Extending the p2 model using triadic social network data: The estimation of dyadic probabilities using the individuals’ perception on the social structure

Two-dimensional (self-reported) social network data is commonly used in social networks analysis to investigate the self-reported social relationships between network members. However, Krackhardt (1987) proposed to use three-dimensional (triadic) data based on the theory of cognitive social structures. Actors are not only asked to report their own relations within a social context, but are also asked to report on the relationships between other actors in the same network. In this thesis we will extend the p2 model by using the triadic data (instead of self-reported data) to estimate dyadic probabilities given the perception of the third actor in a triad. The p2 model is used, because it includes multiple dependencies found in social networks (e.g., reciprocity, describes a relationship where both individuals see each other as friends) which makes the model more realistic to other models (Van Duijn et al, 2004). We build on the application of Bellio and Soriani (2020) who used...Show moreTwo-dimensional (self-reported) social network data is commonly used in social networks analysis to investigate the self-reported social relationships between network members. However, Krackhardt (1987) proposed to use three-dimensional (triadic) data based on the theory of cognitive social structures. Actors are not only asked to report their own relations within a social context, but are also asked to report on the relationships between other actors in the same network. In this thesis we will extend the p2 model by using the triadic data (instead of self-reported data) to estimate dyadic probabilities given the perception of the third actor in a triad. The p2 model is used, because it includes multiple dependencies found in social networks (e.g., reciprocity, describes a relationship where both individuals see each other as friends) which makes the model more realistic to other models (Van Duijn et al, 2004). We build on the application of Bellio and Soriani (2020) who used Maximum Likelihood Estimation with Laplace approximation to estimate the parameters of the p2 model. They provided the C++ and the R code, which we use as a basis for our triadic extension of the model. We programmed the model in C++ and R. We used the triadic high-tech managers data (Krackhardt, 1987) and an aggregated version (as example for self-reported data) to show an application of the triadic model and the p2 model side-by-side. We encountered the problem of multicollinearity when adding dyadic characteristics to the parameter μ of the triadic model. It was possible to converge the model when reducing the number of dyadic-specific comparisons between actors within the density parameter and only include the comparison between actor i and j. For reciprocity and the homophily parameters the standard errors were lower in the triadic model than in the p2 model, indicating more precision. The characteristics of the perceiver added to this triadic model give more information about the effect of the perception of a third actor on the directed ties of other actors. Multiple suggestions for future research are made for overcoming the problem of multicollinearity, such as looking into the correlations between variables and the comparisons for homophily that can be added to our model or not. Besides this, a next step is to perform multiple goodness-of-fit tests. We conclude that this triadic model is a more realistic way to look at the role of the perceiver on the dyadic probability in a social network in combination with the effects of actor characteristics of the sender, receiver and the perceiver.Show less

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Extending the p2 model using triadic social network data: The estimation of dyadic probabilities using the individuals’ perception on the social structure