The statistical sample of the present study included 500 female students of the second period of high school in District 1 and District 2 of Sanandaj city, who were studying in the academic year of 2021 - 2022. The mean and standard deviation of the total age of the students were 17.54 and 0.637, respectively.
Table 1 presents the frequency distribution of demographic information. According to
Table 1, of the total statistical sample of the present study, 82.2% were studying in governmental schools and 17.8% were studying in non-governmental schools. Also, the highest frequency of GPA of students was in the 14 - 16 class and the lowest frequency was related to the 18 - 20 class. In addition, the frequency of age and educational level is almost equally distributed in the classes.
| Class | Year | Grade | GPA | Type of School |
|---|
| 16 - 17 | 17 - 18 | 18 - 19 | First | Second | Third | -14 | 14 - 16 | 16 - 18 | 18 - 20 | Governmental | Non-governmental |
|---|
| Frequency | 167 | 164 | 169 | 163 | 170 | 167 | 129 | 147 | 138 | 86 | 411 | 89 |
| Percentage | 33.4 | 32.8 | 33.8 | 32.6 | 34 | 33.4 | 25.4 | 29.4 | 27.6 | 17.2 | 82.2 | 17.8 |
Descriptive information related to the measured variables is given in
Table 2. According to
Table 2, the mean and standard deviation for the variables of academic engagement are 87.37 (21.27), perception of classroom structure 94.61 (24.57), emotional self-regulation 73.87 (18.31) and for academic self-efficacy 87.45 (18.60), respectively. It is also seen in this table that there is a positive and significant correlation between academic engagement and the perception of class structure (0.794), academic engagement and emotional self-regulation (0.774), academic engagement and academic self-efficacy (0.732), perception of classroom structure and emotional self-regulation (0.853), perception of classroom structure and academic self-efficacy (0.811) and between emotional self-regulation and academic self-efficacy (0.778).
| Variables | Mean ± SD | 1 | 2 | 3 | 4 |
|---|
| Academic engagement | 87.37 ± 21.27 | 1 | | | |
| Perception of classroom structure | 94.61 ± 24.57 | 0.794 a | 1 | | |
| Emotional self-regulation | 73.87 ± 18.31 | 0.774 a | 0.853 a | 1 | |
| Academic self-efficacy | 87.45 ± 18.60 | 0.732 a | 0.811 a | 0.778 | 1 |
Considering that the required sample size for modeling is at least 5 and maximum 15 samples for each observation or question (
26) and there were 98 questions in the questionnaires of this research, so the minimum sample size required there were about 500 people and finally the same number was studied.
In the process of analyzing the compiled model, first, all 98 items of the questionnaires used in the research were entered into the model. Also, perception of classroom structure, emotional self-regulation and academic self-efficacy were considered as three components and academic engagement as four components, all of which are reflective variables.
Figure 2 shows the path diagram along with the standard coefficients in the initial model. As seen in
Figure 2, the path of academic self-efficacy to academic engagement shows a value of 0.095, which is a weak coefficient and is not reliable. Therefore, in the following, by examining the T score, we will be aware of the significance of the paths.
Path diagram along with standard coefficients in the initial model
Figure 3 shows the path diagram along with T coefficients in the initial model. According to the T coefficients in
Figure 3, the path of academic self-efficacy to academic engagement, whose T score is 1.799 and less than 1.96, was not significant. Therefore, to reach the appropriate model, 18 items with weak factor load were removed and the model was analyzed again. The deleted items include item 11 compromise component, 2, 3 and 4 concealings, 18 and 23 motivational tasks, 13 autonomous support, 1 and 3 Proficiency evaluation, 18, 19, 24 and 25 contexts, 15 efforts, 2, 5 and 6 were talents and 18 were cognitive occupations.
Path diagram along with T coefficients in the initial model
Figure 4 shows the path diagram along with the standard coefficients in the final model.
Figure 4 shows that students' perception of classroom structure and emotional self-regulation affects their academic engagement through the mediation of academic self-efficacy. In other words, these variables have the ability to predict students' academic engagement. According to the diagram above, the perception of classroom structure on academic self-efficacy (0.425) and on academic engagement (0.334); and academic self-efficacy has a direct effect on academic engagement (0.176) and emotional self-regulation on academic self-efficacy (0.424) and academic engagement (0.357) in students. Also, in the diagram, the determination coefficient or detection coefficient (R
2) has been determined, which is one of the criteria for checking the fit of the structural model and shows how much of the changes in the dependent variable are explained by the independent variables. According to
Figure 4, in all the endogenous variables of the model, the coefficient of determination is greater than the criterion of 0.33, which is the average quorum. Of course, its lowest value is related to the tolerating component (0.412) and the highest value is related to the behavioral engagement component (0.673).
