Network patterns of university-industry collaboration: A case study of the chemical sciences in Australia

University–industry (U–I) collaboration takes on many forms, from research services, teaching and training, to curiosity-led research. In the chemical industries, academic chemists generate new knowledge, address novel problems faced by industry, and train the future workforce in cutting-edge methods. In this study, we examine the dynamic structures of collaborative research contracts and grants between academic and industry partners over a 5-year period within a research-intensive Australian university. We reconstruct internal contract data provided by a university research office as records of its collaborations into a complex relational database that links researchers to research projects. We then structure this complex relational data as a two-mode network of researcher-project collaborations for utilisation with Social Network Analysis (SNA)—a relational methodology ideally suited to relational data. Specifically, we use a stochastic actor-oriented model (SAOM), a statistical network model for longitudinal two-mode network data. Although the dataset is complicated, we manage to replicate it exactly using a very parsimonious and relatable network model. Results indicate that as academics gain experience, they become more involved in direct research contracts with industry, and in research projects more generally. Further, more senior academics are involved in projects involving both industry partners and other academic partners of any level. While more experienced academics are also less likely to repeat collaborations with the same colleagues, there is a more general tendency in these collaborations, regardless of academic seniority or industry engagement, for prior collaborations to predict future collaborations. We discuss implications for industry and academics.


Introduction
Collaboration between universities and industry is key to scientific discovery and technological innovation. As repositories of knowledge, talent, and technology, universities are a natural first stop for firms reaching beyond their organisational boundaries to boost innovation (Perkmann & Walsh, 2007;Powell & Grodal, 2005). A cross fertilisation of ideas between universities and industry enables the creation of new and useful combinations of knowledge (Gilding et al., 2020;Katz & Martin, 1997;Melin, 2000). Researchers believe that innovation emerges in two ways (Zhang & Luo, 2020): (1) by using existing knowledge elements in a different and fresh way (Carnabuci & Bruggeman, 2009;Fleming, 2001) or (2) from using existing combinations in different ways so that they can be put to new uses and applications (Yayavaram & Ahuja, 2008). However, despite rapidly growing research interest in studies of research teams in the science community (Cummings et al., 2013;Guimera et al., 2005;Newman, 2004;Sun et al., 2013), there remain few systematic empirical findings in a field that is still largely "fragmented and tentative" (see also Perkmann et al., 2013Perkmann et al., , p. 424, 2021. Previous research has indicated that academics' level of experience plays a role in generating collaboration with non-academic organisations, and there is more to be learned on relationship formation between researchers and external partners and, more specifically, what keeps the collaboration going (D'Este & Patel, 2007;D'Este & Perkmann, 2011;Lam, 2011). To address this gap, we apply the theoretical and methodological lens of social network analysis as a framework by which to understand collaboration as a networked system of social interactions that follow certain rules and patterns that can be measured empirically. Social network research focuses on social relations among actors (these can be individuals, work units, or organisations …), and these social relations are the foundation of relational structure (Borgatti & Halgin, 2011;Breiger, 1974;Wellman, 1988).
The competitive advantage of an organisation is associated with its levels of collaboration and resource sharing with partners (Foss et al., 2010). No single organisation has everything it needs-organisations often need other organisations to grow, thrive and survive. The knowledge-based view of the firm suggests that knowledge is the fundamental resource of an organisation (Grant, 1996), and collaboration between organisations is an important way to share knowledge for mutual benefit. As noted by Oppenheimer, "the best way to send knowledge is to wrap it up in a person", making the point that it is the collaboration between people within those organisations by which knowledge is really transferred.
Collaboration, interaction and knowledge transfer between universities and industry have become complex. In addition, the literature has increasingly acknowledged that networks, specifically social networks, make a contribution not only to research and development but also to commercialisation (Aarikka-Stenroos et al., 2014). As such, more and more studies are examining these dynamics using a network perspective (Chang, 2017;Fischer et al., 2019;Mao et al., 2020). As a theoretical perspective focusing on the relational structures, network approaches have been used to explain a wide range of social phenomena (Borgatti et al., 2009;Chen et al., 2022), and provide a natural means by which to represent the interlocking webs of project-based collaboration, and for analysing their dynamic growth and shift over time through statistical modelling.
Network representations of scientific collaboration are most commonly constructed based on co-authorship/co-patent applications, which give an overview of various types of cooperation at play (Liu et al., 2005;Nsanzumuhire & Groot, 2020). It is only since the last decade that attention has been paid to the content of these interactions from a network perspective . However, longitudinal social network studies are not common as data for such studies tend to be costly, time-consuming (Stadtfeld et al., 2020) and difficult to obtain. In this study, we contribute to the literature by examining longitudinal data in the form of research contracts and grants between academics and industry partners and seek to identify patterns of collaborations (via a statistical network model approach)as indicated by the recurrence of certain network effects (or sub-structures)-that occur across the university database of research collaborations contained within its administrative contract and grant data and set out to examine whether experience plays such a role in university-industry collaboration.

