Abstract
A network consists of a group of units where sets of connections may be observed. When these connections are recorded in social settings, a network is depicted as a social network. Nonetheless, a network is realized whenever researchers can offer feasible definitions of rules and boundaries for when these connections among units may be noted. This latter property enables networks to not be constrained to social settings, but rather to take place in an almost infinite set of contexts. The overarching goal of this chapter is to showcase some of these contexts and leverage the power of network analysis to unveil and model meaningful structures in (higher) education research. Accordingly, with the goal to strengthen the study of higher education, this chapter depicts the manners in which network principles are merged with geographical, statistical, and qualitative approaches to test innovative, timely, and relevant hypotheses. Examples of these tools are the analysis of dependence among units, wherein connections can be established considering measures of geographical and/or social proximity. The method-bridging properties resulting from network principles are also used to reveal the mathematical and dynamic structure contained in qualitative data. All the analyses can be freely replicated using the R code and data provided herein – some analyses rely on protected data, accordingly those data and its corresponding code are not included in this chapter but the code is available upon request.
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Notes
- 1.
This is also true for time. All the social and spatial analyses can incorporate spatio-temporal analyses, but these analyses are beyond the scope of the chapter due to space limitations. However, readers may see González Canché (2019c) for an example of this methodology applied to a difference and differences framework.
- 2.
In certain cases, like when dealing with the interconnection between social and spatial network analysis as detailed below, the weights of two-mode matrices are ignored, and such weights are treated as presence (cells with values greater that zero) or absence (cells with zero) of relationships before these transformations take place.
- 3.
- 4.
This example is not implying that gender is binary or constant but is simply used as an example of a possible characteristic of actors configuring the network.
- 5.
Visit https://nces.ed.gov/ipeds/datacenter/data/EF2016C.zip to directly access these data.
- 6.
For visualization purposes, when reading this edgelist as a network, analysts should execute an extra line of code g <− simplify(g), where g is the graph retrieved from Eq. (12.6) to remove self-loops or self-selections while keeping all isolated actors in the network.
- 7.
Vectorized figures in color can be accessed in the following link as those figures do not lose resolution and can be zoomed in: https://drive.google.com/file/d/11BBOhUdULZN4Kp-oiXh8gSU1yyV8n_6f/view?usp=sharing
- 8.
Once more, these procedures can be replicated using the code provided in the appendix.
- 9.
Cross-walk refers to a merging procedure where there is no direct link between datasets, but there is one intermediary dataset that contained a common key for this merging process to be conducted.
- 10.
The social network data analyzed herein is provided in the R code appendix available. Although the institution-level data cannot be shared, the code provided in the appendix will enable replication of such analyses when analysts apply these procedures to their own databases.
- 11.
Following Bivand et al. (2013), the zI score for the statistic is computed as: \( {\mathrm{z}}_{\mathrm{I}}=\frac{\mathrm{I}-\mathrm{E}\left[\mathrm{I}\right]}{\sqrt{\mathrm{V}\left[\mathrm{I}\right]}} \), where \( \mathrm{E}\left[\mathrm{I}\right]=\frac{-1}{\left(\mathrm{n}-1\right)},\mathrm{and}\ \mathrm{V}\left[\mathrm{I}\right]=\mathrm{E}\left[{\mathrm{I}}^2\right]-\mathrm{E}{\left[\mathrm{I}\right]}^2 \)
- 12.
See Bivand et al. (2013), for a detailed explanation of the process to deal with spatial dependence of the error terms in SAR.
- 13.
Another example of the use of lagged variables can be seen in González Canché (2014) who captured mean proportion of nonresident students attending neighboring institutions for institution i to test the hypothesis that this lagged indicator should be negatively associated with tuition prices charged to nonresident students at such an institution i. The rationale behind this hypothetical relationship was that, to the extent neighboring institutions attract more nonresident students, a given institution would be losing those students if such an institution makes no changes to the final tuition charges modified to attract nonresident students. A hypothesis that was corroborated. González Canché (2014) also tested for the proportion of neighboring institutions for institution i that were research intensive to test for the hypothesis that these institutions would help institution i increase its tuition prices given a spillover effect (González Canché, 2017d) of being located in close proximity to highly selective colleges who tend to charge higher tuition prices. This hypothesis was also corroborated.
- 14.
These analyses can be replicated with the code provided but the corresponding output table is not included herein due to space limitations.
- 15.
This form of bias becomes a problem when indicators that may be associated with the outcome of interest are not included in the model and therefore become part of the error term (as in the population, not the model residuals realized from our sample). It follows then that if at least one of these omitted indicators is correlated with an observed variable included in our models, then this observed variable will be correlated with the error terms which would bias our estimates.
- 16.
RQDA is a free and powerful version to conduct qualitative analysis. It can be found here http://rqda.r-forge.r-project.org/
- 17.
The qualitative codes were created from the written information contained in a set of interviews and followed a rigorous qualitative coding process. No differentiation of participants’ roles were performed when the codes were generated. After complete transcription of the interviews through open codes (Creswell & Creswell, 2017; S. Lewis, 2015) in NVivo (Charmaz, 2011) and process coding (Bogdan & Biklen, 2007) to highlight practices, interpretation, and activities. The codes identified were compared and refined through two additional rounds of review and deliberation. Redundant codes were collapsed to generate larger categories.
- 18.
Note that human actors are represented in squares and codes in circles. See color figures online as indicated in footnote 7.
- 19.
These exchanges can also be downloaded from this link https://drive.google.com/file/d/1-bXjtlgUJ3qbWTjFG6-dKUtEA522KVRB/view?usp=sharing
- 20.
See color version here https://drive.google.com/file/d/11BBOhUdULZN4Kp-oiXh8gSU1yyV8n_6f/view?usp=sharing
- 21.
Distance considerations are particularly important for community college students who tend to enroll in college much closer than their public four-year counterparts, despite of college availability. For example, in the ELS sample, students have a median and mean home to community college distance of 7.68 and 11.37 miles (s.d. = 12.28 miles) regardless of whether they attended college. Notably, these distances are similar when compared to home to a public four-year college (median = 9.92, mean = 14.85 [s.d. = 15.13] miles). However, compared to their four-year counterparts, community college students attended college within 9.92 (median) and 49 miles (mean) from their high school home (s.d. = 191.65 miles), whereas public four-year students enrolled within a median and mean distances of 62.572 and 130 miles (s.d. = 241.36 miles) from their parents’ home.
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Appendices
Appendices
12.1.1 Appendix A: Code for Simulated Example
12.1.2 Appendix B: Code Geographical Network Analysis
12.1.3 Appendix C: Social Dependence Procedures
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González Canché, M.S. (2019). Geographical, Statistical, and Qualitative Network Analysis: A Multifaceted Method-Bridging Tool to Reveal and Model Meaningful Structures in Education Research. In: Paulsen, M.B., Perna, L.W. (eds) Higher Education: Handbook of Theory and Research. Higher Education: Handbook of Theory and Research, vol 34. Springer, Cham. https://doi.org/10.1007/978-3-030-03457-3_12
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