This study explores the emergence of district-university partnerships in the context of a multi-year, grant-funded initiative to promote equity-centered school leadership. The initiative involved eight large urban school districts in the United States and began in 2021.
We use an ecological model and explanatory mixed-methods design to investigate the evolution of collaborative relationships between university and district partners during the first two and a half years of the initiative.
Our analysis of social network survey data illustrates that strong partnerships took two years to emerge. While the number of university partners did not change significantly, they became more central to and integrated in the work. Insights from our qualitative analysis suggest that the growth of collaborative relationships was promoted by shared goals and strategic actions by both the partners and the funding organization. The district and university partners in our study shared a commitment to advancing equity in schools and engaged in mandated as well as voluntary collaboration.
Our insights contribute to the knowledge base on how intentional networks can promote alignment between university leader preparation programs and district-specific equity needs and give rise to new collaborative structures and processes that are mutually beneficial to both partners.
Introduction
Institutes of higher education play a critical role in preparing leaders who can advance equity in schools (Herman et al., 2022). But how can these institutions ensure that the leaders they are graduating are equipped to meet the specific needs of the metropolitan areas they will serve? The paper focuses on the development of district-university partnerships that were intentionally established as part of the Equity Centered Principal Pipeline Initiative (ECPI). Funded by The Wallace Foundation, the ECPI is a five-year national initiative that launched in 2021 and involves eight large urban districts in the United States. This initiative seeks to deliberately enhance district capacity to promote and advance equity in educational settings through strategic partnerships.
A main tenet in the ECPI theory of action is that intentional cross-organizational partnerships are key to promoting equity-centered leadership in schools (The Wallace Foundation, 2021). Districts participating in the grant initiative were asked to form District Partnership Teams (DPTs) that would include district staff, representatives from two institutes of higher education, a state education agency, and a community organization. We focus our inquiry on district-university partnerships in particular, and explore their evolution during the first two and half years of the grant (September 2021–December 2023).
We chose to center our inquiry on district-university partnership for several reasons. First, universities and school districts have a long history of partnering to improve educational experiences for students. These types of partnerships have only increased in recent years (e.g. Gomez et al., 2020). Exploring these partnerships offers valuable insights into processes that can support districts’ efforts to advance equity in schools. Second, the ECPI presents a unique context for examining such partnerships. Unlike many existing studies that focus on research-practice partnerships—wherein university actors apply their research expertise to address district-level inquiries (e.g. Swick et al., 2021)—the ECPI emphasizes the intentional collaboration between districts and universities for the preparation and support of school leaders.
In addressing these considerations, the study is guided by the following research questions:
How did the professional relationships between the district and its university partners evolve over time, and across all eight ECPI districts?
What key factors shaped the evolution of these partnerships?
What tangible outcomes resulted from the partnerships?
We adopt an ecological approach to our inquiry into district-university partnerships that takes into account the larger context of the ECPI without delving deeply into other types of partnerships, such as those between districts and state agencies or community organizations. Our methodological approach employs an explanatory mixed-methods design (Creswell and Clark, 2010). We use social network analysis to discern patterns in the evolution of district-university partnerships. We then leverage qualitative data to explain these patterns and describe the tangible outcomes that the partnerships make possible. Our insights contribute to the knowledge base on how intentional networks, such as the DPT, can promote alignment between university leader preparation programs and district-specific equity needs, and give rise to new collaborative structures and processes that are mutually beneficial to both partners (see Reyes-Guerra et al., 2022).
All authors are researchers affiliated with research projects funded by The Wallace Foundation as part of the ECPI. The main goal of our projects is to explore the districts’ work on the ECPI and communicate our findings to the field at large so they can inform similar efforts in the future.
Literature review
District-university partnerships are considered key to the preparation of high-quality leaders that can meet the pressing needs of school districts. A recent report on an initiative sponsored by The Wallace Foundation that involved university and district partners documented a number of important benefits to both organizations (Herman et al., 2022). Districts had access to more qualified principals that “might feel committed to staying in the district and taking on a leadership role” (p. 76), and universities benefitted by making changes that “ensured that the programs were more rigorous, coherent, and authentically connected to the work of on-the-ground school leaders” (p. 109).
There is emerging literature on the ways in which district-university partnerships advance equity in schools. One collaborative practice is inquiry into district practices through the lens of equity, also known as equity audits (Hanover Research, 2020). These audits provide valuable opportunities for districts to engage in systematic explorations of data that make visible how equity is playing out in their systems (Theoharis et al., 2022). They also give districts access to the voices of a range of stakeholders, including community members (Green, 2023). Other partnerships have a specific focus, such as increasing the participation of underrepresented groups – e.g. bilingual educators – in teacher pathways (e.g. Chu and Weems, 2024), or re-envisioning the professional learning that districts makes available to educators (Reyes et al., 2020). Importantly, district-university partnerships can transform the structures and practices of both partners. For example, these partnerships can shape the ways in which teacher leaders are involved in teacher education (e.g. Napolitan et al., 2019).
Some scholarship examines how district-university partnerships contribute specifically to diversifying school leader pathways and expanding school districts’ access to leaders prepared to advance equity in schools. District-university partnerships can play an important role in shaping school leader pathways, and increasing the access of aspiring leaders of color to high-quality preparation programs. Reyes-Guerra et al. (2022) illustrate that a robust multi-year partnership between a district and a university can help establish “a leadership candidate pool which has allowed the district to hire diverse instructional leaders into newly opened positions and address the student-leader demographic imbalance” (p. 59). Yamashiro and colleagues (2022) discuss a partnership between a university, districts, and community partners that supports the recruitment of leaders of color into a leader preparation program, which focuses on cultural responsiveness and social justice. The partnership was mutually beneficial for the districts and the university: it increased the number of qualified leaders of color that districts could recruit, and at the same time prompted the university to refine its “curriculum offerings to focus more directly on anti-racist and culturally responsive leadership approaches” (p. 43).
This cursory look at the literature offers examples of the ways in which district-university partnerships can help promote equity in school by diversifying the pool of school leaders and preparing them to lead for equity. The literature synthesis also illustrates how these partnerships transform both institutions, and increase their capacity to meet the needs of historically underserved children and families. This was also the purpose of the district-university partnerships in our study.