Patterns of U-I collaboration
Collaboration by universities with private industry and other non-academic organisationsalso referred to as University-Industry (U-I) collaboration-is of key strategic importance, with governments increasingly incentivising U-I activities in hopes of fostering technological innovation, especially in the face of ever-increasing global competition and shrinking domestic industrial sectors (Australian Academy of Technology & Engineering, 2016). As a result, there has been a surge of research interest in drivers and outcomes of U-I collaboration, with recent work focused on describing the individual, organisational and institutional precursors to collaborative activity (Ankrah & Al-Tabbaa, 2015;Perkmann et al., 2013Perkmann et al., , 2021Vick & Robertson, 2018). From a network perspective, scientific collaboration between academia and industry is embedded in both the social networks of the people and their organisations and involves complex interactions of knowledge and resources Guan & Liu, 2016;Wang & Hsu, 2014).
A network perspective plays an important role in identifying patterns and trends in university-industry collaborations and a number of indicators have been applied to measure the structural characteristics of collaboration networks (Barrat et al., 2004;Chen et al., 2022;Newman, 2003). These indicators include: the average shortest distance of the network, the degree distribution, and the aggregation degree. While these indicators are applied to static networks and can be modelled and observed to track network dynamics, scholars acknowledge that it is difficult to discover the factors that drive collaborations. In this study, we use stochastic actor-oriented models (SAOMs) (Cao et al., 2017;Zhang & Luo, 2020) to examine how the macro structure of a project-based collaborative network evolved over time and how related micro-mechanisms collectively underpin the network's evolution.
As mentioned earlier, in this case study, we examine longitudinal data in the form of research contracts and grants between academics and industry partners and seek to identify patterns of collaborations (via a statistical network model approach)-as indicated by the recurrence of certain network effects (or sub-structures)-that occur across the university database of research collaborations contained within its administrative contract and grant data and set out to examine whether experience plays such a role in university-industry collaboration.
At the individual level, the primary motive for academics is recognition amongst peers (Lee, 1996). Individuals engage in "status competitions" in the form of publications, conferences and research grants and perhaps, for some, personal financial gain (Becher, 1994;Siegel et al., 2004). In fact, research has identified four main reasons for academics to engage with industry: (1) commercialisation, (2) learning, (3) access to funding and (4) access to in-kind resources (Glaser & Bero, 2005;Perkmann et al., 2021). D' Este and Fontana (2007) suggest that most will engage with industry to further their own research, and although commercialisation of technology is also a reason for academics to collaborate with industry, it does not carry the same weight as obtaining the means to undertake their own research. However, collaboration with industry is fraught with difficulties and individual researchers can mitigate the barriers to collaboration in several ways. They can engage in repeat collaboration by working on projects and publishing with the same group of individuals repeatedly (Dahlander & McFarland, 2013;Leahey, 2016). Another way is to engage with like-minded others who share areas of expertise, methodological approaches or theoretical perspectives.
Extant literature indicates that individual characteristics are more important than organisational characteristics in clarifying why scientists' industrial engagement activities differ (Boardman & Ponomariov, 2009;D'este & Perkmann, 2011;D'Este & Fontana, 2007;Perkmann et al., 2013). One of the key findings in the literature is that seniority and experience (measured in years as an active researcher) have been observed to correlate positively with engagement outside of academia (Boardman & Corley, 2008;Bozeman & Gaughan, 2007;D'este & Perkmann, 2011;Dietz & Bozeman, 2005;Lawson et al., 2019). D' Este andPatel (2007) andFontana (2007) show that professors were significantly more likely to engage with industry. Boardman and Ponomariov (2009) have similar results-US tenured scientists are more likely to engage with industry in a number of ways. In addition, Boehm and Hogan (2014) confirmed that, generally, senior academics are more likely to establish and manage collaboration with industry (Perkmann et al., 2021). Seniority or academic status (how high an individual ranks in the academic hierarchy) has also been linked to U-I engagement (Abreu & Grinevich, 2013;Lawson et al., 2019;Tartari & Breschi, 2012).
Evidence suggests that U-I collaboration is more common when the academic is more experienced and/or advanced and having previous experience in collaborative projects is a strong predictor of collaboration (Sjöö & Hellström, 2019). However, contrary evidence also exists. Van Rijnsoever et al. (2008), using data from a Dutch university, did not find a link between academic rank and industry collaboration. In Norway, Gulbrandsen and Smeby (2005) found an increased probability in patenting with behaviour (with industry) linked with being a professor, but not so for types of collaboration (i.e. start-ups, consultancy work, development of new products) (Giuliani et al., 2010). This raises the question of how academic experience plays out in U-I collaboration in the context of Australia. From an industry perspective, and particularly in Australia in which most businesses are small to medium enterprises (SMEs), it is possible that industry looks to experts in the field, hoping to get the most 'bang for their buck' in terms of investment from their limited R&D funds. Consequently, it is quite possible that the heuristic of reputation, and thus the proxy of academic ranking-something correlated with experience-may strongly influence research contract investment from industry or from public funds. An academic's reputation is measured by their publishing record (De Rond & Miller, 2005;O'Loughlin et al., 2015), the quantity of papers published in high-ranking journals and the number of citations they obtain (Meho, 2007;Moed, 2005Moed, , 2009Van Dalen & Henkens, 2012). Given the reward system in academia which is very much based on 'publish-or-perish', the output of high quantity and quality papers plays a central role in an academic's recruitment, tenure and promotion process (Harley et al., 2010).
Di Maria et al. (2019) suggest that U-I collaboration positively impacts the performance of firms, but not of professors. Indeed, professors' performance (measures in terms of academic publications) is not positively associated with academic engagement. Conversely, firms' financial performance is positively associated with U-I collaboration focused on knowledge transfer for environmental innovation; in fact, the higher the contracts the better the economic performance. Despite these findings by Sjöö and Hellström (2019), we propose that more experienced academics are more likely than less experienced academics to be involved in collaboration with industry. Beyond this, we take a principled exploratory approach derived from the literature to look for other established network patterns of collaboration that might exist in this relational database of collaborations between university and industry.

