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PROFESSIONAL FILE ARTICLE 136

© Copyright 2015, Association for Institutional Research APPLICATIONS OF IN INSTITUTIONAL RESEARCH

Ning Wang better served. Traditional descriptive publications, faculty collaboration and inferential statistics, from simple on research projects, peer influence About the Author frequencies and cross-tabulations, among students with specific ethnic Ning Wang is the Director of to the whole family of regressions, or social backgrounds, mentorship Institutional Research at University of to more-advanced techniques such between faculty members and California, San Francisco. as survival analysis and structural students, formation of learning equation modeling, have sufficiently communities among students with Abstract fulfilled a large part of IR’s analytical shared academic interests, and so forth. (SNA), with functionality. At the same time, the Relations also extend beyond people: its distinct perspective on studying large amount of data found in IR for example, majors within a discipline relations and its exceptional capability and the nature of IR research that are interrelated by overlapping course to visualize data, should be embraced emphasizes identification of patterns, offerings, colleges and universities are by institutional researchers as a predictions, and possible interventions, interrelated by students transferring promising new research methodology coupled with high-capacity in and out, and states form a network complementary to inferential and such as SAS, have made exploratory through out-of-state student exploratory statistics. This article statistics a new frontier in IR. The recent enrollment. introduces SNA through discussion of interest in and predictive three analytical studies on topics highly modeling exemplifies this shift. Such networks of relations are relevant to institutional research (IR): extensive in higher education, but few (1) double-majors, (2) gatekeeping However, a missing piece of IR analytics studies have addressed their dynamics courses, and (3) STEM pipeline leaking. is the study of relations. Traditional and implications, partly because of The unique approach of SNA in statistical methods assume the the methodological limitations of exploring, analyzing, and presenting observation independence—that is, inferential and exploratory statistics. data has great potential for advancing they assume that observations of a As Wasserman and Faust (1994) in their IR’s analytical capacity. study are not related to one another, classic book of social network analysis but rather can be independently (SNA) stated, “The focus on relations, INTRODUCTION examined by various internal and and the patterns of relations, requires external attributes (Chen & Zhu, a set of methods and analytic concepts Institutional research (IR) professionals 2001). The observations in higher that are distinct from the methods of frequently adopt new analytical tools education settings, however, often traditional statistics and data analysis” and research methodologies. This has are not independent. The activities (p. 3). The inadequate understanding allowed more sophisticated studies of higher education and the people of relations and interactions among to be carried out that better inform involved are relational and interactive the various entities in higher education ’ policy making, which leads in nature. Examples of these activities calls for the addition of network in the long term to students being include co-authorship of scholarly analysis into IR’s analytical paradigm.

