Structural Equation Modeling (SEM) focuses on the impact of the social-ecological environment on individual behavior. We apply it to exploring the inner relationship between college students' psychological factors and physical exercise. We conducted a questionnaire survey on several college students and established a sports psychology model influencing factors table. The results show that the physical exercise model of college students contains unique characteristics of psychological factors. 2) The structure of the cooperative assessment scale for college students’ physical learning is reasonable and has good reliability and validity. This has met the relevant requirements of psychometrics. Therefore, we believe that the psychological factors of students are inherently related to physical exercise.

#### Keywords

- Structural equation model
- Psychological factors
- Physical exercise
- Inner relationship

#### MSC 2010

- 62H05

Leisure sports originated in western developed countries in the 1960s. This is the way of life and behavior of people. Its quality affects people's physical and mental health to a large extent. Sports has always been one of the research contents of leisure theory abroad, and about 80% of the leisure activities widely developed abroad are sports activities [1]. After being introduced to China, leisure sports have different interpretations. Such as “leisure sports”, “leisure sports”, “leisure sports”, “entertainment sports” and so on.

Some researchers believe that people's main motivations for participating in leisure sports are self-realization, friendship, exercise, self-esteem, self-control, etc. Some studies believe that occupation, age, marital status, and income affect leisure sports motivation. The recreational sports behaviors of the urban middle class indicate that the motives that influence recreational sports are diverse. Most of these studies study the factors that influence the motivation of participating in leisure sports from different factors or a single dimension of leisure sports. According to the literature, many factors affect the motivation of leisure sports, and the motivation of leisure sports is also multi-dimensional. So how do different factors affect the motivation of leisure sports? We conducted a questionnaire survey among students from 5 colleges and universities in Jiangsu Province [2]. The article uses the structural equation modeling (SEM) method to study the relationship between leisure sports motivation and its influencing factors. We explore the multi-dimensional relationship between the two from theoretical and empirical perspectives.

In the scale design, we first reviewed past leisure sports motivation and the factors affecting leisure sports motivation. At the same time, we analyze and sort out the literature. According to the research purpose of this article, we changed the “Leisure Motivation Scale” to “Leisure Sports Motivation Scale” to form the initial questionnaire. The scale consists of 18 items and five dimensions. External norms (WZGF) include threats, force, respect for Others. The engagement norm (TLGF) includes attention and welcome. The identity norm (RTGF) includes technology, life skills, and expectations [3]. Intrinsic motivation (NZDJ) includes pleasure and autonomy. Unmotivated (WDJ) includes helplessness and incompetence.

The scale of influencing factors of leisure sports motivation contains 20 items. Students use the Likert five-point scale to answer. The score ranges from “strongly disagree” to “strongly agree.”

After the initial questionnaire is formed, we then select 120 college students as participants. We distributed 120 questionnaires and received 107 valid questionnaires. The following three criteria are used to screen the questions through the returned questionnaires to concise the overall questionnaire items: (1) The topic part correlation method. (2) Internal consistency and effectiveness standard method. (3) The factor load judgment method. To improve the effect of factor analysis, we need to delete items with factor loadings less than 0.4 and items with multiple factor loadings greater than 0.4. Then we perform exploratory factor analysis on the remaining items. Before conducting exploratory factor analysis, we must first check whether the scale can be used for factor analysis. The questionnaire KMO=0.814, Bartlett sphere test=1500.21, sig.=0.000. This is suitable for us to perform factor analysis. The extraction method adopts principal component analysis. According to the principle that the eigenvalue is greater than 1, the factor extraction is performed, the oblique rotation is performed, and the axis of rotation converges to 5 iterations. Finally, the number of factors affecting the leisure sports motivation questionnaire is 5. These five factors cumulatively explain 59.287% of the variance (Table 1).

Factor cumulative total variance decomposition

Factor loading sum of squares (before rotation) eigenvalues | Variance contribution rate | Cumulative contribution rate | Factor loading sum of squares (after rotation) eigenvalues | |
---|---|---|---|---|

3.934 | 24.587 | 24.587 | 2.615 | |

2.094 | 13.089 | 37.676 | 2.031 | |

1.28 | 8 | 45.676 | 1.736 | |

1.11 | 6.94 | 52.616 | 1.642 | |

1.067 | 6.672 | 59.287 | 1.461 |

The gravel chart shows that the slope has declined significantly after the fifth factor (Figure 1). We name the common factors. After project analysis and exploratory factor analysis, we deleted the “I can learn content related to leisure sports in physical education class” and “The outline of the national fitness plan has little effect on my participation in leisure sports” in the questionnaire affecting leisure sports motivation. The remaining items constitute the final questionnaire affecting leisure sports motivation. The content includes 16 items in 5 dimensions and the load value of each item on five factors (Table 2).