Theoretical framework
To investigate the evolution and impact of district-university relationships, we leverage Urie Bronfenbrenner’s bioecological development theory (e.g. Bronfenbrenner and Morris, 1998). This framework is particularly suitable for our research inquiry for several reasons. First, it emphasizes the multiple contexts that shape district-university partnerships (e.g. the DPT, the university, and the district) and how these contexts interact. Second, the theory enables us to position these partnerships within a larger system of relationships, viewing them as part of an ecosystem that includes state agencies, community organizations, funding entities, and other actors. Third, the bioecological framework is developmental in nature, encouraging a long-term perspective on partnership development that aligns with the focus of our study.
In this section, we first describe Bronfenbrenner’s theory and discuss its adaptation to the context of our study. Bronfenbrenner’s theory is ecological and positions individual experiences within an ecosystem of overlapping relationships. The framework identifies five synergistic contexts of relationships (Bronfenbrenner, 1989) that are mutually dependent and all impact individual development. These five contexts are the microsystem, mesosystem, exosystem, macrosystem, and chronosystem (Bronfenbrenner and Morris, 1998).
The microsystem describes “the complex of relations between the developing person and the environment in an immediate setting containing that person (e.g. home, school, workplace, etc.)” (Bronfenbrenner, 1977, p. 515). In the context of district-university partnerships, the microsystem includes the direct relationships between district staff and university representatives. The embeddedness of these partnerships at this level reflects how immediate interactions and collaborations influence the capacity of individual actors to advocate for and implement equitable practices within schools.
The mesosystem encompasses the interdependence between two or more settings. As Bronfenbrenner states, it “comprises the interrelations amongst major settings containing the developing person at a particular point in his or her life” (Bronfenbrenner, 1977, p. 515). Here, the mesosystem is represented by the District Partnership Teams (DPTs), which include both district and university partners. The mesosystem encompasses interactions and collaborative efforts within DPTs that can lead to shared goals and strategies for addressing equity in leadership preparation. This system emphasizes the importance of mutual support and cooperation among all partners.
The exosystem describes “the linkage and processes taking place between two or more settings, at least one of which does not ordinarily contain the developing person, but in which events occur that influence processes within the immediate setting that does contain that person” (Bronfenbrenner, 2005, p. 148). In our study, the exosystem encompasses the broader ECPI network. This network encompasses relationships across different DPTs as well as the separate institutions whose representatives participate in the DPT (such as the universities themselves, the funding agency, and community organizations). Understanding the embeddedness of district-university partnerships within this larger context highlights how external factors, such as funding priorities and community needs, can shape the development and sustainability of these partnerships.
The macrosystem refers to broader societal influences impacting the individual and surrounding systems. This system encompasses the societal expectations that schools meet the diverse needs of all students, which have influenced the funding agency’s priorities. It emphasizes how societal values and norms can shape the goals of district-university partnerships, driving them to align their efforts with overarching equity initiatives.
Finally, the chronosystem highlights the importance of time in learning and development. It represents change or continuity across time, influencing each of the other systems. It allows us to examine how the evolution of district-university partnerships unfolds over time and how changes in the broader educational landscape can affect the relationships and collaborations within the network.
In this study, we operationalize the five contexts with reference to the ECPI. Connections between individuals (or the microsystem) constitute the network data we collected and are the foundation for all analyses conducted. Our findings primarily focus on the meso- and exosystems, exploring the nuances of relationships within and across DPTs. Acknowledging the embeddedness of these partnerships enables us to systematically explore a range of factors that impact the development of relationships among institutions. This perspective of an embedded ecological system is crucial for sustaining effective collaborative efforts in educational leadership, as it highlights the reciprocal influences that can enhance or hinder the capacity of partnerships to meet the diverse needs of students (Baker and Akiba, 2011; Penuel and Gallagher, 2017).
Methods
We employed a mixed-methods case study approach (Creswell and Clark, 2010), with the ECPI initiative as the focal case. Quantitative data were collected through a social network survey to analyze relationships among ECPI actors over time. Social network analysis was used to identify patterns and changes in these connections. The use of network data and analysis is aligned with the ecological framework of this study and effectively captures the interactions among individuals, collectives, and institutions. Qualitative inquiry complemented the quantitative findings by exploring factors that shaped relationship development and identifying tangible outcomes of the partnerships.
Quantitative design
Data collection
The research team collected data on participants’ collaborative interactions through a structured format specifically designed to gather social network data. Drawing on existing scholarship on network survey design (e.g. Borgatti et al., 2018), we adhered to survey customization processes outlined by Agneesens and Labianca (2022). The survey questions reflected a model of school leader pathways developed by The Wallace Foundation (Turnbull et al., 2021) and addressed all of the model's components. Specifically, the social network instrument was focused on the collaborative efforts that emerged in the context of the ECPI. Participants were asked to nominate individuals they collaborated with on ECPI work using an ECPI actor list. They were also invited to nominate individuals outside this list, allowing for a comprehensive mapping of collaborative interactions. A sample question included: “In the past six months, who did you work with to systematically improve candidate access to principal preparation programs.”
The survey was administered three times in March 2022 (T1), January through March 2023 (T2), and October 2023 (T3). The context in which the survey was administered ranged from ECPI convenings where members of all DPTs were present to district-specific DPT meetings. Despite the difference in context, all DPT members were invited to take the survey, reflecting a total of 156, 185, and 125 participants at each time point respectively. The response rate was 71%, 62%, and 89%. The survey response rates are typical for targeted sampling designs that collect personal network data (Perry-Smith et al., 2018) and acceptable for social network analysis.
Data analysis
We computed several key social network metrics in UCINET software (Borgatti et al., 2002) to assess network cohesion and structural evolution across the exosystem (ECPI Network), mesosystem (DPT-wide ego networks), and microsystem (university partners’ ego networks) (Borgatti et al., 2018). These metrics included average degree centrality (in- or out-degree), arc reciprocity, dyad reciprocity, transitivity, the E-I index, and the Index of Qualitative Variation (IQV). Visualizations of the networks were created using NetDraw (Borgatti, 2002).
Average degree centrality, whether in- or out-degree, measures the number of incoming and outgoing ties for each network member. This metric is often used to indicate the influence and centrality of actors within the network, which helps identify those who play key roles in fostering collaboration and connectivity (Freeman, 2002). Arc reciprocity measures the proportion of outgoing ties that are reciprocated, while dyad reciprocity assesses the extent of mutual relationships across all possible dyads in the network. Transitivity examines the tendency for connections to form triangles within the network, indicating the presence of cohesive subgroups or clusters.