Status and social exchange: the role of experience in U-I collaboration
The importance of exchange has been highlighted in the literature (Lazega & Pattison, 1999;Lomi & Pattison, 2006). Social exchange theory posits that individuals at a lower level of the hierarchy try to exchange status recognition for advice, and advisors are mindful of this recognition of their status and this motivates them to share their expertise or judgment with the advice seeker (Blau, 1963(Blau, , 2017Lazega et al., 2012;Zappa & Lomi, 2016). Because of these status diversions, advice networks can be highly centralized, and display a hierarchy that often follows the hierarchical structure of the organisation (Lazega et al., 2012).
In their study, Lazega and Pattison (1999, p. 86) found evidence for "dyadic exchange of different types of ties". In terms of status, we first consider higher status which can be assigned for multiple reasons. For example, leadership is likely to be important within organisations as it is leaders that play a critical role in its direction-setting, decision-making and resource allocation. As a second example, the value of industry experience in academic research is likely to be quite important for public research organisations keen to engage with industry, commercialise their inventions and derive financial recompense for the efforts. During their career, many researchers change jobs between academia, industry, and government; and some even work in multiple settings simultaneously. What impact, if any, does this combination of acquired skills, and in particular, skills acquired in an industry setting, have on knowledge transfer? Industry experience can give individuals knowledge of industry trends as well as information about processes and how-to information in areas such as production capabilities or service delivery (Delmar & Shane, 2006). In addition, industry experience provides individuals with knowledge about business opportunities and processes (Dimov, 2010). These industry specific skills give individuals the knowledge to better evaluate and understand the environment their business compete in (Chandler & Sweller, 1996) and also enables them to gain uncodified information which cannot be learned from other sources; information that will help them better evaluate opportunities (Delmar & Shane, 2006).
Of course, social situations also have lower status people within them. Lower status people are likely to want to increase their social status and will seek out ways to do so. Collaborating with higher status people is one way to do this via formal organisational attributes (e.g., leadership) or informal qualities that make them a go-to person for knowledge (e.g., industry experience). In this context, those with lower status are likely to be Early Career Researchers (ECRs) who are key stakeholders in efforts to promote change in research culture and practice on a systemic level (Kent et al., 2022).

Materials and methods
Data for the network analysis is drawn from research-related contracts and grants obtained from a leading university in Australia. We focused on grants and contracts arising from three Chemistry-related departments and entities within the university which commenced and/or ended in the years 2013 through late 2019, modelling the last 5 years of that span (refer to "Statistical approach" section for a more detailed explanation of how the dataset was managed). To construct the network dataset, we identified individual academic researchers who were named across more than one project. A similar process was done for industry partners. Data from each year was aggregated into a panel of collaboration for that year. Additional data from Australian Research Council (ARC) grants were linked to identify organisations who joined research grants as partner organisations primarily through ARC Linkage grants-a government grant program specifically aimed at facilitating partnerships between industry and universities. Investigators were differentiated into two general groups-university researchers and industry partners, referring to any external organisation, including government and not-for-profit, as per previous research (Bozeman et al., 2013;Perkmann et al., 2013Perkmann et al., , 2021. Although direct government support for science and innovation in Australia has been concentrated on research funding undertaken by universities, CSIRO and other public agencies, rather than in business, our rationale for including government bodies is that in the case of industrial research the government directly subsidises when industry contribution is lacking (Productivity Commission, 2007, p. 21). There are two key reasons why the government will step in when industry does not come to the party: (1) governments exercise many functions and need to fund R&D to discharge those functions effectively, and (2) spillovers from innovation that cannot be captured by the innovator and that cannot be realised without support from the government. These spillovers arise from research undertaken in universities, businesses and public sector research agencies (Productivity Commission, 2007, p. 53).
Following this, a manual search process was conducted to categorise industry partners according to general sector (e.g., government/public, commercial, etc.). At each year within the dataset, each academic's level of experience was calculated as the difference between the year under investigation, and the first year that that academic appeared in the dataset, dating back to the late 1990s which was the beginning of the dataset. Using variables included in the dataset, projects were differentiated on the basis of government funding scheme and sub-scheme (e.g., National Health and Medical Research Council (NHMRC), ARC Linkage, ARC Discovery), and as either a research grant, or a research contract (with consultancies were treated as a research contract). 1