Analysis of 16 exploratory factors in the questionnaire of factors affecting leisure sports activities motivation

Ltem | Factor | |
---|---|---|

D19 leisure sports activities can shape the body shape and strengthen the physique | .839 | |

D20 leisure sports activities can improve athletic ability | .814 | |

D3 leisure sports activities are the best choice for entertainment and communication | .696 | |

D18 leisure sports activities can give me physical and psychological satisfaction | .633 | |

D17 School venues and equipment | .811 | |

D16 learning task is heavy | .762 | |

D2 school system | .658 | |

D13 Parents’ Attitudes To Leisure Sports | .770 | |

D12 Employer's emphasis on participating in leisure sports | .756 | |

D9 society's attention to leisure sports | .540 | |

Interest D1 likes to follow information about leisure sports and competitions and hobbies | .747 | |

D11 Understanding of leisure sports knowledge and exercise methods | .650 | |

D14 I have liked leisure sports since I was young | .612 | |

I will also go to the D5 dormitory or the activities of the students around | .650 | |

D7 school has special guidance. I am happy to participate | .632 | |

D15 Poor exercise ability, unwillingness to participate in activities | .629 |

After we screened the questions, the final questionnaire was formed. First, the reliability of the questionnaire was tested [4]. The reliability test of the internal consistency of the questionnaire of “leisure sports motivation” is that there is no motivation α=0.638, external norm α=0.749, input norm α=0.613, identity norm α=0.721, and intrinsic motivation α=0.722. The consistency reliability test of the questionnaire of “Recreation Sports Motivation Influencing Factors” was mental attitude α=0.809, restriction factors α=0.634, sports atmosphere α=0.612, interests and hobbies α=0.712, habits and methods α=0.645. These are in line with the statistical requirements of the internal consistency reliability of the scale.

Our discrete choice model based on random utility theory can express personal utility _{in}_{in}_{in}

When we quantify the latent variable _{ikn}_{ikn}_{i}_{ln} of sports enthusiasts. Or we describe it by its corresponding observation variable _{itn}_{ikn}_{ikt}

According to the theory of maximum utility, sports enthusiasts choose the _{in}_{jn}_{in}

After the final questionnaire was formed, we surveyed a total of 520 college students. These students are freshman and sophomore students from 5 colleges and universities [5]. We conducted a questionnaire survey. Four hundred sixty-five valid questionnaires were collected (213 males, accounting for 45.8%, and 307 females, accounting for 66.0%). The effective recovery rate is 89.42%. We use SPSS17.0 and AMOS17.0 software to conduct project analysis, exploratory factor analysis, and structural equation model analysis on the collected questionnaire data.

Confirmatory factor analysis is a special form of Structural Equation Modeling (SEM). It is a statistical method based on the covariance matrix of variables to analyze the relationship between variables [6]. In the surveyed questionnaire data, we used AMOS17.0 software to conduct a confirmatory factor analysis of the factor structure of leisure sports motivation and its influencing factors and form a model (Figure 3, Figure 4).

The overall goodness of fit evaluation of the structural equation model is mainly evaluated from the absolute fit index, comparative fit index, and simplified fit index. Most scholars believe that the model statistical test index GFI, AGFI, IFI, TLI, CFI should be greater than 0.90, RMSEA should be less than 0.8, and ^{2} /

The fitting index of the model shown in Figure 2 is ^{2} /

The goodness of fit indexes of the models shown in Figure 4 are: ^{2} /

The structural equation (SEM) has the following characteristics: (1) Multiple dependent variables can be considered and processed simultaneously. (2) Allow independent variables and dependent variable items to contain measurement errors. (3) Allow latent variables to be composed of multiple explicit indicator variables and estimate the reliability and validity of indicator variables simultaneously. (4) The relationship between latent variables can be constructed, and the degree of agreement between the model and the data can be estimated.

Based on the above advantages of (SEM), we first assume that all dimensions of influencing factors impact all dimensions of leisure sports motivation. So we constructed a first-order factor model of leisure sports motivation and its influencing factors. After many model revisions, the final model of the relationship between college students' leisure sports motivation and the influence of leisure sports motivation is obtained (Figure 5).

The statistical test indexes of the model shown in Figure 5 are ^{2} /

From Figure 5, it can be seen that the structural equation model analysis results of the relationship between the motivation of college students' leisure sports activities and its influencing factors are as follows:

The influencing factors of college students' motivation to participate in leisure sports are composed of five dimensions: cognitive attitudes, restrictive factors, interests and hobbies, sports atmosphere, habits, and methods [9]. These five dimensions have an impact on leisure sports motivation. Among them, habits and methods have the greatest influence on leisure sports motivation activities.