The E-I index was calculated to understand the balance between external and internal connections across actor roles. It ranges from +1 (entirely external ties) to −1 (solely internal ties), with values near 0 denoting balanced interactions (Krackhardt and Stern, 1988). In addition, we included the IQV to assess the diversity or heterogeneity within categorical (nominal) data (Agresti and Agresti, 1978). It quantifies how evenly data points are distributed across different categories, with values ranging from 0 (indicating no diversity) to 1 (indicating maximum diversity). In the current study, it captures the heterogeneity of ties across different actor roles, including the ego’s category. The inclusion of ego’s category reflects the full composition of the network, which provides a more complete picture of how egos and their alters contribute to the diversity of collaborative ties in the ECPI initiative. The IQV is calculated using the formula:
where:
K is the total number of categories, including ego’s category.
is the proportion of all actors (egos and alters) in the ith category.
To examine collaboration dynamics, we analyzed ego networks at both the mesosystem and microsystem levels. At the mesosystem level, the DPT-wide ego networks captured the immediate collaborative ties and influence of DPTs within their direct network neighborhoods. At the microsystem level, the university partners’ ego networks focused on the direct connections surrounding university partners, allowing us to evaluate their bridging roles, tie diversity, and localized collaboration patterns.
Qualitative design
Data collection
Our qualitative analyses rely on (1) artifacts submitted to the Wallace Foundation over the first two years of the initiative, and (2) field notes, interviews, focus groups, and documents our research teams collected as we engaged with district partnership teams (see Table 1).
Qualitative data sources
| Data source | Type/frequency | Date range |
|---|---|---|
| Meeting notes | Team meetings for all 8 districts: monthly | November 2021–June 2023 |
| Day at the Foundation: 1 per year | Spring 2022 and Spring 2023 | |
| ECPI convenings (1–2 days): 3 per year | Fall 2021–June 2023 | |
| Equity reviews | Once | January/February 2022 |
| Initiative deliverables | Grant application | April 2021 |
| Workplan for Year 1 | December 2021 | |
| Definition of equity | February 2022 | |
| Definitions of an equity-centered leader | April 2022 | |
| Interim report | June 2022 | |
| Logic models | September 2022 | |
| Workplan for Year 2 | September 2022 | |
| Community engagement plan | January 2023 | |
| Interviews with university and state partners | Once | August through November 2022, and one in March 2023 |
| Member reflections | 1 per year | Fall 2022 and Fall 2023 |
| Data source | Type/frequency | Date range |
|---|---|---|
| Meeting notes | Team meetings for all 8 districts: monthly | November 2021–June 2023 |
| Day at the Foundation: 1 per year | Spring 2022 and Spring 2023 | |
| ECPI convenings (1–2 days): 3 per year | Fall 2021–June 2023 | |
| Equity reviews | Once | January/February 2022 |
| Initiative deliverables | Grant application | April 2021 |
| Workplan for Year 1 | December 2021 | |
| Definition of equity | February 2022 | |
| Definitions of an equity-centered leader | April 2022 | |
| Interim report | June 2022 | |
| Logic models | September 2022 | |
| Workplan for Year 2 | September 2022 | |
| Community engagement plan | January 2023 | |
| Interviews with university and state partners | Once | August through November 2022, and one in March 2023 |
| Member reflections | 1 per year | Fall 2022 and Fall 2023 |
Source(s): Authors’ own creation
Data analysis
The goal of our research was to describe patterns in the ECPI work within and across each district. We conducted an in-depth analysis of how each district built its capacity to advance equity-centered leadership in schools, and then looked for patterns across districts.
First, we coded the qualitative data using the areas of work described in the principal pipeline model developed by the Wallace Foundation as deductive codes (Turnbull et al., 2021). These areas include leader standards, preparation, hiring, support, evaluation, tracking, and pathway coherence. Given the focus on equity in the ECPI and the emphasis on partnerships, we added two codes to our codebook: equity and partnerships.
Over a dozen members of the research team participated in the thematic coding. Two team leads regularly reviewed coded data and provided feedback to coders. We engaged in regular calibration discussions that helped us refine the codes, build shared understanding around the conceptual model, and increase the consistency of our coding. We first analyzed each DPT separately, and then conducted cross-case analysis.
Findings and discussion
Quantitative data insights
Partnerships are a cornerstone of the ECPI theory of action, and are a way for change processes to be more inclusive, far-reaching, and sustainable (Herman et al., 2022). In this section, we share a variety of evidence to show the expansion and deepening of partnerships between the districts and universities engaged in the ECPI. This evidence is at the meso- and exo-levels of the network and addresses the first research question: How did the professional relationships between the district and its university partners evolve over time, and across all eight ECPI districts?
ECPI network evolution (exosystem)
Figure 1 illustrates the evolution of ECPI networks across DPTs at each time point, highlighting the university partners in their respective ecosystems (mesosystem). In the left column, nodes are colored by DPT, with university partners visually distinguished by their unique shape and rim. The right column categorizes nodes by role, distinguishing university partners (black) from other actors (gray). Edges represent collaborative ties between actors. The corresponding network properties are provided in Table 2.