SPRING 2015 VOLUME | PAGE 1 At the intersection of inferential This article introduces SNA to the IR undirected graph, weight, , statistics, exploratory statistics, and community. As a well-established and . network analysis is data visualization— method that has been widely used in or the representation of data through social sciences, SNA can contribute Borrowed from , the graphical means. However, “data a great deal to IR with its unique interconnected objects in SNA visualization . . . involves more than perspective on relations and its power are represented by mathematical just representing data in a graphical in visual presentation. The following abstractions called vertices (more form (instead of using a table). The will (1) introduce basic concepts in commonly called nodes), while the information behind the data should SNA, (2) present three studies that links that connect some pairs of nodes also be revealed in a good display; used SNA, and (3) discuss issues key to are called edges. The number of edges the graphic should aid the readers or successfully applying SNA in IR. incident upon a node is defined as viewers in seeing the structure in the . Typically, a graph is depicted data” (Chen, Härdle, & Unwin, 2008, SOCIAL NETWORK in diagrammatic form as a set of dots p. 6). As the well-known statistician for the nodes, joined by lines or curves and pioneer in data visualization ANALYSIS AND ITS for the edges. When applied to a study, Edward Tufte stated, “At their best, BASIC CONCEPTS nodes represent the observations graphics are instruments for reasoning SNA is inherently an interdisciplinary of a study, and edges represent the about quantitative information. . . . Of endeavor that uses , relations between the observations all methods for analyzing and , statistics, and graph of a study. If the relations are initiated communicating statistical information, theory. Beginning in the 1970s, from certain observations to others, well-designed data graphics are usually the empirical study of various the edges would be represented the simplest and at the same time the networks has played an increasingly with arrows from the initiators to the most powerful” (Tufte, 2001, p. 13). important role in the social sciences. receivers, and the graph would be Among many of its applications, directed. Conversely, if the relations Founded on graph theory, network SNA has been used to understand between two observations are mutual, analysis is exceptionally well developed the , the the edge would be represented with in generating meaningful and communication of news, the spread a line segment connecting the two, intriguing visual representations of of diseases, the culture and structure and the graph would be undirected. data. While charts and graphs are of social organizations and business A graph is weighted if a value or a integral components of inferential and corporations, the formation of political weight is assigned to each edge. exploratory statistics, graphics is at the views and affiliations, and so forth Depending on the problem at hand, heart of network analysis. It is the way (Carrington, Scott, & Wasserman, such weights might represent a diverse that an underlying network structure 2005). More recently SNA has gained set of attributes of the relationship can be uncovered, while at the significant use in studying online (Hanneman & Riddle, 2005). same time providing the vocabulary communities and such as through which network properties and . For demonstration, Figure 1 is can be described. At a time when a weighted undirected graph effective communication of findings The complicated mathematical representing a hypothetical network to institutions’ administrators and background of SNA is beyond the of faculty collaboration. Nodes 1–10 other constituents is more important scope of this article. However, it would are faculty members. Edges exist than ever to further data-driven be helpful to explain in simple terms between those who collaborated and research-based policy making, several basic yet essential concepts on grant proposals, and weights on network analysis, with its expertise in used in the examples of analytical the edges denote the number of data visualization, can be especially works described in this paper: vertice grant proposals that the two faculty beneficial to IR. or node, edge, degree, directed and members submitted together. As seen

PAGE 2 | SPRING 2015 VOLUME degree, closeness, and betweenness. Degree centrality is defined as the number of edges that a node has. The nodes having higher degrees are related to other nodes, and therefore are at positions in the network that are more central. emphasizes the of a node to all other nodes in the network. focuses on the position of a node between pairs of nodes. The higher betweenness of a node means more nodes depend on it to make connections with other nodes. Centrality can be evaluated with a set of statistics, such as Freeman Degree Centrality, Geodesic Distances, , Hierarchical Reduction, and so forth (Hanneman & Riddle, 2005). This article does not attempt to elaborate on details of these statistics; the readers are encouraged to obtain more information (e.g., Figure 1. Demonstration of Basic Concepts in Social Network Analysis Carrington et al., 2005; Chen et al., 2008; Tufte, 1990, 2001; Wasserman & Faust, 1994). The output of the in the graph, Faculty 2 worked with measure is to compute the difference above-mentioned statistics for the Faculty 1 once, with Faculty 5 once, between the number of edges falling hypothetical network in Figure 1 is and with Faculty 3 three times on within groups and the expected provided in Table 1 (next page). grant proposals; the node representing number of edges in an equivalent Faculty 2, therefore, has a degree of network where edges are placed at For SNA, however, the statistics are three and a weighted degree of five. random (Newman & Girvan, 2004). often not the end product. Unlike Large differences would indicate nodes inferential and exploratory statistics, Modularity is one important measure being densely interconnected while the graphs in SNA are at the core of the network structure. It divides being only sparsely connected with the of explaining and understanding a network into modules, also called rest of the network—in other words, findings, as the relational statistics groups, clusters, or communities. forming modules. Network analysis are incorporated into graphs through Networks possessing community software can generate this measure the visualization process. Figure structures function differently from and partition the network by its 1 shows two modules; Module A, average networks, so identification underlying community structures. consisting of faculty members 1 of such community structures can through5 and faculty member 10, have substantial importance in Centrality is another important and Module B, consisting of faculty understanding the dynamics and measure, examining the relative members 6 through9. Members of properties of the network. The importance of a node within a graph. each module worked more frequently mathematical idea of the modularity There are three main types of centrality: within rather than across the modules.