A social network approach to collaboration
Grant collaboration involving multiple institutions is a growing trend (Ma et al., 2015;Nagarajan et al., 2013). In a recent study, Nakajima et al. (2023) investigated grant collaborations among two or more institutions and denoted collaborations among institutions on research grants as two-mode networks. Their results indicated that there were two differing 1 3 behaviours; some collaboration-rich institutions tended to densely collaborate with each other in research grants involving fewer institutions, whereas other collaboration-rich institutions tended to do so in research grants involving more institutions. One explanation for this occurrence may be the different strategies of these specific institutions regarding interdisciplinary research projects (Nakajima et al., 2023).
Social Network Analysis (SNA) is a distinctive area of methodological and theoretical enquiry, with origins and applications across the social sciences, as well as mathematics, computer science, and physics (Borgatti et al., 2009;Freeman, 2004). A social network is defined as a set of actors (or nodes) and the connections between them. Ties are regarded as building blocks for social structure. Here, a relationship does not exist independent of others-it may be conditional on (interdependent with) other relationships around it, on physical and organisational boundaries, and on the characteristics and resources of the individuals who possess them. From this simple framework, network scholars have developed numerous ways of describing social structure in terms of many different positions, subcomponents, and forms of connectivity (Burt, 2004;White et al., 1976). SNA has been successfully used for a number of ties/nodes that are not strictly speaking 'social', but rather are inanimate objects (e.g., company boards-see Robins and Alexander (2004)).
More specifically, a basic understanding of SNA starts with a few elementary terms and concepts. The dyadic (one-to-one) social relationship, or tie, constitutes the basic unit of analysis. Ties link together individual entities, referred to as nodes (a mathematical/ graph-theoretical term). When applied to individuals, organisations, or other social agents, nodes are often referred to as social actors. Ties between actors can be defined in countless ways, but generally comprise affiliation (e.g., group co-membership), role relationship (e.g., workplace supervision), a cognitive state (e.g., like or dislike), or a relational event (e.g., sending an email). Ties may be undirected, simply existing between two actors (e.g., kinship, membership). We utilise ties in this study as undirected connections between a bounded social system of actors who are university researchers or their research collaborators, and the research projects (contracts/grants).
A statistical approach to social networks describes underlying social processes that are likely to have influenced the formation of the observed network. A statistical network approach may be used to formalise that a single relationship (e.g., a single collaborative project involvement) is not an isolated unit of analysis, but instead is conditionally dependent on (i.e., interdependent with) other relationships (collaborations) around it. In the context of research collaboration, this may include other projects that preceded the current project, other projects that the academic researcher has with other partners, to name just a few possibilities (Lusher & Robins, 2013b). In the current study-we capture a variety of dynamic social processes (Table 1) and look at how research partners are captured as interconnected through their co-participation on the same projects.

Collaboration as longitudinal two-mode network
Large-scale data on collaboration, when drawn from comprehensive administrative records, rarely captures direct one-to-one relationships between actors. Instead, collaboration between two researchers or organisations is typically indexed through their co-participation in a joint endeavour, such as co-authors named on the same paper (Uddin et al., 2013), or co-inventors named on the same patent (CITE). In this way, episodes of collaboration are typically not themselves analysed, but instead treated as indicators of an underlying collaborative relationship. Activity and popularity The likelihood of additional tie formation, given one's current level of involvement in the network. In the two-mode network representation used in this study, activity refers to the behaviour of partners towards multiple potential projects. Conversely, popularity refers to involvement in a particular project by multiple partners

Closure
Repeat collaboration between partners is represented by network closure, or the tendency to complete structures. In the case of two-mode collaboration data over time, closure is represented in the form of 4-cycles, and represents repeated, or multiple collaboration between partners (Koskinen & Edling, 2012) Actor attribute effects The effect that attributes of the individual node (either partner or project) may have on the evolution of network ties. Partners with a certain attribute may be more or less likely to participate in projects. Similarly, projects of certain types may attract more or less involvement (Agneessens & Roose, 2008;Koskinen & Edling, 2012) Homophily The tendency for actors with the same or similar attribute to form a relationship or co-affiliation (Agneessens & Roose, 2008; Koskinen & Edling, 2012;McPherson et al., 2001). In the context of a two-mode collaboration network, it refers to the tendency of actors to join a project alongside a similar actor. This may reflect similar actors choosing to participate on the same project, or an actor choosing to participate on similar types of projects As such, the approach we propose to the two-mode data we have makes an important contribution via two distinct refinements. Our analytic advancement is not only to consider the ties at an individual level rather than at the level of the organisation, but also to consider the data as two-mode with contracts/grants at one level and researchers at the other level. We now detail these contributions.
It is arguably the occurrence and reoccurrence of the projects themselves (and not the underlying relationship) that is the true practical end-goal of universities and private organisations wishing to boost research exchange. Thus, preserving as much information about the actual projects themselves might be considered a worthwhile priority from the standpoint of analysis. An episode of collaboration may have its own attributes, its own specific timeline, and its own make-up of team members. Identifying features of the collaboration itself (and not just characteristics of the collaboration partners) could prove essential to understanding whether collaboration is likely to re-occur in the future, and the kinds of benefits and outputs that should accrue to those involved. (Banal-Estañol et al., 2013;Lin, 2017;Sjöö & Hellström, 2019).
This raw form of collaboration data involving both partners and the joint projects to which they belong is referred to as a two-mode network. This form of data is defined by relational ties existing (only) between two different sets of nodes (but not within the same set). However, because analysis options for two-mode data are more restricted, they are typically converted to one-mode data for analysis (Borgatti & Halgin, 2011). That is, a weighted link is calculated between two researchers/inventors by counting the number of publications they co-author, or the number of patents that they share (Uddin et al., 2013). While this "conversion" approach of turning two-mode data to one-mode data opens up a wider range of analytical options, it comes with a loss of information (Everett, 2013), especially in longitudinal studies (Koskinen & Edling, 2012). As seen in Fig. 1, two very distinct network structures-a two-mode star (Fig. 1A), and a two-mode circuit (Fig. 1B)have the same exact representation in a one-mode projection (Fig. 1C). Given this data loss, whenever possible, a direct approach to analysing two-mode data is preferred.
Conversion of two-mode networks can also degrade information on the episodic nature of collaboration. Projecting two-mode data on collaborative projects into a one-mode collaborator network reduces an episode of collaboration into simply a component of how strong a tie is between pairs of actors during a broad timeframe. This viewpoint on collaboration thus calls for longitudinal data, for tracking the formation, maintenance, and cessation of relations and exchange over time.
Yet, longitudinal studies of external engagement are rare (Ahuja, 2000), relying more often on cross-sectional surveys (Bstieler et al., 2017). One barrier to the use of longitudinal data in collaboration is the fact that publicly-available collaboration data-in the form of publications and patents-typically lack detail on when the underlying collaborative work actually took place. Instead, they are generally trailing indicators of collaboration, Fig. 1 The same one-mode projection results from two distinct two-mode network configurations 1 3 coming months or years after the actual collaborative exchange. Therefore, examining copublication or co-patenting can give only a rough timeframe on collaboration, and are only able to look backwards, not contemporaneously. This likely results in missed opportunities for evidence-based relationship-building opportunities and strategies at the time when collaborations are ongoing.