Network properties of ECPI, DPT-wide, and university partners’ ego networks (T1–T3)
| T1 | T2 | T3 | |
|---|---|---|---|
| ECPI network | |||
| Network size (number of actors) | 219 | 298 | 590 |
| Number of collaborative ties | 256 | 408 | 1,358 |
| Average degree (in- or out-degree) | 1.17 | 1.37 | 2.30 |
| Actor-level reciprocity | 0.30 | 0.29 | 0.34 |
| Dyad reciprocity | 0.18 | 0.17 | 0.21 |
| Transitivity | 0.34 | 0.29 | 0.58 |
| DPT-wide ego network | |||
| Network size (number of actors) | 209 | 291 | 575 |
| Number of collaborative ties | 249 | 408 | 1,358 |
| Average degree (in- or out-degree) | 1.19 | 1.40 | 2.36 |
| Actor-level reciprocity | 0.31 | 0.29 | 0.34 |
| Dyad reciprocity | 0.18 | 0.17 | 0.21 |
| Transitivity | 0.34 | 0.29 | 0.58 |
| University partners’ (UP) network profile | |||
| Number of UPs (egos) | 47 | 53 | 61 |
| Engaged UPs (degree centrality >0) | 32 | 46 | 53 |
| Percentage of engaged UPs among all UPs | 68% | 87% | 85% |
| Degree centrality of engaged UPs1 | 2.35 (3.97) | 2.57* (4.07) | 5.24*** (7.35) |
| UPs in brokering role (betweenness centrality >0) | 6 | 10 | 17 |
| Percentage of UPs in brokering role | 13% | 19% | 28% |
| University partners’ (UP) ego network | |||
| Network size of UP’s 1-step ego neighborhood | 78 | 94 | 198*** |
| Number of collaborative ties | 117 | 202 | 951 |
| Average degree (in- or out-degree) | 1.50 | 2.15 | 4.80 |
| Actor-level reciprocity | 0.38 | 0.44 | 0.40 |
| Dyad reciprocity | 0.23 | 0.28 | 0.25 |
| Transitivity | 0.52 | 0.46 | 0.68 |
| UP’s 1-step ego network reach across ECPI network | 36% | 32% | 34% |
| UP’s 1-step ego network reach across DPT-wide network | 37% | 32% | 34% |
| UP’s IQV2 in 1-step ego network | 0.31 (0.36) | 0.26 (0.34) | 0.54*** (0.28) |
| Network size of UP’s 2-step ego neighborhood | 119 | 166 | 279 |
| UP’s 2-step ego network reach across ECPI network | 54% | 56% | 47% |
| UP’s 2-step ego network reach across DPT-wide network | 57% | 57% | 49% |
| T1 | T2 | T3 | |
|---|---|---|---|
| ECPI network | |||
| Network size (number of actors) | 219 | 298 | 590 |
| Number of collaborative ties | 256 | 408 | 1,358 |
| Average degree (in- or out-degree) | 1.17 | 1.37 | 2.30 |
| Actor-level reciprocity | 0.30 | 0.29 | 0.34 |
| Dyad reciprocity | 0.18 | 0.17 | 0.21 |
| Transitivity | 0.34 | 0.29 | 0.58 |
| DPT-wide ego network | |||
| Network size (number of actors) | 209 | 291 | 575 |
| Number of collaborative ties | 249 | 408 | 1,358 |
| Average degree (in- or out-degree) | 1.19 | 1.40 | 2.36 |
| Actor-level reciprocity | 0.31 | 0.29 | 0.34 |
| Dyad reciprocity | 0.18 | 0.17 | 0.21 |
| Transitivity | 0.34 | 0.29 | 0.58 |
| University partners’ (UP) network profile | |||
| Number of UPs (egos) | 47 | 53 | 61 |
| Engaged UPs (degree centrality >0) | 32 | 46 | 53 |
| Percentage of engaged UPs among all UPs | 68% | 87% | 85% |
| Degree centrality of engaged UPs1 | 2.35 (3.97) | 2.57* (4.07) | 5.24*** (7.35) |
| UPs in brokering role (betweenness centrality >0) | 6 | 10 | 17 |
| Percentage of UPs in brokering role | 13% | 19% | 28% |
| University partners’ (UP) ego network | |||
| Network size of UP’s 1-step ego neighborhood | 78 | 94 | 198*** |
| Number of collaborative ties | 117 | 202 | 951 |
| Average degree (in- or out-degree) | 1.50 | 2.15 | 4.80 |
| Actor-level reciprocity | 0.38 | 0.44 | 0.40 |
| Dyad reciprocity | 0.23 | 0.28 | 0.25 |
| Transitivity | 0.52 | 0.46 | 0.68 |
| UP’s 1-step ego network reach across ECPI network | 36% | 32% | 34% |
| UP’s 1-step ego network reach across DPT-wide network | 37% | 32% | 34% |
| UP’s IQV2 in 1-step ego network | 0.31 (0.36) | 0.26 (0.34) | 0.54*** (0.28) |
| Network size of UP’s 2-step ego neighborhood | 119 | 166 | 279 |
| UP’s 2-step ego network reach across ECPI network | 54% | 56% | 47% |
| UP’s 2-step ego network reach across DPT-wide network | 57% | 57% | 49% |
Note(s): Values in parentheses represent standard deviations. IQV denotes the Index of Qualitative Variation, which measures the heterogeneity of an individual’s direct connections. 1Paired sample t-test on degree centrality between T1 and T2 is t = 1.828, p = 0.036; between T2 and T3 is t = 4.761, p < 0.001. 2Paired sample t-test on university partners’ IQV between T1 and T2 is t = 1.828, p = 0.036; between T2 and T3 is t = 4.761, p < 0.001. Ego network reach is measured by the proportion of university partners’ ego network size relative to the ECPI or DPT-wide ego network size
Source(s): Authors’ own creation
We observed notable changes in network structure across the three time points. First, as illustrated in Table 2, the ECPI network size increased from 219 actors at T1 to 590 at T3, accompanied by a rise in collaborative ties from 256 to 1,358. The greatest change occurred at T3, or at the beginning of the third year of the ECPI initiative, suggesting expansion of participation and collaboration within the network. The average degree also demonstrates this trend.
The left column of Figure 1 highlights the emergence of more cohesive and integrated clusters within DPTs over time. At T1, the ECPI network was characterized by isolated actors and small clusters. By T2, these clusters began to consolidate, with university partners linking previously disconnected groups. At T3, the network shows dense clusters within DPTs, indicating improved collaboration and stronger connections. Reciprocity remained modest but stable over time, with actor-level reciprocity increasing slightly from 0.30 at T1 to 0.34 at T3. Dyad reciprocity rose from 0.18 to 0.21 during the same period, suggesting more mutual connections between actors over time. Transitivity increased from 0.34 at T1 to 0.58 at T3, indicating the formation of more cohesive clusters, as seen in the denser clusters at T2 and T3. Despite the growth, some peripheral clusters remained at T1, T2 and T3. These clusters represent actors with few or no connections. Compared to T1 and T2, however, the number of isolated actors and clusters decreased at T3, indicating improved integration overall.
The visualization and network metrics reveal a positive trend in university partners’ collaborative activity over time. The ECPI network maps, particularly the right column of Figure 1, highlight their progressive growth and increasing connectivity. At all time points, university partners (black nodes) occupied central or brokering positions, underscoring their critical role in facilitating collaboration. By T3, their role as connectors within and across DPTs became even more pronounced, emphasizing their influence in bridging diverse actor groups and fostering broader collaboration. The network metrics further reinforce these findings (see Table 2). At T1, 68% of university partners (32 of 47) were engaged in collaborative activity (degree centrality >0), occupying central positions primarily within smaller, isolated clusters. By T2, engagement increased to 87% (46 of 53), with university partners beginning to link previously separate groups, contributing to a more integrated network. At T3, 85% of university partners (53 of 61) remained engaged, with their degree centrality increasing significantly from an average of 2.35 (T1) to 2.57 at T2 (t = 1.828, p = 0.036) and further to 5.24 at T3 (t = 4.761, p < 0.001), which indicates their expanded collaborative roles. Furthermore, university partners also played an increasing role in brokering connections across the network. The percentage of university partners serving as brokers rose from 13% at T1 to 28% at T3, reflecting their growing influence in linking DPTs and facilitating broader collaboration. The network maps at T3 illustrate this progression, with university partners positioned as connectors both within and across DPTs, supporting the network’s overall cohesion and the ECPI initiative’s evolving collaborative framework.