SPRING 2015 VOLUME | PAGE 3 Table 1. Demonstration of Basic Relational Statistics Output in Social Network Analysis

Id Label Modularity Degree Weighted Closeness Betweenness Eigenvector Class Degree Centrality Centrality Centrality

1 Faculty 1 0 2 3 0.47 0.00 0.44

2 Faculty 2 0 3 5 0.50 0.01 0.57

3 Faculty 3 0 3 6 0.53 0.03 0.59

4 Faculty 4 0 3 4 0.53 0.22 0.49

5 Faculty 5 0 6 7 0.75 0.65 1.00

6 Faculty 6 1 4 6 0.60 0.18 0.71

7 Faculty 7 1 4 7 0.60 0.18 0.71

8 Faculty 8 1 2 3 0.41 0.00 0.40

9 Faculty 9 1 2 4 0.41 0.00 0.40

10 Faculty 10 0 1 1 0.36 0.00 0.14

Faculty 5 worked mainly with faculty Degree of 7), as a good collaborator failed before dropping out of the 1 through4, but also worked once with all other researchers by the high ; and (3) a study of STEM with faculty6 and once with faculty closeness centrality (shown in Table (science, technology, engineering, 7, thus bridging the two modules. 1 as 0.75), and as the key person for and mathematics) pipeline leaking A closer look at the departmental promoting interdisciplinarity between that examined students who started affiliation shows that faculty in Module the two fields by the high betweenness in STEM majors but subsequently A are from the department, centrality (shown in Table 1 as 0.65). graduated in non-STEM majors. and faculty in Module B are from the psychology department. Faculty5, APPLICATION OF The three studies were conducted a professor in biology, has research using the open source software Gephi interests in neuroscience and has SOCIAL NETWORK (http://gephi.org). As a tool specifically actively collaborated with professors in ANALYSIS IN THREE developed for network analysis, Gephi psychology. Faculty 10 is a statistician STUDIES has at its core a set of , called from the mathematics department layouts, that detect and generate who built a collegial relationship with This section will describe the graphical representations of network Faculty 4 and who was once asked to application of SNA through three structures. The layout ForceAtlas, for work with him on a grant. examples of small-scale analytical work: example, probably the most used (1) a study of double-majors that used force-directed layout, simulates It can also be observed that Faculty 5 is the modularity measure of SNA to a physical system in which nodes at the center of the network in all three reveal the connectivity among majors repulse each other like magnets, while centrality measurements. Faculty 5 is that can inform student advising; edges attract their nodes like springs. identified as an active researcher in the (2) a study of gatekeeping courses These forces create a movement that two fields of biology and psychology that used the measure of centrality to eventually converges to a balanced by the high degree centrality (shown identify major-specific and general- state of spatialization of the nodes in Table 1 as Degree of 6 and Weighted education courses that students and edges, revealing the structure and

PAGE 4 | SPRING 2015 VOLUME features of the network. Layouts have their specialties that suit networks of different sizes and emphasize different features. Layouts such as ForceAtlas2 and OpenOrd work with big networks, Circular and Radial Axis emphasize ranking, and GeoLayout uses latitude/ longitude coordinates to visualize geographical networks.

The software also provides calculations of relational statistics unique to network analysis. Measures for modularity and centrality, among other statistics, can be generated with relative ease. The statistics can then be used in visualization; for example, the computed modularity allows partitioning of nodes into groups and reveals the of the network. The statistics can also be saved into the data set and used in Figure 2. Double-Major Combinations of Bachelor’s Degree Recipients other statistical analysis; for example, the eigenvalue for centrality of each Five years (2009–13) of undergraduate employed. Three areas of study observation can be a new predictive degree data were compiled to ensure appeared prominently in the graph variable in a regression model. adequate sample size and to minimize where double-majors concentrated— fluctuations over the years. The data /business, arts/humanities, Graphs generated through Gephi are file contained majors, combinations and biological sciences/psychology. the main tool used to present findings of double-majors, and the number Four free-standing yet strongly tied of the three studies. Main features of students awarded degrees in each pairs of majors were also identified— are shown, while detailed institution- double-major. After applying the international affairs/, specific figures that could have been layout of ForceAtlas, the housing/consumer economics, exercise shown as labels accompanying the partitioning based on the statistics and sport science/athletic training, and nodes and edges are removed from of modularity, and the filtering that consumer foods/dietetics. Clustering the graphs. eliminated majors with fewer than of majors into groups provides an five students graduating with double- empirical verification that double- Study 1: Double-Majors majors every year over the study majors occur most often within Many college students concurrently period, a network structure emerged disciplines where connectivity between pursue studies in two or more majors. with more than 1,500 baccalaureate course offerings, degree requirements, Faculty and student advisors may graduates in two of the approximately and administrative procedures anecdotally know some of the popular 40 or (Figure 2). facilitates the pursuit of double-majors. combinations of majors in their The font size of the major titles is discipline; IR analysts, however, would Majors clustered into groups based on proportionate to the weighted degree want to approach the phenomenon of their connections with one another of the major—that is, the number double-major with empirical evidence. after the modularity measure was of students in this major who also

