Open Source Software projects are communities in which people “learn the ropes” from each other. The social and technical activities of developers evolve together, and as they link to each other they get organized in a network of changing socio-technical connections. Traces of those activities, or behaviors, are typically visible to all, in project repositories and through communication between them. Thus, in principle it may be possible to study those traces to tell which of the observable socio-technical behaviors of developers in these projects are responsible for the forming of persistent links between them. It may also be possible to tell the extent to which links participate in the spread of potential behavioral influences. Since OSS projects change in both social and technical activity over time, static approaches, that either ignore time or simplify it to a few slices, are frequently inadequate to study these networks. On the other hand, ad-hoc dynamic approaches are often only loosely supported by theory and can yield misleading findings. Here we adapt the stochastic actor-oriented models from social network analysis. These models enable the study of the interplay between behavior, influence and network architecture, for dynamic networks, in a statistically sound way. We apply the stochastic actor-oriented models in case studies of two Apache Software Foundation projects, and study code ownership and developer productivity as behaviors. For those, we find evidence of significant social selection effects (homophily) in both projects, but in different directions. However, we find no evidence for the spread (social influence) of either code ownership or developer productivity behaviors through the networks.
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The problem of causal inference is not limited to the study of epidemiological processes.
Also, these alternative models generally lack fundamental statistical data fitting ability.
We built separate models for each consecutive wave and estimated parameters for each separate model to test this assumption. These parameter estimates were then compared across models. There were no significant departures in these tests to indicate non-constant parameter estimates across time.
Not to be confused with the SIENA model rate parameter, described in Section 5.1.4.
Note that this is equivalently the smallest such β.
Axis2/Java had high fluctuations in activity (both social and technical) towards the beginning its lifetime. As a result, model estimations which included these time periods proved difficult to estimate; in particular, the number of ministeps required before arriving at the time for the next wave became too large. As we are interested in the average social and technical behaviors of projects, the offending waves were removed from the analysis for this project.
The authors also attempted to use an equal number of days as a separator of waves. However, this led to extreme skew and imbalance in network size (nodes and ties) as projects tend to have “burst” activity behavior; earlier waves were much less varied compared to later waves.
In particular, there were instabilities in estimating the network rate parameters – the number of “chances” an actor has to change its ties.
The choice of 8 waves is likely specific to our data – SIENA supports any number of waves, though time complexity increases with more waves.
We initially built models on 3 projects: Ant, Axis2/Java, and Derby. However, Derby results were similar to Axis2/Java results (e.g. positive behavioral selection). As we are interested in presenting case studies of the application of the SAOM method in OSS, we only discuss results for Ant and Axis2/Java.
An exception to this rule exists if the ego X alter interaction selection effect is most significant. In this case, one must control for the lower level structures of ego value and alter value when estimating the interaction effect. This is standard practice in general statistical modeling.
Note that z j is used here to represent actor j’s behavioral value, while the z parameter is missing from the function signature. This is to emphasize that z j here is treated as a covariate and is not modeled by the network objective function.
For file ownership behavior in Axis2/Java (Table 6), addition of the influence effect of average alter caused high instability in estimation of the model. As a result, the model for high file ownership behavior only includes the linear shape and quadratic shape parameters. The exclusion of this parameter in the model should not appreciably affect our outcomes or goodness of fit as the score-type test of this parameter suggested insignificance
Evidence of clustering initially raised a concern with the authors that the constructed networks had extreme levels of clustering. Further analysis showed that this was not the case; the clustering is at an acceptable level according to prior work in these social networks.
Recall that we did not estimate average alter influence for the high file ownership model in this case.
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The authors want to thank Mohammad Gharehyazie for sharing his ASF project data. We thank Saheel Godhane for fruitful discussion during the early stages of the project. We thank anonymous reviewers for their helpful suggestions on prior versions of manuscript. The authors gratefully acknowledge support from the Air Force Office of Scientific Research, award FA955-11-1-0246, and a faculty grant from UC Davis. The authors are thankful for generous support from UC Davis.
Data and scripts used in this work can be found at http://web.cs.ucdavis.edu/~filkov/software/ASF-Siena/.
Communicated by: Emerson Murphy-Hill
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Kavaler, D., Filkov, V. Stochastic actor-oriented modeling for studying homophily and social influence in OSS projects. Empir Software Eng 22, 407–435 (2017). https://doi.org/10.1007/s10664-016-9431-y
- Actor oriented models
- Open source
- Social influence
- Social selection