Statistical approach
To analyse the dynamic changes in social network structure over time, we use stochastic actor-oriented model (SAOM) 2 for the evolution of two-mode networks (Koskinen & Edling, 2012;Snijders et al., 2010aSnijders et al., , 2010b. We do so because existing traditional approaches (e.g., regression analysis) assume at some level that observations are independent of one another. However, the assumption may not hold in network models, where there is some level of complex dependence in the data (Robins et al., 2012).
Designed to model transitions in networks between discrete time points, SAOM can be used to analyse longitudinal data on social networks jointly with changing attributes of the actors: dynamics of networks and behaviour (Snijders et al., 2010a(Snijders et al., , 2010b. SAOM tests the evolution of social ties within a bounded group of interconnected social actors (e.g., an organisational unit, neighbourhood, school). SAOM can be used to estimate a range of network-based social processes, distinguishing between internal, self-organising network patterns (i.e., endogenous effects), such as activity and closure (see Table 1 above), and exogenous network patterns tied to individual attributes, such as homophily and heterophily (Lusher & Robins, 2013a, 2013b. Analysts can select a set of effects in a theorydriven manner, but some controls are needed to account for dependence among ties. The SAOM is a sequential discrete-choice model, where actors, here people, choose between new contracts based upon the current patterns of the two-mode network. Patterns that may factor into their choices include their own past behaviour as well as the past behaviours of everyone else. Consequently, you can test whether, for example, actors are more likely to collaborate on a project with others if they have past collaborations. As the exact timings at which decisions are made are never observed, the sequence of (opportunities) to make decisions are treated as missing data in SAOM (see Snijders (2001) and Snijders et al. (2010aSnijders et al. ( , 2010b for further details). In this study, our model selection was guided by the conceptual framework of SAOM. By taking this approach, the primary aim of the research was to identify processes that underlie the addition of new collaborative links within a whole network. SAOM was originally proposed by Snijders (2001), building on work by Holland and Leinhardt (1977) and Wasserman (1980), realising that if you want to model dynamic change in networks, you need to do it in continuous time as suggested for non-network data by Kalbfleisch and Lawless (1985) (the implications of modelling networks in discrete-time, on the one hand, and continuous-time, on the other, is discussed in Block et al. (2018)). SAOM has since been elaborated upon to include joint changes networks and behaviour (Steglich et al., 2010); two-mode networks (Koskinen & Edling, 2012); dynamically changing diffusion models (Greenan, 2015); the co-evolution of one-mode and two-mode networks ; multiplex networks, to name a few. For two-mode networks, Conaldi et al. (2012) show how the activities of programmers in an open source software project are structured by endogenous processes and network properties of both bugs and developers. In addition, treating students' health behaviours as affiliations, Adams et al. (2022) found evidence for both selection of friends based on life-style choices, as well as selection of life-style choices based on those of their friends. In terms of modelling the process of tie-formation in affiliation networks in our setting, it difficult to think of an alternative modelling approach that manages to model decisions as informed by both monadic properties as well as the constraints and opportunities presented by the "current" state of the network (or system).
Permutation models such as Multiple Regression Quadratic Assignment Procedure (MRQAP) (Krackhardt, 1988) make no distributional assumptions, and are as such very robust and offer straightforward inference for overall patterns. By the same token, these models do not offer interpretations in terms of actor choices or allow for testing of competing mechanisms. A similar argument can be made for other network regression approaches, such as discrete-time Exponential Random Graph Models (ERGMs) (Robins & Pattison, 2001) (also refer to Block et al. (2018)).
The gravity model for trade has been argued to be one of the most successful empirical models in economics (Anderson, 2011) and models flows or volumes for ties between entities. This is distinctly different from a network model that models dependencies among binary ties (Koskinen & Lomi, 2013).
While ERGMs are primarily models for cross-sectional models, you can specify a longitudinal ERGM (Koskinen & Lomi, 2013;Snijders & Koskinen, 2013). Like SAOMs, the longitudinal ERGM is defined in continuous time, but data observed at discrete points in time. In our case this model would translate to modelling how ties are created contingent on the local social neighbourhood without being contingent on the specification of a choice model. These models can be estimated using the RSiena software and are useful but in our case, we do have two distinct nodes where people nodes lend themselves to some sort of agency. For our data and setting, the actor-oriented framework lends itself most readily to examining our research questions as these are specifically expressed in terms how decisions reflect the local dependencies of actors. For a comprehensive review of the main classes of statistical models for networks see Snijders (2011).
Method of moments (MoM) (Snijders, 2009) is used to estimate parameters. 3 In RSiena, actors' choices to join projects (in this instance, by both academic and external partners) are simulated according to the model specifications, generating a sequence of changes. Model parameters are adjusted by matching features of the simulated data to the observed longitudinal network data. Simulated data are also used to assess the goodness of fit of the 1 3 fitted model (Lospinoso & Snijders, 2019). For each effect, a statistically non-significant parameter means that that effect plays no role in how actors choose to join projects (leaving projects are not modelled). The parameters themselves are the conditional log-odds in the discrete-choice model. The fitted model is sufficient for explaining the data to the degree that the data simulated from the model replicates features from the observed network data.
In the current analysis, we model only the addition of project involvements, 4 conditional on project collaborations over the preceding 2 years. Thus, the analysis as a whole is based on a rolling 3-year window, modelling the addition of ties on top of a network from the prior 2 years. By contrast, project expirations were not modelled, as we assume project expiry to be an externally imposed condition of a grant or contract, rather than a strong indicator of any voluntary choice to end the collaboration. Nevertheless, the continuation of these projects over time may influence the initiation of other new projects around it. External academics were included in the dataset, but analysed in an exogenous fashion, meaning that their affiliation with a project could be used to help predict whether other (internal) academics and organisations joined that project; however, their membership was not itself estimated. Likewise, certain types of project involvements were disallowed in the data, such as industry involvement in ARC Discovery and NHMRC projects. Finally, to obtain a better-fitting model, we also fixed project involvements in large projects involving more than 15 partners overall.