SPRING 2015 VOLUME | PAGE 5 graduated with a degree in another major. It can be seen that finance, psychology, biology, international business, and economics had the most students graduating with double- majors. The thickness of the edges is proportionate to the number of students taking on the corresponding pair of majors. It is then observed that over the five-year period psychology/ biology, housing/consumer economics, international affairs/political science, finance/international business, and finance/economics were the top five most popular double-major combinations.

As Edward Tufte (2001) stated, “Modern data graphics can do much more than simply substitute for small statistical tables” (p. 9). The visual presentation in Figure 2 of the double-major data not only conveys information in a more coherent and succinct fashion than a tabular presentation, but also reveals the data at multiple levels not conveniently available in table form. It provides a broad overview of the areas of study within which double-majors tend to form, as well as the details of specific majors and major combinations. Figure 3. Failing Courses and Last Major of Undergraduate Dropouts As groupings of majors surface through the modularity measure of SNA, more insights emerge. . These patterns Study 2: Gatekeeping Courses This study tracked students from four of double-majors that graduates Entry-level gatekeeping courses have first-time, full-time freshmen cohorts have successfully followed can serve been known to pose challenges to (Fall 2004–Fall 2007) to identify as evidence for student advisors students and to potentially lead to dropouts—those who had neither in their discussions with students attrition, particularly in STEM majors. graduated nor remained enrolled six contemplating taking on another major It is very important for institutions years after their initial matriculation. of study. University administrators focused on retaining and engaging For those dropouts who had failing might want to strengthen existing students to help those students grades on record, the failed courses partnerships or explore new linkages succeed in courses that most frequently and the majors that they last enrolled between majors to enrich students’ serve as gatekeepers. Identification of in before leaving the institution were educational experiences and promote these courses is inevitably the first step. compiled. Over 1,500 students from 17 their future employability.

