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The gap between public evaluations and interactional status in social networks

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Abstract

Actors occupying central positions in networks created from deferential interactions are perceived as high in social status and quality. Status can also be read from increasingly ubiquitous third-party evaluations of actors involved in interactions based on surveys of field participants (e.g., publicly observable ratings). Although evaluations can be reflections of interaction-based positions, I argue the two measures of status can also be discrepant for two reasons: (1) tie formation being a more constrained process than evaluation and (2) differences in determinants of social construction. I propose a creative use of exponential random graph models focused on poorly fit configurations to analyze the divergence between evaluations and statused social networks. I test my framework on a network of PhD exchange relations and peer evaluations. I find that evaluations ‘undervalue’ both elite and mid-ranked departments relative to their structural positions. I discuss potential explanations and implications of these findings.

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Data availability

The data for this project were sourced publicly and are available from the sources mentioned under the Data section. The data will be made available at a publicly available website post-publication.

Notes

  1. The structural reciprocity parameter needs to be included in the models to be able to include reciprocity based on nodal attributes. Rather than all ties being independent of each other, the inclusion of the reciprocity parameter implies that only ties that occur between the same nodes are interdependent.

  2. Although multicollinearity could be an issue in these models, tests demonstrate this to not be a concern. Multicollinearity in ERGMs is generally assessed in two ways: (1) the variance inflation factor (VIF) of coefficients and (2) the stability of model coefficients (Duxbury 2018). The highest VIF for estimates in Models 1–4 were below concerning levels. Rerunning Models 1–4 multiple times also yielded highly stable coefficients.

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Acknowledgements

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The author did not receive support from any organization for the submitted work. The author declares they have no financial interests. The author declares they have no non-financial interests.

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  1. Department of Sociology and Faculty of Computing & Data Sciences, Boston University, Boston, USA

    Neha Gondal

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  1. Neha Gondal
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All work including conceptualization, data collection and curation, analysis, and writing were done by the sole author, NG.

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Correspondence to Neha Gondal.

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Appendix

Appendix

1.1 Mediation analysis for the sociology hiring network

The first ‘structural’ model in Table 3 shows positive and significant estimates for an alternating-in-star parameter alongside alternating transitive and downward triangulation (indicative of closure among popular actors). These findings, consistent with the results above, show that the network is characterized by considerable inequality in popularity alongside closure among popular actors. The model also shows that inequality-mitigating transitive closure is also important to the construction of the network.

Subsequent models reveal consistently significant estimates for the alternating transitive triad parameter, confirming that transitive closure is not captured adequately by evaluations. In contrast, alternating downward triads lose significance and value, showing that evaluated positions are well suited to accounting for hiring between popular departments. The models also show that ratings in their unaltered form are better at capturing the overall spread of the indegree distribution (as captured by the alternating-in-star parameter). Cubed and exponentiated ratings do worse in this regard because, while transformations are better at capturing the tail of the distribution, they underpredict middling to high levels of popularity. Nevertheless, fit statistics (not shown) confirm that models with cubic and exponentiated ratings do better at explaining dense elite closure (T1 type triads), which tends to be underpredicted by the straightforward ratings model. Overall, the ongoing statistical significance of endogenous parameters reveals that, while there is a high degree of consistency between evaluations and the network, mechanisms beyond those captured in evaluation undergird the production of transitive closure in the sociology network.

Table 3 ERGM results for the for the sociology hiring network including structural and USN evaluation parameters
Full size table

1.2 Generalizability model for the history hiring network

Model coefficients (not shown) for the history network are remarkably similar to those for sociology. Table 4 shows goodness-of-fit results. Ratings offer far superior fits than rankings, but fail to replicate areas of dense elite closure, extreme differences in popularity and transitive triangulation. Similar types of improvements are evident when ratings are cubed and exponentiated. However, unlike sociology, general clustering and transitive triangulation continue to remain underexplained in the final model. A detailed examination of the degree distribution reveals that rankings and ratings considerably underpredict departments with popularity in the 6–15 range, but cubed ratings improve accuracy. Fit for transitive triangulation follow similar patterns (Table 5).

Table 4 Goodness-of-fit (GOF) statistics for select structural features for the history hiring network. Columns show t-ratios ((observed-mean of simulated)/standard deviation of simulated) from 1000 simulations. Smaller t-statistics, indicative of better fit, are preferred
Full size table
Table 5 ERGM results for the for the sociology hiring network including USN evaluation and regional homophily parameters
Full size table

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Gondal, N. The gap between public evaluations and interactional status in social networks. Soc. Netw. Anal. Min. 13, 97 (2023). https://doi.org/10.1007/s13278-023-01099-4

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