Descriptive results
A description of the types of investigators and projects can be found in Tables 2 and 3, respectively.

Results of statistical model of collaboration network dynamics
The stochastic actor-oriented model estimates results, with some of the effects discussed in Table 1, are presented in Table 4. Effects are listed in four general categories: effects that control the rate at which actors (partners) can make tie choices as part of the simulation; effects that control the distribution of actor choices; effects that control the distribution of project nominations; and effects pertaining to the proposed potential effects. Our discussion will relate largely to this fourth group. As can be seen, there are significant positive effects (indicating these are more likely to happen) for network closure (4-cycles) and the interaction effect representing more experienced academics' choice of contracts. On a nodal level, the use of interaction effects is very simple. As both academics and organisations are "partners" as opposed to "projects", we use a nodal attribute to partition the two, and allow them different formation tendencies. Thus, any additional nodal effects (i.e., academic × experience) are simply to provide one partition some additional explanatory detail. On a network level, interaction effects are a key aspect of model building strategy. Given the nested interdependence of network structures, it is necessary to account for low-order structures that are a part of higher-order structures. (e.g., popularity/activity structures are nested within 4-cycles).
There are negative effects (indicating these are less likely to happen) for project-based academic homophily, the interaction between project-based academic homophily and years of experience. The exact specification in RSiena is provided in Appendix 1.
Indicators of goodness of fit of the model revealed an adequate fit (see Appendix 2 for further details).

Key results and discussion
A summary of the most relevant and significant effects from the statistical network model is presented in Fig. 2; and Fig. 3 shows a two-mode network of projects (black dots), academic partners (white dots) and industry partners (grey dots) in 2018.
In Fig. 2, we can see six effects or patterns that are of note. Effects A-E are significant and positive, indicating that partners favour choosing projects that result in those patterns over those that do not. In contrast, Effect F is significant and negative, indicating that experienced (or inexperienced) partners do not engage in repeat collaboration with the same (experienced) partner and in fact avoid those types of repeated collaborations. We discuss each of these below.
Our general research aim was to examine to the patterns of academic collaboration with non-academic external industry partners within the contracts and grants collaboration of a high-profile university in Australia.
First, we proposed that there might be some association between higher academic experience and industry engagement. We find support for this as there was a positive relationship between years of experience as an academic and being involved in research contracts (see Fig. 2A).
Second, we find that more experienced academics are significantly more likely to become involved in multiple projects of any kind, not just industry ones (Fig. 2B). This could indicate either overlapping projects and/or a quicker churn through these projects, or  both. This illustrates that with experience comes a tendency to split time between multiple projects simultaneously or in quick succession because of the greater number of collaborative partners. It is common for more senior academics to take on the role of 'rainmaker', bringing in research funding that can pay for the positions of more junior staff, and this effect supports this potential scenario. Third, the network model estimates show that academics have a greater tendency to be involved with industry than not (Fig. 2C). The data source is a contracts and government grants database, which underscores that the data is relatively rich with external industry collaboration, compared with academic-only research grants.
Fourth, senior academics are significantly more likely to be a part of multi-partner projects that attract both industry partners and other academic colleagues regardless of their academic colleague's level of seniority (Fig. 2D). This suggests that senior academics are partnering with other non-senior academics on projects involving industry (whether those projects be contracts or government grants). This does suggest that U-I collaborations are not just undertaken with more senior academics but that some form of mentorship, support of junior staff, or simply that specific and needed skills reside in more junior academics who are also on a project. While we discussed the 'rainmaker' above, which may be at play here, it is also possible that more junior academics are creating such project opportunities and bring on more senior academics for research guidance, credibility to either the university or industry partner, or because of some normative function that promotes having more experienced staff on projects. It would be interesting to unpack these issues in future research.
Fifth, a very interesting finding is that we see evidence for repeat collaboration between two partners, regardless of whether they are industry or academic (see Fig. 3E). What this effect indicates is that research collaborations often involve multiple attempts at working together, in other words a focus on "repeated" and "enduring" (Podolny & Page, 1998) "sustained" (Huggins, 2001) interactions or relationships is needed (Huggins et al., 2012). Gulati (1999, p. 401) argues "most alliances involve prolonged contact between partners, and firms actively rely on such networks as conduits of valuable information" and repeated collaboration is likely to better engender trust (Al-Tabbaa & Ankrah, 2016;Mora-Valentin et al., 2004;Plewa et al., 2013) which can reduce transaction costs and lead to better research outcomes. As noted by Woolthuis, Hillebrand and Nooteboom (Woolthuis et al., 2005), research contracts can show commitment to a relationship, and repeated contract is a critical indicator of commitment.
Finally, with the effect in Fig. 2F we see that, given the other effects (particularly Fig. 2E), more senior academics are unlikely to be involved in repeat projects with the same other academics in general.
Taken together, these results reaffirm and further describe the role of experience in working with external organisations, suggesting two different modes of external collaboration. First, greater involvement by more experienced academics in contracts (compared to more junior colleagues) may indicate an underlying comfort and familiarity with managing direct research contracts, and the project management skill that goes with it. For less experienced researchers, collaboration with industry may not be top of mind or sought out, as for this group of researchers (irrespective of their employment status-tenured or contracted), promotion metrics are driven largely driven by publications rather than collaboration with industry. In addition, as they are less experienced, junior researchers may not have yet developed the contacts and relationships needed to enable collaborative projects and this situation would be alleviated if more experienced researchers create opportunities for less experienced members of their teams to engage with industry.
Further, less experienced researchers may in fact be engaged in research with industry. However, as some Australian (i.e., ARC) grants do not allow a named researcher to be paid from the grant, less experienced researcher may find that they are not listed on the grant so that their wage can be covered by the grant. From an industry perspective, the investment of money into research is a big decision and it is reasonable that industry may invest their limited financial resources in more experienced academics whom they see as less of a risk with their research investment.
On the other hand, more experienced academics also tend to be involved in projects that bring together multiple academics and industry partners. 5 This research is presumably more complex and multidimensional, requiring the coordinated input of multiple academics to meet the needs of the aims of project. This involvement could indicate a leadership and coordination role on curiosity-led research. It could also be a sign of mentorship and reputation-lending, providing a tangible pathway by which less experienced academics might harness the knowledge and skills of more experienced academics. It is unclear from this analysis the degree to which these tendencies are embodied in the same individual academics, versus two different subgroups of experienced academics. Support for the tendency of more experienced academic partners to be involved in multiple concurrent projects indicates that experienced academics have a wider circle of collaborations. In this context, it is unsurprising that experienced academics may not be doing repeat collaborations with other academics because they have a widening circle of research projects. Anecdotal evidence from the field suggests several potential personal collaboration strategies at play, with some academics preferring to utilise grants and contracts as a way to diversify their networks. Repeat collaboration with favoured colleagues still happens, but through other, non-contractual means. Thus, repeat collaboration may indeed be in play, leading to collaborative outputs such as publications. However, it may not be evident through the contract record as repeat academic collaboration is an inherently evolving and multi-modal endeavour. Thus, to understand U-I collaboration as a wider networked system, it may be necessary to draw on multiple sources of collaboration data to capture the totality of exchanges that are occurring.
The general pattern of repeat collaboration within the system as a whole (Fig. 2E) is nevertheless intriguing and leaves open future possibilities to understand collaboration. It would be interesting to see if these repeat collaborations are between certain subsets of the system, such as more specific subfields of chemistry, informal subcultures of academics, or even between the industry partners themselves.