PAGE 6 | SPRING 2015 VOLUME majors with 42 potential gatekeeping centrality in this course-major network. graph. Perhaps factors like a large- courses were included in the study. Failing of certain major-specific courses lecture form of pedagogy, one-way was potentially related to dropping passive learning, or an emphasis Figure 3 is the visual representation out of these majors. For example, on memorization over critical of relations between failed courses, two foundation courses in computer thinking, might have contributed indicated by green nodes, and last science, Systems Programming to the students’ failings. Strategies majors, indicated by red nodes. Plotting [CSCI1730] and Discrete Mathematics could then be developed to engage was based on the degree centrality for [CSCI2610], both the faculty and the students of the majors in this course-major were probably weeding out students. to change these gatekeepers into network. The star network at the center An introductory accounting course, gateways of student success. The of the graph made it clear that most Principles of Accounting I [ACCT2101] department head of biology might of the dropouts left the institution and an introductory economics learn from the graph that for students with an unspecified major—in other course, Principles of Macroeconomics intending to major in biology, words, they left early in their college [ECON2105], were stumbling blocks Freshman Chemistry I (CHEM1211) life before declaring a major—and for some students in prebusiness. The and II (CHEM1212) together with the many courses surrounding the introductory statistics course [STAT2000] Principles of Biology I (BIOL1107) were unspecified major were the failed might have been a source of struggle for the most challenging courses, and courses that could be potential some students with sociology, speech that for students who succeeded in hurdles to student retention. Among communication, international affairs, these courses and officially enrolled them, five introductory courses— and psychology majors. in biology as a major, the next set of Precalculus (MATH1113), American courses in the sequence—Modern Government (POLS1101), Elementary One of the principles that Tufte (1990) Organic Chemistry I (CHEM2211) Psychology (PSYC1101), Freshman suggested for the good practice of and II (CHEM2212), and Principles Chemistry I (CHEM1211), and Basic statistical graphics is “enhancing of Biology II (BIOL1108)—were road Concepts in Biology (BIOL1103)—have the dimensionality and density of blocks. A long-term plan focusing on prominent edges in the graph. The portrayals of information” (p. 9). building a solid foundation for further thickness of the edges between these Figure 3 combined three dimensions study in this major may be needed. courses and the unspecified major of information—the gatekeeping Curriculum and pedagogy designed is proportionate to the number of courses, the majors that lost students, with intentional sequencing may help students with an unspecified major and the relationship between majors ensure adequate preparation and who failed these courses. Furthermore, and courses—in one graph, while smooth transition of students for each these five courses were actually the the same information in tabular form section of the course sequence. most challenging for students from would have been cumbersome and all majors, as indicated by the size lacked clarity. Instead of providing Study 3: STEM Pipeline Leaking of their title in the figure. The size is an isolated view of students and Government, educators, and industry proportionate to the total number courses confined to a specific major, leaders have long been concerned of students who failed these courses Figure 3 allows examination of more about STEM pipeline leaking, where regardless of their major. comprehensive course-taking patterns students depart from academic and across majors. More importantly, career paths in science, technology, The university also lost students in the the graph vividly points to possible engineering, and mathmatics. other red-node majors—computer directions for further investigation According to the BusinessHigher science, prebusiness, psychology, and action. University administrators Education Forum (2010), only 4 percent biology, and so forth. These majors might want to evaluate teaching of the 4 million ninth-graders in the are located on the periphery of the and learning in the five introductory United States in 2001 would be STEM graph because of their relatively low courses revealed as gatekeepers in the college graduates by 2011. This study

SPRING 2015 VOLUME | PAGE 7 attempted to revealan aspect of the leakage along the STEM pipelineby identifying undergraduate students in STEM majors who changed their academic pursuit to non-STEM majors.

Students from five first-time full-time freshmen cohorts (Fall 2003–Fall 2007) were tracked through fiscal year 2013 for bachelor’s degree attainment. Those who first declared a major in STEM (based on the National Science Foundation definition) and later graduated in non-STEM majors, and whose major GPA was 3.0 or above when leaving STEM, constituted the group for this study.

A using the Circular Figure 4. STEM Major Students Graduating in Non-STEM Majors Layout was built to show the migration between majors. For focus and clarity, only STEM majors with ten or more in STEM majors at the institution is science in family and consumer students in the five freshmen cohorts illuminated. The graph does not intend sciences; and so on.. Certificate who later graduated in non-STEM to address the many facets of the programs can be another option—for majors were retained. The results in issue, but rather to show the non- example, a certificate program in Figure 4 represent about 800 students STEM destinations for STEM majors science journalism could be an option in eight starting STEM majors who who were in solid academic standing for students in biology or chemistry graduated in ten non-STEM fields. The in their STEM major. These students who are also interested in journalism; blue nodes on the left side represent might intend to pursue postgraduate a program in math education could be starting STEM majors, sorted and sized professional programs, or plan for an option for mathematics students by the number of students leaving for careers other than basic research, or who have an interest in education; or a any non-STEM major. The yellow nodes simply want to explore studies beyond program in health promotion could be on the right side represent ending non- STEM. Instead of a divisive view of a good fit for biology students aspiring STEM majors classified into disciplines STEM versus non-STEM, the linkages in to a career in health professions. If the by the first two digits of the major CIP the graph present an opportunity for demanding workload of a STEM major code, sorted and sized by the number cooperation between the two fields. prohibits formal pursuit of another of students transferring in from all area of study, an area of emphasis STEM majors. The thickness of the edge A major-minor partnership can be that blends in courses from a relevant between two nodes is proportionate one way to the two fields. non-STEM major may meet students’ to the number of students changing Possibilities exist for interdisciplinary needs. Other possibilities may include majors. collaboration between computer joint projects or the incorporation of science and management information governmental, societal, or cultural Figure 4 is mainly descriptive. By systems in business; mathematics and implications of science and technology mapping the migration of students, econometrics or finance in business; into the teaching of STEM. the status of retention and persistence biology and dietetics study or nutrition