The main factors affecting students' intrinsic motivation to participate in leisure sports activities are habits and methods, restrictive factors, cognitive attitudes and interests, and hobbies. The path coefficients showing significant effects are 0.70, −0.37, 0.27, and 0.16, respectively. This study suggests that the main task of our school education is to cultivate the habit and awareness of students to engage in lifelong physical exercises. We need to teach them how to exercise. In addition, it is necessary to develop more leisure sports curriculum resources projects to improve and optimize school facilities [10]. This will ensure that students can smoothly carry out leisure sports activities, formulate effective incentive policies, and improve students' hobbies and subjective initiative. Only in this way can we attract more students to participate in leisure sports activities.

The main factors affecting students' participation in leisure sports activities without motivation are “interests and hobbies,” “restrictive factors,” and “cognitive attitudes.” The path coefficients are −0.55, 0.51, −0.23. No motivation is a lack of motivation. Its negative effect is similar to learned helplessness. Undergraduates in a state of unmotivated disagree with any active explanation for participating in leisure sports activities [11]. This suggests that our students lack interest and hobbies, increased external constraints and pressures, and have low cognitive attitudes. That is, the increase in helplessness will lead to less enthusiasm for participating in leisure sports activities.

Restrictive factors are another main factor that affects the motivation of college students to participate in leisure sports activities. Except that the constraints have a significant negative correlation with intrinsic motivation and identity norms, the constraints have a significant positive correlation with external norms, input norms, and no motivation. Once the leisure restriction factors are involved, the individual will give up participating in the leisure activity. The research results are consistent [12]. This shows that students' study, employment pressure, and school rules and regulations directly affect students' participation in leisure sports activities.

Cognitive attitudes have a significant positive impact on the two dimensions of “identification norm” and “intrinsic motivation” of leisure sports motivation. At the same time, it has no significant negative correlation with the two dimensions of “external norm” and “no motivation.” The path coefficients are 0.16, 0.27, −0.14, −0.23, respectively. This suggests that we should focus on improving students' awareness of leisure sports to internalize students' external motivations continuously. This makes it a positive factor for college students to participate in leisure activities.

The sports atmosphere has a significant positive impact on the two dimensions of “identification norms” and “investment norms” in leisure sports motivation. The path coefficient is also 0.21. The sports atmosphere reflects the highly individualized atmosphere of people in sports activities, and it is also the emotional experience of people in sports activities. It directly affects people's behavior and emotions. This shows that parents, schools, and society pay attention to leisure sports to make students realize the importance of participating in leisure sports.

This study changed the “participation in certain leisure activities” to “participation in certain leisure sports activities” in the original scale item. The rationality and effectiveness of such an adapted questionnaire need to be further tested. At the same time, many factors affect leisure sports motivation. “Climate factors,” “teacher factors,” “motor skills factors,” and so on need to be further explored. The sample size used in this study is college students. It is more convenient to take samples from college students. But they can only represent a certain part of leisure sports activities. Future research should expand the scope of research sampling.

#### Analysis of 16 exploratory factors in the questionnaire of factors affecting leisure sports activities motivation

Ltem | Factor | |
---|---|---|

D19 leisure sports activities can shape the body shape and strengthen the physique | .839 | |

D20 leisure sports activities can improve athletic ability | .814 | |

D3 leisure sports activities are the best choice for entertainment and communication | .696 | |

D18 leisure sports activities can give me physical and psychological satisfaction | .633 | |

D17 School venues and equipment | .811 | |

D16 learning task is heavy | .762 | |

D2 school system | .658 | |

D13 Parents’ Attitudes To Leisure Sports | .770 | |

D12 Employer's emphasis on participating in leisure sports | .756 | |

D9 society's attention to leisure sports | .540 | |

Interest D1 likes to follow information about leisure sports and competitions and hobbies | .747 | |

D11 Understanding of leisure sports knowledge and exercise methods | .650 | |

D14 I have liked leisure sports since I was young | .612 | |

I will also go to the D5 dormitory or the activities of the students around | .650 | |

D7 school has special guidance. I am happy to participate | .632 | |

D15 Poor exercise ability, unwillingness to participate in activities | .629 |

#### Factor cumulative total variance decomposition

Factor loading sum of squares (before rotation) eigenvalues | Variance contribution rate | Cumulative contribution rate | Factor loading sum of squares (after rotation) eigenvalues | |
---|---|---|---|---|

3.934 | 24.587 | 24.587 | 2.615 | |

2.094 | 13.089 | 37.676 | 2.031 | |

1.28 | 8 | 45.676 | 1.736 | |

1.11 | 6.94 | 52.616 | 1.642 | |

1.067 | 6.672 | 59.287 | 1.461 |

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