Recommendations
This study is one of the few to make use of university database of research contracts to analyse U-I collaboration.
The results suggest more senior (i.e., experienced) academics are integral to U-I collaboration. More senior academics are more likely to be engaged in contracts with industry, more likely to have multiple projects going, and more likely to be part of larger projects involving industry and other academics (of any level). This last effect suggests that more senior colleagues may be acting in mentorship with more junior academics in terms of engaging with industry, or that senior academics add some credibility (to industry or the university) to the funded project. More research is needed in this instance to understand how more junior researchers fit into such U-I collaborations because they represent the future 'senior' academics who feature so prominently in these collaborations.
With a decline in total research funding worldwide (Daniels, 2015) but an increasing number of researchers in most countries (de Winde et al., 2021), funding for early career 1 3 researchers is particularly low worldwide (Christian et al., 2021;Powell, 2016). The ability to obtain funding is important for the career progression of early career researchers (ECRs) in Science, Technology, Engineering, Mathematics, and Medicine (STEMM) fields (Pickett, 2019;Wright & Vanderford, 2017). Research has shown that institutions can play an important role by providing access to professional and personal mentorship networks and developing training for more senior researchers on how to be effective mentors and, by doing so provide ECRs with the required support as they navigate their career (Andrews et al., 2020;Lyall & Meagher, 2012).
When collaborating with industry, it may be in the interest of the university to create formalised processes (if it does not have them already) that enable more junior scientists to build experience via these U-I collaborations. Formalised processes could include the requirement of an ECR in every U-I project and may be useful for inclusion and building of further relationships with industry.
A strong contribution of this paper is the use of a potentially powerful source of data that typically goes under the radar-that which universities hold about grants and contracts, but which often remains unanalysed-at least from a relational, network perspective which is a highly principled and thus more informative way to understand relational data of collaboration. Having unified and comprehensive records that can be integrated with other databases (e.g., patents and publications) and include attributes of the organisations, such as size, location, and the employment of former students, could all serve to expand the utility of this network approach to analysing collaboration, as these characteristics can be factored into the model. With this data and network models in hand, universities would be able to draw stronger conclusions regarding researchers' qualities and choices to collaborate, and what leads to a successful U-I project. Such a longitudinal network approach to collaboration as well could be used to evaluate, for example, any such formalised processes a university might take to support its ECRs, such as that mentioned directly above. Further, longitudinal network studies such as may reveals the 'spread' of tacit knowledge over time as knowledge gets passed down through different researcher generations (Everett et al., 2018).