Overall, the ECPI network’s evolution demonstrates a significant growth in network size and interconnectivity, with university partners playing a progressively active role in fostering collaboration and bridging across DPTs. The emergence of more integrated collaborative ties contributes to the development of a more cohesive and connected ecosystem.
DPT-wide ego networks (mesosystem)
The network properties outlined in Table 2 highlight the similarities and subtle differences between the ECPI network and the DPT-wide ego network. The ECPI network includes all DPT partners as well as technical assistance actors, while the DPT-wide network encompasses only the 1-step ego network of DPT partners, which include district staff and representatives from institutes of higher education, state education agencies, and community organizations. The inclusion of technical assistance actors in the ECPI network resulted in slightly larger network sizes across all time points; however, the number of technical assistance actors was relatively small (approximately 10–15). Consequently, the overall patterns in network properties, such as the number of collaborative ties, average degree, reciprocity, and transitivity, are very similar between the two network systems.
While the ECPI network provides a broader view of collaboration by including technical assistance actors, the DPT-wide ego network focuses more narrowly on the immediate relationships among DPT partners. The similarity in their network properties suggests that the technical assistance actors, though few in number, do not dramatically alter the overall structural patterns observed in the ECPI initiative.
University partners’ ego networks (microsystem)
Building on the mesosystem level of the DPT-wide ego network, the university partners’ ego networks shift the focus to the microsystem by examining the immediate, 1-step relationships surrounding university partners within the ECPI initiative. These networks provide insight into how university partners connected and collaborated directly with other actors, offering a more granular view of their roles and influence in the broader system. Figure 2 presents university partners’ ego networks across DPTs over time, with node positions fixed across time points and colors denoting different attributes. The lower part of Table 2 outlines the corresponding ego network properties.
University partners’ ego networks across DPTs (microsystem) at T1, T2, and T3
Over time, the size of university partners’ 1-step ego neighborhoods grew gradually, increasing from 78 at T1 to 94 at T2. This early growth phase reflects a steady expansion of direct connections. However, the size rose dramatically to 198 at T3. This statistically significant increase (p < 0.001) is indicative of a major expansion in university partners’ direct connections and collaborative roles during the latter part of the initiative. This growth was accompanied by a rise in the number of collaborative ties, which expanded from 117 at T1 to 951 at T3, indicating the growing scope of direct relationships. The first column of Figure 2 reveals that, over time, the actors in the network became increasingly clustered by DPT. At T1, isolated actors and small clusters dominate the network, but by T3, these fragmented groups had integrated into larger, more cohesive clusters, reflecting improved collaboration and stronger ties between university partners and other DPT actors. While the tendency for actors to reciprocate ties remained stable, the increase in transitivity from 0.52 at T1 to 0.68 at T3 suggests that actors were more likely to form connections with each other’s collaborators, creating tightly-knit groups within the 1-step neighborhoods.
As seen in the second column of Figure 2, university partners (black nodes) consistently held prominent positions across all time points. They maintained connections with actors from various roles, including district (green), state (orange), community (red), and technical assistance (cyan). These relationships strengthened over time, as reflected in the increasing average degree, which rose from 1.50 at T1 to close to 5 at T3. This suggests that university partners became increasingly central to fostering direct collaboration within their immediate networks.
The findings from Figure 3 highlight the evolving nature of collaboration within university partners’ ego networks by emphasizing the balance between internal and external ties. The E-I index shows that university partners gradually increased their external connections with actors from other roles, rising from 0.17 at T1 to 0.48 at T3. This progression reflects their expanding role in bridging diverse groups within the ECPI network and fostering cross-role collaboration. This trend is further supported by the university partners’ increasing Index of Qualitative Variation (IQV), which measures the heterogeneity of their connections (Table 2). The IQV rose significantly from 0.31 at T1 to 0.54 at T3 (p < 0.001) within their 1-step ego networks, indicating that university partners formed more diverse connections with actors from different roles over time. Together, these findings underscore university partners’ growing capacity to act as bridges across the ECPI network, enhancing collaboration among otherwise disconnected groups.
E-I index of ECPI network and university partners’ ego network over time
In contrast, district actors exhibited an increasingly internal focus, as shown by their declining E–I index from −0.24 at T1 to −0.52 at T3. This shift indicates a preference for within-role ties (homophily), reinforcing internal collaboration over external connections. This pattern, evident in both the ECPI network and the T3 ego network of university partners, suggests that district actors played a stabilizing role by consolidating internal connections within their own groups. While university partners broadened their bridging role across diverse actor groups, district actors prioritized internal cohesion, which likely strengthened the operational stability of DPTs. Together, these complementary roles demonstrate how different actors contributed uniquely to the evolving structure and functionality of the ECPI network.
The findings from Figure 4 further underscore the evolving patterns of engagement across roles within the DPT-wide ego network. University partners and district actors show distinct trends in engagement over time, as reflected in both degree and betweenness centrality. The number of engaged university partners increased steadily from 32 at T1 to 52 at T3, while district actors exhibited a dramatic rise from 79 at T1 to 200 at T3. This reflects their growing presence and activity within the network. Betweenness centrality highlights differences in how these actors contributed to the network’s structure. University partners’ betweenness centrality increased from 6 at T1 to 17 at T3, reinforcing their role as important bridges connecting diverse groups. In contrast, district actors showed a more pronounced rise in betweenness, from 17 at T1 to 72 at T3, reflecting their expanding influence as connectors within and across clusters. Together, these trends illustrate how university partners maintained their bridging roles, while district actors took on increasingly active roles in facilitating network cohesion.
Number of engaged actors across DPT-Wide ego network disaggregated by DPT role
Figure 5 highlights the dynamic nature of tie formation and dissolution within university partners’ ego networks. Between T1 and T2, university partners accounted for 47% of new ties and 29% of lost ties, reflecting their ongoing efforts to expand their collaborative networks. However, between T2 and T3, district actors became the dominant contributors to new ties (61%), signaling their growing engagement in the initiative, while university partners’ role in new tie formation decreased to 20%. This shift suggests that university partners maintained a more stable network while district actors became increasingly active in expanding their collaborative efforts.