Path diagram along with standard coefficients in the final model
Figure 5 shows the path diagram along with T coefficients in the final model. According to the T coefficients in
Figure 5, all the obtained values are greater than 2.58. Therefore, the coefficients of all investigated pathes are significant with 99% confidence.
Path diagram along with t coefficients in the final model
In
Table 3, the effect size or factor load of each item in three questionnaires of academic engagement, perception of classroom structure and academic self-efficacy on its component is given in the form of measurement model or external model. According to the results of
Table 3, all factor loads of the items of the three mentioned questionnaires are statistically significant.
| Items | Factor Load | t | P-Value | Items | Factor Load | t | P-Value | Items | Factor Load | t | P-Value |
|---|
| Questionnaire of Academic Engagement | Questionnaire of Perception of Classroom Structure | Questionnaire of Academic Self-efficacy |
| 1 | 0.861 | 58.769 | 0.001 | 2 | 0.782 | 44.769 | 0.001 | 1 | 0.664 | 18.517 | 0.001 |
| 2 | 0.884 | 78.052 | 0.001 | 4 | 0.752 | 30.010 | 0.001 | 3 | 0.706 | 34.074 | 0.001 |
| 3 | 0.766 | 31.659 | 0.001 | 5 | 0.858 | 57.147 | 0.001 | 4 | 0.691 | 26.093 | 0.001 |
| 4 | 0.816 | 46.130 | 0.001 | 6 | 0.862 | 59.756 | 0.001 | 7 | 0.781 | 40.981 | 0.001 |
| 5 | 0.782 | 28.910 | 0.001 | 7 | 0.807 | 38.373 | 0.001 | 8 | 0.768 | 40.400 | 0.001 |
| 6 | 0.946 | 68.312 | 0.001 | 8 | 0.850 | 46.402 | 0.001 | 9 | 0.736 | 40.958 | 0.001 |
| 7 | 0.911 | 67.740 | 0.001 | 9 | 0.729 | 29.823 | 0.001 | 10 | 0.768 | 34.145 | 0.001 |
| 8 | 0.889 | 66.222 | 0.001 | 10 | 0.828 | 40.873 | 0.001 | 11 | 0.786 | 36.123 | 0.001 |
| 9 | 0.858 | 59.346 | 0.001 | 11 | 0.866 | 56.609 | 0.001 | 12 | 0.789 | 35.065 | 0.001 |
| 10 | 0.873 | 65.335 | 0.001 | 12 | 0.801 | 49.487 | 0.001 | 13 | 0.683 | 24.978 | 0.001 |
| 11 | 0.876 | 70.186 | 0.001 | 14 | 0.790 | 34.887 | 0.001 | 14 | 0.820 | 26.410 | 0.001 |
| 12 | 0.847 | 59.746 | 0.001 | 15 | 0.833 | 48.348 | 0.001 | 16 | 0.824 | 30.426 | 0.001 |
| 13 | 0.838 | 55.769 | 0.001 | 16 | 0.778 | 34.461 | 0.001 | 17 | 0.831 | 32.927 | 0.001 |
| 14 | 0.849 | 42.101 | 0.001 | 17 | 0.824 | 45.735 | 0.001 | 20 | 0.748 | 40.531 | 0.001 |
| 15 | 0.905 | 65.887 | 0.001 | 19 | 0.841 | 53.512 | 0.001 | 21 | 0.781 | 39.072 | 0.001 |
| 16 | 0.793 | 40.462 | 0.001 | 20 | 0.880 | 68.762 | 0.001 | 22 | 0.742 | 36.331 | 0.001 |
| 17 | 0.838 | 53.816 | 0.001 | 21 | 0.833 | 46.490 | 0.001 | 23 | 0.788 | 39.147 | 0.001 |
| 19 | 0.906 | 75.573 | 0.001 | 22 | 0.869 | 64.389 | 0.001 | 26 | 0.763 | 31.189 | 0.001 |
| 20 | 0.866 | 60.613 | 0.001 | 24 | 0.849 | 48.874 | 0.001 | 27 | 0.748 | 30.652 | 0.001 |
| 21 | 0.847 | 45.758 | 0.001 | 25 | 0.837 | 47.391 | 0.001 | 28 | 0.765 | 31.942 | 0.001 |
| 22 | 0.843 | 49.590 | 0.001 | 26 | 0.826 | 49.549 | 0.001 | 29 | 0.681 | 19.725 | 0.001 |
| - | - | - | - | - | - | - | - | 30 | 0.758 | 29.284 | 0.001 |
In
Table 4, the factor load of each item in the emotional self-regulation questionnaire is presented on its component in the form of an external model. According to the results of
Table 4, all factor loadings of the emotional self-regulation questionnaire items are statistically significant.