PAGE 8 | SPRING 2015 VOLUME Figure 4 illustrates many opportunities in an online learning environment of them can achieve balance between to bridge the gap between STEM (Dawson, 2010); peer influence on information accuracy and visual and non-STEM, and suggests the student persistence and retention attractiveness, and can ultimately need for an orchestrated effort from (Eckles & Stradley, 2012; Thomas, facilitate understanding of the data. departments on both sides to foster a 2000); the extent to which size and The graph should lead the viewer campus-wide culture change geared density of a student’s social network to think about the substance and to to encourage students to stay in STEM predict academic achievement see the differences, rather than be without missing opportunities present (Fletcher & Tienda, 2009; Skahill, distracted by the graphic design. Most in non-STEM fields. 2003); and the effect of roommate often, multiple aspects of the data and friend network on racial attitude set can be presented in one graph; a DISCUSSIONS and cultural competency (Levin, van clear focus serving a clear explanatory Laar, & Sidanius, 2003; van Laar, Levin, purpose is thus important for the graph In addition to the Gephi software that Sinclair, & Sidanius, 2005); faculty to be meaningful. Sometimes details was used to conduct the above three co-authorship and co-citation (Girvan are sacrificed to render the graph with studies, other open source software & Newman, 2002; Mählck & Persson, clarity; tabular and verbal descriptions for network analysis include UCINET, 2000; Otte & Rousseau, 2002; Perianes- of the data set then must be closely Pajek, and R. All offer functions such as Rodríguez, Olmeda-Gómez, & Moya- integrated with the graph for full importing and filtering data, visualizing Anegón, 2010). However, few studies reporting of the findings. And above and spatializing network structures, have been done on the formation of all, “an ill-specified model or a puny generating relational statistics, and network, or on the university social data set cannot be rescued by a visually manipulating and exporting graphic network as a whole in which the appealing graph” (Tufte, 2001, p. 13). presentations (Bastian, Heymann, & student network, the faculty network, Jacomy, 2009). Their flexible interfaces and the staff network interact. More SNA is not meant to replace inferential and interactive ways of analyzing data robust and varied studies on SNA and exploratory statistics, but make them accessible to IR analysts of are needed to enrich the literature in rather is a complement that greatly different levels. higher education in general and in IR enriches traditional model- building in particular. by allowing the study of unique There are two issues critical to the research questions concerning a successful application of SNA in The second issue is how to visually network type of relationships. IR has IR. First is an open mind that sees present the data with proper been a relative latecomer to network relations and tries the network functionality and aesthetic form. analysis. However, as more relational approach in conducting research on Excellence in data visualization data (e.g., institutional records, email topics old and new. Network analysis, lies in the delivery of patterns and corpora, online learning management especially, allows new leverage their implications uncovered from a systems, and social media Web sites) for answering traditional research data set in an intuitive, informative, are collected and become more easily questions in IR. Relational statistics and productive way, to improve accessible, IR researchers will have generated in SNA can provide understanding and encourage more opportunities to apply SNA and alternative explanations to traditional audience engagement (Friedman, thus to appreciate the unique insights theories, or can explain additional 2008). The various network analysis this method offers. SNA should emerge variance when they are being entered software products provide highly as an important tool as IR increasingly into established models. Studies that configurable layout algorithms for assumes the role of a local and national provide good examples of SNA include generating graphs, and tools for key player in educational statistics, work investigating social network and modifying the display parameters of analytics, and policy making. college students’ sense of community the graphs. They are readily available (Dawson, 2008); student networking to the analyst, but only the right use

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