Role percentages of individuals with new or lost ties in university partners’ ego networks (T1–T2, T2–T3)
Role percentages of individuals with new or lost ties in university partners’ ego networks (T1–T2, T2–T3)
The reach of university partners’ ego networks across the broader ECPI and DPT-wide networks showed notable shifts over time (Table 2). Their 1-step ego network reach within the ECPI network declined slightly, from 36% at T1 to 34% at T3, while their reach within the DPT-wide network similarly decreased from 37% to 34%. This pattern suggests that university partners increasingly focused on localized collaboration within their immediate networks rather than extending their influence broadly across the exosystem.
At the same time, the size of university partners’ 2-step ego neighborhoods expanded significantly, growing from 119 actors at T1 to 279 actors at T3. Despite this growth, their 2-step network reach across the ECPI network decreased from 54% at T1 to 47% at T3, and their reach across the DPT-wide network dropped from 57% to 49%. This indicates that as university partners built larger direct networks, their influence within the broader 2-step network became more concentrated, reflecting a strategic focus on strengthening immediate, high-quality connections within their microsystem.
Overall, the results demonstrate that university partners’ ego networks grew in size, connectedness, and diversity over time. These changes highlight their increasingly active role in fostering localized collaboration within their microsystem, while maintaining connections across various roles and DPTs. The increasing E-I index and growing diversity of ties emphasize their evolving role as bridges across actor groups. Furthermore, the shifting dynamics of tie formation, with greater engagement from district actors over time, suggest a broader distribution of collaborative efforts. This evolution points to a network that is becoming more participatory and interconnected at multiple levels within the microsystem.
Between-DPT (exosystem) in relation to Within-DPT (mesosystem) networks
The evolution of district-university relationships highlights a predominantly localized structure, with most ties occurring within individual DPTs (mesosystem) and relatively few spanning across DPTs (exosystem), as illustrated in Figure 1 and supported by Figure 4 [1]. The “cross-DPT activity” data in Figure 4 reveal that between-DPT connections remained rare across all time points. District actors consistently demonstrated the highest level of cross-DPT activity, increasing from 9 actors at T1 to 13 actors at T3, indicating their critical role in fostering limited but critical cross-DPT collaborations. University partners, though smaller in number, showed a steady increase in between-DPT ties, from 0 at T1 to 7 at T3, reflecting their growing but still secondary role in connecting DPTs.
In contrast, other roles, including state and community actors, exhibited negligible or no cross-DPT connections, which suggests their focus on localized collaborations within their respective DPTs. The data on “within-DPT activity” in Figure 4 reinforce this observation, with a significant and consistent majority of actors across roles maintaining ties exclusively within their own DPTs.
These findings suggest that while university partners are expanding their bridging role, the ECPI network remains primarily structured around independent DPTs. District actors dominate both within- and between-DPT collaborations, supporting the operational cohesion of their DPTs and the broader network. The limited cross-DPT connections underscore the importance of DPTs as localized hubs for district-university partnership development, reflecting the ECPI framework’s emphasis on mesosystem-level interactions.
Qualitative data insights
Factors that supported the development of district -university partnerships
In this section, we leverage the insights from the qualitative data to help explain the patterns described in the previous section and provide important background information. This section addresses research question #2: What key factors shaped the evolution of these partnerships? We highlight three factors: (1) the lack of turnover among university partners, (2) a shared sense of urgency around equity, and (3) the existence of externally imposed collaboration structures. The findings reported here focus on the mesosystem, and where relevant illustrate ways in which the exosystem impacted relations within the DPT.
At the meso-level, our documentation of participants in DPT meetings in the first 2.5 years of the grant indicates that the composition of the university partner teams did not change considerably over time. All higher education institutions engaged in the grant remained the same, and only two partners left (one for personal reasons, and one because of retirement). The university partner representation in the DPTs was therefore stable, with the individuals who were engaged at the beginning of the grant generally still being involved, and in some cases inviting others to join them.
The exploration of interviews that we conducted with all university partners suggests that one of the main reasons for the stability in the actors engaged in the ECPI may have been the shared sense of urgency around improving the educational experiences of historically underserved students. The university partners were deeply committed to serving the district by preparing leaders who have the knowledge and skills to advance equity. As one partner put it, “I’m just thrilled to be part of this work. And I think that we can really make an impact” (interview, 03/23). The strong commitment to improving the educational experiences and wellbeing of historically underserved students helped promote a sense of trust between the district and university partners. In the words of one partner, “Every time we meet, as a [District Partnership] Team, there’s just a large amount of trust with that team” (interview, 9/22).
The sense of “trust and genuine commitment” are a key factor in promoting inter-organizational collaboration (e.g. Popp et al., 2014). The ECPI’s focus on equity at the exo-level seems to have contributed to this sense of trust in all DPTs at the meso-level. The initiative’s focus on equity was also a product of the priorities of the funder, which were shaped by macrosystem commitments to addressing disparities in outcomes and educational opportunities for historically marginalized children and youth.
The expectations that were part of the ECPI supported the deepening of collaborative relationships between the districts and their university partners as well. One such expectation was that all university partners would go through a rigorous self-assessment process for the purpose of strengthening the equity focus of their programs. The tool that the university partners used for this self-assessment was Quality Measures. (This tool was developed with support from the Wallace Foundation.) All university partners were encouraged to involve district staff in this process, and they completed it in the summer or fall of 2022. While our interviews with university partners suggest that the extent of district engagement in this process varied, in general the Quality Measures process provided a formal context for district staff to shape university program redesign and boosted district-university collaboration. The following excerpts illustrate the ways in which two university partners described the impact of the self-assessment process on their collaboration.
Excerpt 1: “the perspective of [the district] from the standpoint of what they are seeing and what they are seeing isn’t happening particularly with leaders and what’s missing. I think that certainly will be very helpful in designing our program and, even in the very beginning with just doing Quality Measures, they were part of that” (interview, 08/22).
Excerpt 2: In a more official sense, a couple of the city schools folks are on our quality measures, self-study team. So that’s provided another point of overlap for us (interview, 09/22).