| Items | Factor Load | t | P-Value | Items | Factor Load | t | P-Value | Items | Factor Load | t | P-Value |
|---|
| Emotional Self-regulation Questionnaire |
| 1 | 0.852 | 64.503 | 0.001 | 10 | 0.892 | 72.996 | 0.001 | 17 | 0.887 | 69.603 | 0.001 |
| 5 | 0.806 | 39.987 | 0.001 | 12 | 0.736 | 30.973 | 0.001 | 18 | 0.886 | 68.173 | 0.001 |
| 6 | 0.873 | 44.557 | 0.001 | 13 | 0.732 | 33.717 | 0.001 | 19 | 0.800 | 39.752 | 0.001 |
| 7 | 0.750 | 30.445 | 0.001 | 14 | 0.841 | 46.311 | 0.001 | 20 | 0.840 | 47.648 | 0.001 |
| 8 | 0.739 | 29.046 | 0.001 | 15 | 0.868 | 50.271 | 0.001 | --- | | | 0.001 |
| 9 | 0.768 | 32.811 | 0.001 | 16 | 0.832 | 45.400 | 0.001 | --- | | | 0.001 |
Table 5 shows the reliability and validity of the measurement and structural model. According to the results of
Table 5, Cronbach's alpha coefficient in all variables is at an excellent level. Also, composite reliability values were excellent in all variables. On the other hand, the convergent validity of the model has been confirmed using the average variance extracted, which is more than 0.5. In addition, the Q
2 criterion, which determines the predictive power of the model in the dependent variables, is (close to or) greater than 0.35, which indicates the strong fit of the model predictor.
| Latent Variable | Average Variance Extracted (AVE) | Weighted Average | Composite Reliability (CR) | Weighted Average | Cronbach's Alpha Coefficients | Weighted Average | Predictive Fit of the Model (Q2) | Weighted Average |
|---|
| Perception of classroom structure | | | | | | | | --- |
| Proficiency evaluation | 0.655 | 0.661 | 0.938 | 0.969 | 0.924 | 0.966 | 0.924 | |
| Autonomous support | 0.720 | | 0.911 | | 0.869 | | 0.619 | |
| Motivational tasks | 0.699 | | 0.942 | | 0.928 | | 0.648 | |
| Emotional self-regulation | | | | | | | | --- |
| Concealing | 0.649 | 0.648 | 0.902 | 0.950 | 0.863 | 0.947 | 0.511 | |
| Adjusting | 0.681 | | 0.927 | | 0.905 | | 0.602 | |
| Tolerating | 0.722 | | 0.928 | | 0.904 | | 0.545 | |
| Academic self-efficacy | | | | | | | | 0.374 |
| Talent | 0.599 | 0.675 | 0.913 | 0.938 | 0.893 | 0.930 | 0.503 | |
| Effort | 0.751 | | 0.919 | | 0.824 | | 0.578 | |
| Context | 0.639 | | 0.824 | | 0.714 | | 0.407 | |
| Academic engagement | | | | | | | | 0428 |
| Factorial engagement | 0.677 | 0.706 | 0.913 | 0.974 | 0.881 | 0.971 | 0.510 | |
| Behavioural engagement | 0.703 | | 0.953 | | 0.938 | | 0.747 | |
| Cognitive engagement | 0.722 | | 0.948 | | 0.936 | | 0.648 | |
| Emotional engagement | 0.746 | | 0.923 | | 0.889 | | 0.649 | |
Table 6 presents the Fornell-Larcker matrix to check divergent validity. As indicated in
Table 6, the values on the main diameter of the matrix are greater than all the values in the corresponding column and it indicates that the fitted model has a good diagnostic validity.
