Influencing factors of firm innovation in cooperative network based on meta-analysis

: To address the problem of inconsistent empirical results in the literature on factors influencing corporate innovation, this paper uses meta-analysis to analyze 60 empirical research papers with 17,911 independent samples. It was found that a total of 12 factors significantly affect firm innovation, with trust having the highest degree of influence and structural hole having the lowest degree of influence. It was also found that industry type, location factor and performance type have moderating effects on corporate innovation and its influencing factors. This paper sorts out the influencing factors of corporate innovation, which to a certain extent solves the problem of inconsistent findings in related studies and provides some reference for the subsequent innovation activities of enterprises.


Introduction
China is facing the "neck" problem in the core of key technologies, and it is urgent to enhance the strength of science and technology through innovation. As an important force in combining science and technology and economy, enterprises should play a major role in technological innovation decision making, R&D investment and transformation of scientific research results. In recent years, the specialization of enterprises has deepened, and it is difficult to gather the resources needed for innovation of individual enterprises, so strategic alliances have become the cooperative innovation mode for enterprises. Enterprises participate in the cooperation and make decisions about the relationship between them, which requires a proper understanding of the innovation network, and the network can also promote enterprise innovation and industrial development. In the network, how companies use network resources to innovate becomes a key issue, so exploring the factors influencing corporate innovation has received key attention from scholars and companies. Many scholars have conducted research on the relationship between corporate innovation and related influencing factors and have achieved certain results. However, there are still data discrepancies in some of the literature, and there are even studies with very different results. For example, there are inconsistent results regarding the relationship between centrality and firm innovation.DYER 1 argues that firms with high network centrality are at the center of the innovation network, and firms become the core of technology and knowledge exchange. However, Andrew 2 argues that firms with high network centrality have many linkages and the formed network relationships will impose limitations on firms to engage in exploratory collaborative innovation due to inertia. Another example is the findings of the relationship between relationship closeness and firm innovation. In view of this, this paper adopts a meta-analytic approach to systematically sort out empirical studies on the factors influencing corporate innovation, to quantitatively analyze the relevance and degree of correlation as well as the moderating effects, and to provide scientific explanations for the inconsistency of findings in current empirical studies . In the course of the study, this paper attempts to address the following three questions: (i) Identify and screen the published relevant literature on the factors influencing firms' innovation in networks. (ii) Identify the key influencing factors of firm innovation. (iii) Analyze whether contextual and measurement factors play a moderating role on firm innovation.

Corporate Innovation
Innovation can be seen as an output process. As an output, it is the result of the innovation process, the type of innovation created by the firm or the actual implementation of a new product or service. Innovation also refers to the development and commercial exploitation of a new idea or invention. Both the innovation process and the resulting innovation output affect the firm performance of SMEs. At present, scholars have mostly studied corporate innovation from the perspectives of social environment, government, and firms themselves, usually analyzing corporate innovation from a single perspective; in this paper, we will investigate the network perspective consisting of multiple participants, including society, government, and firms, in order to explore the influencing factors of corporate innovation more comprehensively 3 .

Cooperation network
According to social network theory, a network is a relatively stable system consisting of various social relationships among individuals.Due to the externality and complexity of technology, frequent communication between enterprises in the process of exploring technology is inevitable, and the cooperation between enterprises is gradually networked due to the increase in the number of R&D subjects and the increase in the complexity of relationships. In the analysis of social networks, network structure and network relationships are usually considered as the two main attributes, the former focusing on the status and rights of nodes in the network, and the latter emphasizing the density and strength of linkage relationships between nodes. Currently, network structure includes network location, structural hole, network size, centrality, and network density, and network relationships include trust, information sharing,joint problem solving, communication, commitment, relationship quality, and relationship strength.

Moderating variables
Moderating effects in meta-analysis refer to the effects caused by the many factors included in the analyzed sample that facilitate the explanation of more methodological differences, generally from two sources: contextual factors and measurement factors. Drawing on the results of previous studies, this paper selects two contextual factors, industry type and location factor, and one measurement factor, performance type, as moderating variables.
(1) Type of industry In this paper, the industry types of the research sample are divided into high-tech and non-high-tech enterprises. Most of these high-tech enterprises pay more attention to the use of modern information tools such as databases and networks to improve the overall competitive strength of enterprises than non-high-tech enterprises, aiming to provide information support for the smooth implementation of innovation activities, so such enterprises focus on cooperation with partners as a way to achieve complementary resources to carry out their innovation activities .
(2) Location factors Generally speaking, the innovation function elements in economically developed regions are more unique and relatively perfect, and the innovation atmosphere is better, which facilitates enterprises to obtain the innovation resources they need. On the other hand, economically underdeveloped regions have relatively scarce resources, complex and unstable market environment, high degree of market competition, rapid iterations of information updates, more delayed or even lagging information transfer, and enterprises cannot respond quickly, and their innovation efficiency will be reduced as a result.
(3) Type of performance Performance measurement indicators can be divided into subjective and objective indicators, both of which can be used to measure the innovation performance of a company. Compared with objective performance indicators such as revenue and profitability achieved by collaborative innovation, positive and positive psychological expectations tend to have a more direct impact on the subjective feelings of decision makers; and compared with subjective performance, it often takes a longer time to wait for these objective performance such as the conversion of inter-firm trust into revenue. Based on the above theories, the model of factors influencing firms' innovation in cooperative networks constructed in this paper is shown in Figure 1.