The Quality Measures process is an example of how structures that originated at the exo-level as ECPI-wide expectations strengthen meso-level collaborative relationships. More specifically, the formal context of the Quality Measures extended the boundaries of meso-level interactions beyond DPT meetings. They enabled district and university DPT members to collaborate around the redesign of university programs, thus strengthening the relationships between the two institutions (district and university). In the following section, we describe the outcomes of this collaboration and the specific changes that university partners made to their programming.
Tangible outcomes of district-university collaboration
In this section, we address the third research question: What tangible outcomes resulted from the partnerships? We illustrate that the district-university partnerships were consequential for the development of new structures and practices. We use two criteria to explore the impact of the partnerships: the involvement of the university partners in activities that go beyond preservice leader preparation, and the establishment of district-specific preparation programs by university partners. These examples illustrate how the original mesosystem of the DPT gave rise to other mesosystem collaborative contexts within both the district and the university. The expansion of mesosystem collaborative context matters because it is an indication of the sustainability of partnerships beyond the scope of the grant.
In all districts but one, the work of the university partners expanded beyond leader preparation (see Table 3). Importantly, these activities point to new areas of collaboration within the district and the university. An example of a new collaborative context within the district is the engagement of university partners in the development of principal supervisors. An instance of a new collaborative context within the university is the use of the district’s principal selection tool in candidate selection for the university’s leader preparation program. These findings illustrate the expansion of the mesosystem from the DPT to other areas of joint work that are located across partner institutions.
University partner engagement beyond leader preparation
| District | Area of work | Description |
|---|---|---|
| 1 | Equity-centered leader definition, community engagement | Used a design thinking approach to gather information from school staff about what an equity-centered leader is |
| 2 | Professional learning | Facilitated a summer institute for district principals and assistant principals |
| 3 | Professional learning | Designed an EdD program for sitting leaders |
| 4 | Professional learning | Provided a coaching program for district leaders |
| 5 | Equity-centered leader definition | Informed the development of the district’s equity-centered leader definition through weekly collaborative meetings |
| 6 | Sustaining systems: Building coherence across systems | Incorporated the district’s principal selection tool into its process for selecting program candidates, and engaged district staff in its candidate selection process |
| 7 | Principal supervision | Engaged principal supervisors in professional learning, including through an autoethnography project |
| District | Area of work | Description |
|---|---|---|
| 1 | Equity-centered leader definition, community engagement | Used a design thinking approach to gather information from school staff about what an equity-centered leader is |
| 2 | Professional learning | Facilitated a summer institute for district principals and assistant principals |
| 3 | Professional learning | Designed an EdD program for sitting leaders |
| 4 | Professional learning | Provided a coaching program for district leaders |
| 5 | Equity-centered leader definition | Informed the development of the district’s equity-centered leader definition through weekly collaborative meetings |
| 6 | Sustaining systems: Building coherence across systems | Incorporated the district’s principal selection tool into its process for selecting program candidates, and engaged district staff in its candidate selection process |
| 7 | Principal supervision | Engaged principal supervisors in professional learning, including through an autoethnography project |
Source(s): Authors’ own creation
The second criteria we used to determine the impact of the collaborative relationships was the establishment of district-specific leader preparation programs by the university partners. In more than half of the districts, the university partners launched district-specific cohorts of aspiring leaders by the end of Year 2. The university partners in all districts launched new cohorts of aspiring leaders in Year 3 (fall 2023 to summer 2024). The design and implementation of such programs was one of the main goals of the ECPI.
For many of the institutes of higher education, the equity-focused redesign of their programs involved close collaboration with the district partner. Each partnership seemed to have distinctive features. Some examples from different DPTs include:
- (1)
The university partner used the district’s equity-focused screener to select candidates for their program, and the district’s equity definition to inform the coaching that its candidates received during the program.
- (2)
The university partner designed a district-specific version of its program by working closely with the district partner. This work involved travel to the district, regular planning meetings between the district-based coordinator and district staff, and collaborative examination of student work. In addition, the partnership built the capacity of district staff to teach in the program by paying them to audit specific courses.
- (3)
The university partner incorporated the district’s classroom observation protocol into the clinical experiences of its students, and organized meetings between the students and principal supervisors in the district so the students could receive feedback on their growth as school leaders.
We interpret the two activities highlighted in this section as an indication that relationships between partners may be sustained beyond the scope of the grant. The expansion of partnerships across a range of tasks suggests that both partners are establishing new meso-level structures of communication and collaboration. The creation of district-specific programs also indicates that the university partners have become more fully integrated into the districts’ leader pathways. This integration may enable the partners to sustain the relationship even when additional funding is not available, because it would have already become mutually beneficial.
Implications and conclusion
Our study explores the evolution of district-university partnerships within the context of an equity-centered grant initiative, leveraging an ecological framework to understand how these relationships developed across multiple system levels. The social network analysis demonstrates that while the number of university partners remained relatively stable over the first two and half years of the initiative, their role became increasingly central and influential. The qualitative analysis helps explain these patterns by identifying three key factors that supported the development of district-university partnerships: stability in university partner participation (with only two partners leaving across all districts), shared commitment to equity, and externally imposed collaboration structures like the Quality Measures process. These factors contributed to the establishment of trust between partners and supported sustained engagement in collaborative work.
Our mixed-methods analysis contributes several key insights about the nature and development of these partnerships. The thorough exploration of the evolution of networks at the exo-, macro-, and micro-level illustrates that strong, reciprocal relationships between the districts and university partners took at least two years to emerge. Collaborative relationships between the partners increased even as the actual number of university partners engaged in the initiative remained relatively constant. In addition, our analysis suggests that the university partners connected different clusters of actors. In other words, the university partners played the important role of brokers, thus increasing the access of district staff to relevant resources and expertise.
It seems important, therefore, to approach district-university partnerships as long-term endeavors. Embarking on district-university partnerships seems to require consistency, plans for minimizing staff turnover, and mechanisms for knowledge transfer to new partners. This may include onboarding processes or collaboration tools that can help maintain continuity even when staffing changes occur. From a policy standpoint, it may be important for policy makers to invest in multi-year programs that allow scaffolding of objectives and provide the space for partnerships to evolve. Equity metrics could help guide district-university partnerships in adopting meaningful policies that address disparities in leadership preparation and school outcomes. Policymakers can help encourage cross-sector collaborations by establishing regional or statewide networks that connect additional districts and universities engaged in leadership pipeline initiatives to share best practices and provide opportunities for collective problem solving.
