In recent decades, a large amount of research has linked academic collaboration with educational empirical research output quality, and it is generally thought that scientific research collaboration has a positive impact on the sustainable improvement of educational empirical research output quality [17]. A study published in Nature analyzed 25 million articles from 1981 to 2012 included in the WOS database, finding that most of these high-quality academic research articles were produced by collaborations [18]. Through conducting research on collaborative academic research articles after the 17th century, Beaver and Rosen [19] demonstrated that the scientists who held a collaborative attitude had better conditions for academic research production; they also found that the sense of collaboration can positively predict increases in the scope and fame of the scientists. Zhu et al. [20] conducted a case study on a university in China and found that collaborative research articles usually had a significantly higher citation frequency than individual articles. Lv [21] conducted an analysis to explore the application of the quantitative research method in Chinese educational empirical research and suggested that the major research institutions usually obtain more prominent results through networking.

A consensus has been reached in the academic field that scientific research collaboration predicts the sustainable improvement of educational empirical research output quality; however, the specific mechanism and extent of the effect of the number of collaborators on the sustainable improvement of educational empirical research output quality are still controversial [22]. Some scholars have suggested that the number of collaborators has a positive relationship with educational empirical research output quality [23]. For example, through analyzing articles in the field of cancer, Lawani [24] demonstrated that increasing the number of participants in the project increased the proportion of high-quality publications, whereas the proportion of total self-citations decreases. Chen and Sun [25] considered a physicist and their scientific research team as a case study to explore the relationship between the number of authors and their article citations; the results showed a positive correlation. However, other scholars believe that the number of collaborators and the sustainable improvement of educational empirical research output quality cannot simply be attributed to a correlation or a linear relationship: instead, there is an optimal scale phenomenon. Franceschet and Costantini [26] divided collaborators into groups of three people and divided the quality of the articles into four grades according to the frequency of citations in the overall sample. The results showed that small-scale collaborations were more effective. By analyzing the data of several disciplines in the WOS database, Liu [27] obtained the density distribution curve of the relationship between collaboration scale and the quantity of research articles. Liu found the existence of an optimal phenomenon of scientific collaboration as well. Based on this point of view, Yang and Li [28] analyzed the data from the JCR journal and found that the scale of collaboration cannot be expanded indefinitely: the best collaboration scale was found to be 2–4. 

Collaborative production relationships are essential to the sustainable improvement of educational empirical research output quality and are embodied in aspects of identity, institution, region, and discipline [29,30].

Collaborative identity mainly refers to teacher–student, colleague, and student collaboration relationships [31]. Among them, teacher–student collaboration is the main collaborative type of relationship in scientific research [32]. One study divided the student–teacher collaboration into “teacher ahead and student behind” (teacher as the first author) and “student ahead and teacher behind” (student as the first author) according to the authorship order; this suggested that the “student ahead and teacher behind” mode is the main style of teacher–student collaboration, accounting for 80% of all teacher–student collaborative articles [33]. In the research on collaborative identity and the sustainable improvement of educational empirical research output quality, Zuckerman [34] explored the data of 92 American scholars who won the Nobel Prize before 1972 and found that more than half of the winners were former Nobel Prize winners’, students or postdoctoral associates. AlShebli et al. [35] conducted a bibliometric analysis of 215 million research articles published before the year 2020 and found that teacher–student collaboration can positively predict a higher academic influence of the students. Further examining the relationship between authorship order and the influence of scientific research articles, Xie et al. [36] used authorship order as one of the important index parameters to evaluate the influence of the authors, finding that the authorship order can affect the influence of the authors and their research articles. However, many different findings have been voiced. For instance, Mccann and Meg [37] explored the collaboration characteristics of team heads and their impact on scientific research production and found that authorship order has no significant influence on scientific research production.

The relationships of institutions can be divided into school–school, school–enterprise, and government–school collaboration, etc., from the perspective of different types of institutions [38,39,40]. They can also be divided into within-institutional and cross-institutional collaboration from the perspective of institutional span [41]. In the research on the relationship between collaborative institutions and the sustainable improvement of educational empirical research output quality, Abramo et al. [42] reported that, compared to single-institution collaboration, the output of cross-institutional collaboration in Italian universities from 2001 to 2003 was published in journals with higher impact factors on average. In China, Ling et al. [43] found that school–enterprise cooperation had a significant positive effect on scientific research output. Moreover, Liu and Shao [32] conducted a descriptive statistical analysis of research articles published in 18 educational journals and found that, in the field of higher education research compared to other authors in same-level units, the authors in the same faculty had a higher cooperative output. In cross-level units, compared to school–enterprise cooperation, school–school cooperation was found to have a higher output. However, this research did not reveal the relationship between the type of cooperative organization, the span of the organization, and the influence of higher education research articles.

The region of collaboration can be mainly divided into intra-city, cross-city, and international collaboration [44]. Some of the studies divided regional collaboration into international and domestic collaboration [45,46]. Proximity theory provides the framework to explain the occurrence of intra- and cross-city collaboration [47]. Geographical proximity considerably increases the frequency of face-to-face interaction and the efficiency of information exchange between scientific research collaboration institutions, thereby improving the quality of collaborative articles [48]. Most of the research focused on the relationships between international collaboration and outputs of scientific research [49,50]. Barjak and Robinson [51] reported that international collaboration has a positive impact on the output and quality of scientific research articles by EU research teams. Moreover, based on the data on published research articles from the top 110 universities in the USA, Adams et al. [52] found that international collaboration has a significant positive impact on the citation frequency of the research article; however, a negative correlation was found with scientific productivity. In China, He and Li [53] analyzed the data of State Key Laboratory research articles published between 2005 and 2014. The result showed that international collaboration is an important factor for improving the journal level in which the article is published; however, the impact on the frequency of citations is not significant. This means international collaboration may have effects on the sustainable improvement of educational empirical research output quality.

In collaborative disciplines, the main categories are based on colleagues and departments [54], whereas research majors and directions have been regarded as the basis to identify if the collaboration is cross-discipline [55]. The analysis of the relationship between cross-disciplinary degrees and the sustainable improvement of educational empirical research output quality is one of the important contents of cross-discipline research; this kind of relationship has been reported differently in various studies [56]. Steele and Stier [57] claimed that the stronger the cross-discipline degree of the article, the larger the number of citations. Larivière and Gingras [58] found that high degrees of disciplinary and cross-discipline research articles have little influence. Li et al. [59] indicated that no correlation necessarily exists between cross-disciplinary collaboration and cross-disciplinary citation preference and article influence. Some scholars found an inverted U-shaped relationship between the degree of cross-disciplinary research and the quality of the research article [53]. In the field of educational research, Ma and Yao [55] analyzed the core authors from 2015 to 2019 and suggested that cross-disciplinary research helps improve the output of educational empirical research; however, their findings did not reveal the relationship between cross-disciplinary collaboration and the influence of the research article. In summary, disciplinary interactive collaboration may have effects on the sustainable improvement of educational empirical research output quality.