Limitations
The network analysis of U-I collaboration presented here is subject to some limitations. First, the data represent a single case study of a major Australian university over a recent but limited timeframe. Therefore, the results cannot be regarded as representative of U-I collaboration nationwide or more generally. Second, the database of administrative records analysed here was a picture of relative success, leaving out unsuccessful attempts at collaboration. Of course, just because a contract was signed, and a project went ahead does not mean the project was successful. However, what we do not have here are unsuccessful grant attempts or initial contract negotiations that stalled. As such, the results cannot be fully interpreted as motivation or goals, but rather, an indistinct (and perhaps inconstant) mix of motivation, obligation, and success. It may not be (only) the case that senior academics have a greater preference for academic engagement, but (also) that they are more successful, and perhaps more obligated, to engage externally. Nevertheless, these results are an indication of the involvements that actually take up the time and energy of academics (notwithstanding the time and energy that go into unsuccessful bids for funding). Second, the network model presented here largely assumes that longitudinal dynamics are assumed to be constant over time. However, different dynamics at different time periods may nevertheless exist (indeed, the model contains one such heterogeneity in 2018) as a 1 3 result of external events such as major shifts in policy or research funding priorities. We have assumed that the process is homogenous over time. In this respect the model fits well. However, we suspect that some effects might be stronger or weaker in some periods. This can be investigated with the time-test in RSiena (Lospinoso et al., 2011).
Finally, this illustrative analysis could include a range of further variables. For example, what role might gender play? What industry factors such as a company being local or international make? There are a range of more nuanced factors that could be included in such statistical network models of collaboration that may offer further insights into U-I collaboration.

Conclusion
This study examined the role of experience in academics' collaborative patterns with industry, focusing on 5-years' worth of grants and research contracts in chemistry within a research-intensive university. We preserved the original two-mode structure of contract and grant database, retaining valuable information on the episodic nature of collaboration, rather than converting it to one-mode data as is commonly practiced. Harnessing this underutilised but rich source of data, we used a longitudinal statistical network approach to analyse the data as a two-mode network and found two distinct means of industry collaboration by senior academics, namely direct research contracts, and larger multi-partner projects. We find that there is a more general tendency, independent of academic seniority or industry engagement, for two researchers to be involved in repeat collaborations, but also find that more experienced academics are less likely to repeat collaborations with the same colleagues. Although early career researchers are involved in contracts, we find that it is less so. Further research is required to assess whether this is due to an underlying perceived risk from industry or whether it is an outcome of the academic reward system which is focused on publishing rather than industry collaboration. .08 (.02) *** Having more projects continuing from preceding 2 years increases the frequency of new project choices Effect of first appearance ± on rate (RateX)

Appendix 1: Full SAOM results
1.19 (.29) *** Industry partners make more frequent choices in the first year that they appear in the dataset. This is an effect for industry partners only; entrant academic partners were fixed to obtain better fit Effects controlling partner choices (outdegree of partners) Outdegree of at least 1 (OutTrunc) Fixed Fixed to high number as a model constraint so that active partners choose at least one project Academic (egoX) 3.25 (1.38) Baseline tendency for academics to join projects Academic partner × activity (egoX × outAct) − .36 (.17) * The tendency of academic partners to join additional projects Academic experience (egoX × egoX) − 1.05 (.30) *** The effect of years of experience on the tendency of academics to join projects Academic experience × Activity (egoX × egoX × outAct) .27 (.04) *** The tendency of more experienced academic partners to be involved in multiple concurrent projects Year 2018 × activity (egoX × outAct) 2.52 (.38) *** A dummy variable for outdegree activity in the year 2018, added to improve goodness of fit. The positive significant effect refers to an increase in project overlap that year Effects controlling project nominations (indegree of projects) Indegree of at least 1 (antiInIso) Fixed Fixed to high number as a model constraint so that active projects are chosen by at least one partner Indegree of at least 2 (antiInIso2) .29 (.40) The tendency for projects to have at least 2 partners Popularity (inPop) − 1.49 (.38) *** Preferential attachment. The tendency for projects with many partners to attract yet more partners Contract ( .20 (.26) The tendency of academics to be involved in projects that are popular among academics, and also popular among industry partners Potential experience effects Academic × experience × contracts (egoX × egoX × altX) .23 (.10) * An interaction effect for academics choosing contracts and years' experience Academic × experience × industry popularity (egoX × egoX × inPopX) .01 (.08) The tendency of more experienced academics to be involved in projects that are popular among industry partners Academic × experience × academic popularity × industry popularity (egoX × egoX × inPopX × inPopX) .08 (.03) ** The tendency of more experienced academics to be involved in projects that are popular among both academic and industry partners 4-Cycles (cycle4) .33 (.06) *** A tendency towards repeat collaboration between two partners, regardless of whether they are industry or academic Academic × 4-cycles (egoX × sameX-Cycle4) − .05 (.09) A tendency towards repeat collaboration between two academics, regardless of either academic's experience level Academic × tenure × 4-cycles (egoX × egoX × sameXCycle4) − .09 (.04) * A tendency by more experienced academics to repeat collaboration with other academic partners ***p < .001; **p < .01; *p < .05 ± For industry organisations only

Further model constraints
Several additional modelling constraints were assumed.
-The collaborations of Academics in their first year appearing in the dataset were fixed as there was not previous history to build on and to achieve better goodness of fit. -Participation in very high-degree projects (n < 15) does not lend itself to modelling as accumulated dyadic participation and were kept fixed in the estimation. -Certain non-industry schemes (e.g., ARC Discovery grants) were constrained so as to disallow industry partners from joining those projects.

Two mode clustering co-efficient
Funding Open Access funding enabled and organized by CAUL and its Member Institutions. This research was funded by the Australian Research Council Advanced Training Centre for the Chemical Industries (Project IC170100020).

Conflict of interest
The authors have no financial or proprietary interests in any material discussed in this article.