Another key insight is that the partnerships benefitted from organic as well as formal collaborative structures. The self-assessment process in which the university partners participated, for instance, was required by the funder and deliberately created a space in which district staff could be engaged in the process of revising university leader preparation programs. It may be important for district staff, university staff, and policy makers to consider how they can strengthen and sustain a district-university partnership through spaces in which collaboration naturally evolves as well as more formal structures for collaboration.
A third important implication of our analysis is that both districts and universities play important roles in equity-centered leader preparation. The creation of new mesosystem spaces in which district and university partners come together supports both institutions in advancing equity in schools. Such collaboration seems to strengthen university leader preparation programs by making them more responsive to districts’ equity needs (in terms of both leader demographics and leader knowledge and skills), more aligned with districts’ equity priorities, and more coherent in their internal emphasis on equity. Districts, on the other hand, benefit from university partners’ expertise and research related to leadership for equity, and from increased access to leaders who are well prepared to recognize and address educational disparities in schools. Equity-centered leader preparation seems to be a rich and important area of district-university collaboration.
Future research might examine how these partnerships continue to evolve beyond the initial phase documented here, particularly investigating whether the increased centrality and brokering roles of university partners persist after the conclusion of the grant initiative. Studies could also explore how the variations in partnership structures across districts (from formal program redesign to collaborative candidate selection) impact the preparation of equity-centered leaders. Additionally, longitudinal research could investigate whether these strengthened partnerships ultimately influence principal effectiveness and school-level equity outcomes. Finally, future research could explore the durability of district-university partnerships and the role of external funding on contextual factors such as district size and capacity, resource availability, and overall policy environments that influence the success of different partnership structures.
This analysis would not be complete without a discussion of limitations. We address limitations related to the survey data first, and those related to the qualitative data second. One key limitation of the survey data is survey respondents’ evolving understanding of the nature and importance of the social network survey and analysis. At the beginning of the initiative, very few (if any) of the respondents were familiar with this type of analysis. Therefore, many did not fill out the survey because they did not consider it relevant. Another limitation is the burden of filling out the survey. Describing each collaborative relationship a person has is time-consuming, and the principal pipeline model is complex. This meant that if we wanted to gain an accurate picture of the tasks in which the DPTs were engaged, we needed to ask many questions (fourteen to be exact). A third limitation of the survey was that it was administered in different settings over which we had little control. The schedule of the ECPI convenings was determined by the Wallace Foundation. (The survey was administered during such convenings at T1 and T3.) In some cases this schedule was conducive to the cadence of survey administration, and in some cases it was not. At T2, when we administered the survey during the regularly occurring monthly DPT meetings, the time that we respondents had available depended on the flow of the meeting and varied considerably across DPTs.
The qualitative analysis also has a number of limitations. Our work with the DPTs began at the onset of the initiative, and in Year 1 most of the contact between us and the teams was virtual. Even as our knowledge of each team increased steadily with each meeting we observed, that knowledge remained narrow and related primarily to the work on the grant initiative. We do not fully understand the equity-related work that each district had done prior to the initiative, and our grasp on the equity assets and challenges of each district is limited.
This research was made possible by support from the Wallace Foundation. The opinions described herein are solely those of the authors. We want to express our deep appreciation for all participants, who devoted time and energy to supporting our research.
The first two authors contributed equally to the work and led the conceptualization and analysis of the study.
Notes
RSiena results indicate that tie formation within the DPT-wide network is significantly influenced by shared DPT affiliation and actor roles over time. The results also indicate that actors with higher outdegree are increasingly active in initiating connections over time ( Appendix).
References
Appendix
RSiena parameter estimates and standard error for the effects on University partners’ DPI-wide network change over time
| Period 1: T1–T2 | Period 2: T2–T3 | |||
|---|---|---|---|---|
| Effect | Parameter estimate | Standard error | Parameter estimate | Standard error |
| Rate 1 | 23.236 | 8.112 | 200.144 | 31.704 |
| Outdegree (density) | −5.139*** | 0.275 | −3.553*** | 0.210 |
| Reciprocity | −2.237*** | 0.251 | 1.827*** | 0.358 |
| Transitive triplets | 0.506*** | 0.136 | 0.234*** | 0.049 |
| Transitive reciprocated triplets | −0.282 | 0.250 | ||
| Indegree popularity | 0.053 | 0.044 | ||
| Outdegree popularity | 0.162** | 0.085 | −0.170*** | 0.022 |
| Outdegree activity | 0.042** | 0.015 | −0.006 | 0.009 |
| Out isolate | 4.896*** | 0.376 | ||
| Same role | 0.311** | 0.090 | 0.225*** | 0.053 |
| Same DPT | 2.459*** | 0.226 | 2.765*** | 0.162 |
| Stayer alter | 0.590** | 0.166 | 0.493*** | 0.132 |
| Stayer ego | 0.284† | 0.113 | −0.094 | 0.079 |
| Same stayer | 0.284* | 0.113 | 0.083 | 0.070 |
| Period 1: T1–T2 | Period 2: T2–T3 | |||
|---|---|---|---|---|
| Effect | Parameter estimate | Standard error | Parameter estimate | Standard error |
| Rate 1 | 23.236 | 8.112 | 200.144 | 31.704 |
| Outdegree (density) | −5.139*** | 0.275 | −3.553*** | 0.210 |
| Reciprocity | −2.237*** | 0.251 | 1.827*** | 0.358 |
| Transitive triplets | 0.506*** | 0.136 | 0.234*** | 0.049 |
| Transitive reciprocated triplets | −0.282 | 0.250 | ||
| Indegree popularity | 0.053 | 0.044 | ||
| Outdegree popularity | 0.162** | 0.085 | −0.170*** | 0.022 |
| Outdegree activity | 0.042** | 0.015 | −0.006 | 0.009 |
| Out isolate | 4.896*** | 0.376 | ||
| Same role | 0.311** | 0.090 | 0.225*** | 0.053 |
| Same DPT | 2.459*** | 0.226 | 2.765*** | 0.162 |
| Stayer alter | 0.590** | 0.166 | 0.493*** | 0.132 |
| Stayer ego | 0.284† | 0.113 | −0.094 | 0.079 |
| Same stayer | 0.284* | 0.113 | 0.083 | 0.070 |
Note(s): Period 1:’ Modeling with 4,383 iteration steps. Convergence t ratios all <0.1. Overall maximum convergence ratio = 0.1664. Model 2: Modeling with 6,362 iteration steps. Convergence t ratios all <0.1. Overall maximum convergence ratio = 0.1234. †p < 0.1; *p < 0.05; **p < 0.01; ***p < 0.001
Source(s): Authors’ own creation





