 | 0.0004 | − .0025 | − .0009 | 18.99% |
Direct effect | − .0072 | 0.0034 | − .0138 | − .0006 | 81.01% |
Total effect | − .0089 | 0.0033 | − .0154 | − .0023 | |