| Components and Variables | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 |
|---|
| 1. Proficiency evaluation | 0.809 | | | | | | | | | | | | | | | | |
| 2. Autonomous support | 0.454 | 0.848 | | | | | | | | | | | | | | | |
| 3. Motivational tasks | 0.571 | 0.388 | 0.836 | | | | | | | | | | | | | | |
| 4. Perception of classroom structure | 0.684 | 0.745 | 0.760 | 0.813 | | | | | | | | | | | | | |
| 5. Concealing | 0.339 | 0.421 | 0.533 | 0.677 | 0.806 | | | | | | | | | | | | |
| 6. Adjusting | 0.357 | 0.478 | 0.574 | 0.678 | 0.465 | 0.825 | | | | | | | | | | | |
| 7. Tolerating | 0.362 | 0.451 | 0.297 | 0.601 | 0.357 | 0.408 | 0.850 | | | | | | | | | | |
| 8. Emotional self-regulation | 0.540 | 0.611 | 0.725 | 0.765 | 0.717 | 0.695 | 0.642 | 0.804 | | | | | | | | | |
| 9. Talent | 0.483 | 0.328 | 0.566 | 0.538 | 0.284 | 0.292 | 0.342 | 0.555 | 0.773 | | | | | | | | |
| 10. Effort | 0.423 | 0.326 | 0.676 | 0.661 | 0.571 | 0.376 | 0.387 | 0.656 | 0.441 | 0.866 | | | | | | | |
| 11. Context | 0.377 | 0.377 | 0.588 | 0.542 | 0.262 | 0.529 | 0.194 | 0.525 | 0.511 | 0.437 | 0.799 | | | | | | |
| 12. Academic self-efficacy | 0.600 | 0.482 | 0.694 | 0.791 | 0.557 | 0.494 | 0.537 | 0.791 | 0.677 | 0.759 | 0.670 | 0.821 | | | | | |
| 13. Factorial engagement | 0.518 | 0.489 | 0.511 | 0.703 | 0.612 | 0.377 | 0.456 | 0.657 | 0.412 | 0.553 | 0.442 | 0.650 | 0.823 | | | | |
| 14.Behavioural engagement | 0.507 | 0.317 | 0.539 | 0.635 | 0.576 | 0.327 | 0.434 | 0.627 | 0.355 | 0.580 | 0.247 | 0.527 | 0.556 | 0.838 | | | |
| 15. Cognitive engagement | 0.519 | 0.354 | 0.526 | 0.626 | 0.561 | 0.274 | 0.334 | 0.588 | 0.392 | 0.573 | 0.186 | 0.583 | 0.492 | 0.671 | 0.850 | | |
| 16. Emotional engagement | 0.422 | 0.343 | 0.429 | 0.564 | 0.538 | 0.290 | 0.401 | 0.571 | 0.394 | 0.554 | 0.284 | 0.517 | 0.594 | 0.702 | 0.586 | 0.863 | |
| 17. Academic engagement | 0.840 | 0.610 | 0.521 | 0.628 | 0.782 | 0.656 | 0.425 | 0.474 | 0.785 | 0.571 | 0.664 | 0.442 | 0.722 | 0.797 | 0.820 | 0.757 | 0.770 |
In
Table 7, the co-linearity index, direct, indirect and total effects as well as the effect size of the research model are presented. According to the results of
Table 7, the tolerance level and the variance inflation factor (VIF) are between 0.2 and 5, which means that the non-collinearity condition is met. All T coefficients are also significant and the effect size values show an average and acceptable level.
| Paths | Co-linearity (VIF) | Direct Effects | Effect Size (f2) |
|---|
| B | T | P-Value |
|---|
| Perception of classroom structure → Academic self-efficacy | 3.867 | 0.425 | 9.429 | 0.001 | 0.141 |
| Perception of classroom structure → Academic engagement | 4.412 | 0.334 | 5.178 | 0.001 | 0.067 |
| Emotional self-regulation → Academic self-efficacy | 3.861 | 0.424 | 8.931 | 0.001 | 0.139 |
| Emotional self-regulation → Academic engagement | 4.303 | 0.357 | 6.047 | 0.001 | 0.103 |
| Academic self-efficacy → Academic engagement | 3.011 | 0.176 | 3.265 | 0.001 | 0.033 |
| Indirect Effects |
| Perception of classroom structure → Academic self-efficacy → Academic engagement | | 0.092 | 3.355 | 0.001 | - |
| Emotional self-regulation → Academic self-efficacy → Academic engagement | | 0.071 | 3.454 | 0.001 | - |
| Total Effects |
| Perception of classroom structure → Academic self-efficacy → Academic engagement | | 0.426 | 7.073 | 0.001 | - |
| Emotional self-regulation → Academic self-efficacy →Academic engagement | | 0.428 | 8.856 | 0.001 | - |
In the modeling of structural equations using the partial least squares method, unlike the covariance-based method, there is no index to measure the entire model, but an index called the goodness of fit (GOF) index is used to measure the overall performance of the model, which is the fit of the structural part, and calculates the measurement simultaneously. To calculate this criterion, Wetzels et al. (
33) have provided the following formula:
According to the obtained value (GOF = 0.616), the overall fit of the final model in the current research is at a strong level.