Research Methodology
Meta-analysis, as a quantitative literature review method through statistical analysis, is a way of aggregating the results of multiple independent empirical studies on the same issue to draw generalized conclusions. The metaanalysis is divided into three main steps: (i) a comprehensive search of existing research in a certain field by developing a reasonable search strategy; (ii) the development of literature selection criteria and coding of the selected literature in relation to one's research objectives; and (iii) the analysis and description of the data using meta-analysis software. This study uses meta-analysis methods to analyze the empirical literature related to corporate innovation and thus conclude a more scientific research conclusion.

Results of literature coding
In this paper, we searched the literature until June 2022 and obtained 60 papers (including 22 English papers and 38 Chinese papers) and 118 effect values, all with frequencies greater than 2.

Overall effect results
(1) Heterogeneity test  The results of the heterogeneity test are shown in Table 1 for Q.The Q values were all statistically significant (p<0.001). The total effect value Q of the included metaanalysis independent variables was 11313.942, which is greater than the chi-squared value with a degree of freedom of 143 and 95% confidence interval and p<0.001. In addition, I 2 =98.736% in Table 1 indicates that only 1.264% of the observed variance was caused by random variance error, indicating that the observed differences mainly originated from differences in literature effect values, again demonstrating the presence of study heterogeneity of the study, i.e., the existence of potential moderating variables. The results of all the above analyses suggest that potential moderating variables affect the relationship between the included independent variables and firm innovation.
(2) Publication bias  Figure 2, it is easy to see that most of the effect sets are distributed more centrally at the top of the graph, and the two ends of the average effect values are also distributed more evenly, so it can be tentatively concluded that there is no publication bias. Further, this paper uses the quantitative method for further testing, i.e., comparing the loss of safety coefficient with the critical value. The critical value is calculated using 5K+10, where K represents the number of studies, and when the loss of safety coefficient > the critical value, it means that there is no publication bias. As can be seen from the table, the loss of safety coefficient is 67224, which is much larger than the critical value, so there is no publication bias.
(3) Overall effect value The 60 documents included in the database were coded to identify a total of 42 influencing factors. Referring to the inclusion criteria of the meta-analysis, and the terms characterizing the same meaning were combined, such as interaction and communication, 12 influencing factors were included as the final meta-analysis objects of this paper, and the results of the overall effect analysis are shown in Table 2. There are various critical reference values to assess the effect values, and this paper adopts the classification criteria proposed by Cohen .The critical values are 0.5, 0.3, and 0.1. An effect value greater than 0.5 is strongly correlated, greater than 0.3 is moderately correlated, and greater than 0.1 is weakly correlated. According to Table 2

Results of the adjustment effect
In this paper, two situational factors and one measurement factor were selected as moderating variables, and the moderating effects were tested using random effects, as shown in Table 3.
(1) Moderating effect of industry type. By examining the moderating effect, it is found that industry type has a significant effect on innovation in the cooperative network (Q value of 4.112, p=0.043). Specifically, the innovation of high-tech enterprises in the cooperative network is more significant compared with non-high-tech enterprises (0.692>0.500), and the moderating effect values of both are greater than 0.5, showing a strong correlation, but the difference between them is not very large.
(2) Moderating effect of location factors By examining the moderating effect, it can be found that the location factor has a significant effect on the innovation of firms in the cooperative network (Q value of 4.607, p=0.032), specifically, the innovation of economically developed regions in the cooperative network is more significant than that of non-economically developed regions (0.650>0.526), and the moderating effect values of both are greater than 0.5, which is strongly correlated, but The difference between the two is not very large.
(3) Moderating effect of performance type By testing the moderating effect, it is found that the type of performance has a significant effect on firm innovation in the cooperative network (Q value of 8.028, p=0.005), specifically, innovation measured by subjective performance indicators is more significant than innovation measured by objective performance indicators in the cooperative network (0.549>0.341), and the moderating effect values of both are greater than 0.5. There is a strong correlation, but the difference between the two is not significant.

The intensity of the role of factors influencing corporate innovation
In this paper, we dimensionally divide the influencing factors of corporate innovation in cooperative networks from structural and relational dimensions, and the specific division results are shown in Table 4.As shown in Table  2, all influencing factors are significantly and positively correlated with enterprise innovation. Among the strongly correlated influencing factors, from the structural dimension, there are two influencing factors, centrality and network size, where the significance of network size is the highest (r=0.562 ,p<0.01),which indicates that network size occupies an important position in the cooperative network, and the size of the network is related to the number of connections involved in the network by the enterprise, and the number of connections is related to the quality and quantity of resource acquisition, which has a significant impact on innovation of the firm is also highly relevant. In terms of the relationship dimension, there are five influencing factors of trust, communication, information sharing, relationship quality and relationship strength, and the significance of trust is the highest (r=0.644 , p<0.001), which indicates that trust is an important factor in the stability of cooperative relationships, and when trust is strong, enterprises can establish relationships with each other beyond general transactions and reach strategic partnerships. Therefore, companies should focus on the cultivation of trust with their network partners in order to establish long-term cooperative relationships. In the course of the study, it was found that strongly correlated influencing factors presented a high degree of consistency, with only a few findings that were inconsistent. For example, the factor of relationship strength, most scholars agree that the greater the strength, the better the relationship between firms and the more beneficial to their innovative activities; however, a few scholars believe that when the value of strength reaches its maximum value, the effectiveness of the firm decreases subsequently.The reasons for such results may be due to the differences in culture, type of industry, and other factors that affect the innovative activities of firms in different cultural backgrounds or in different industries with different degrees of interaction and exchange of resources between firms. Therefore, companies should consider the influence of various factors in the innovation process in order to better carry out their innovation activities. Moderate correlation is more prone to inconsistent research findings, which is consistent with the results obtained by other scholars, such as the influencing factor of network density in this paper, where most studies show that high-density networks have high stability, trust base is easier to build, and resources and information can be exchanged efficiently, thus enhancing innovation performance, but CRESPO argues that large network size and high network density would implies high information redundancy and higher costs for firms to screen information, which in turn is detrimental to business development. In the medium correlation, research findings are more prone to inconsistency, which also reveals that scholars need to pay more attention to such factors in future studies so that they can better promote corporate innovation.

The role of moderating variables
Compared to the non-high-tech category, high-tech enterprises innovate more obviously in cooperative networks, and high-tech enterprises have stronger network innovation characteristics, which accelerate the flow of innovation knowledge and make it easier to introduce heterogeneous information to optimize their own inherent innovation patterns, thus obtaining higher innovation efficiency. However, there are not many studies on non-high-tech enterprises, and only 23 of the 137 papers included in the meta-analysis were studies conducted on non-high-tech enterprises. Therefore, nonhigh-tech firms should carry out more innovative activities and produce more innovations. Scholars should also pay more attention to the innovation of non-high-tech enterprises in subsequent studies. The innovation of firms in collaborative networks is more evident in economically developed regions, where firms are embedded in more networks, and the diversity and breadth of network embedding enables firms to access more heterogeneous resources and thus enhance their networked innovation capabilities to significantly improve their innovation performance. Similarly, this paper found less research in non-economically developed regions during the study. Therefore, firms in economically developed regions should take more advantage of their own environment to carry out innovation activities, and non-economically developed regions should also actively learn from partner firms to improve their own innovation capabilities. Finally, in terms of the type of performance, subjective performance is more evident for firm innovation; subjective performance, such as the stability of the partnership network, the satisfaction of the partnership and subjective feelings such as the ability to innovate, shortens the waiting time and thus rapidly improves the firm's innovation performance, which suggests that firms can use subjective performance rather than objective performance, which requires a long waiting time, when studying innovation outcomes in the future. Therefore, this suggests that firms can focus on these subjective feelings of satisfaction when measuring innovation performance in order to better cultivate relationships with partners.

Conclusion
Through meta-analysis, this paper synthesizes 60 research papers exploring firms' innovation influencing factors in cooperative networks, identifies 12 key influencing factors, clarifies the relationship between firms' innovation and their influencing factors and explores the reasons for the existence of heterogeneity, provides relevant additions to existing studies, and also provides guidance for subsequent empirical studies. On the one hand, this paper classifies the influencing factors into strong and moderate correlations, among which the most relevant one is trust, which provides ideas for how to cultivate cooperative relationships in future cooperative networks. On the other hand, the influence of subjects on enterprise innovation was analyzed through moderating effects, with higher innovation output and more innovation outcomes measured by subjective performance in economically developed regions and hightech enterprises. This explains, to some extent, the heterogeneity between corporate innovation and its influencing factors. There are some limitations in this paper, the literature collected in this paper is based on published papers, but unpublished papers are not counted, thus some valuable literature may be missed. In addition, some of the empirical papers that lacked correlation coefficients and were not judged by outliers were excluded, which resulted in a loss of sample size. Due to the limitation of the researcher's ability, this paper did not consider the literature in other languages and only searched the literature in Chinese and English, so some valuable contents may be missed.