Goodness of fit for stochastic actor-oriented models

We propose a Mahalanobis distance–based Monte Carlo goodness of fit testing procedure for the family of stochastic actor-oriented models for social network evolution. A modified model distance estimator is proposed to help the researcher identify model extensions that will remediate poor fit. A limited simulation study is provided to establish baseline legitimacy for the Mahalanobis distance–based Monte Carlo test and modified model distance estimator. A forward model selection workflow is proposed, and this procedure is demonstrated on a real data set.

[1]  P. Mahalanobis On the generalized distance in statistics , 1936 .

[2]  Alessandro Lomi,et al.  A model for the multiplex dynamics of two-mode and one-mode networks, with an application to employment preference, friendship, and advice , 2013, Soc. Networks.

[3]  Tom Fawcett,et al.  An introduction to ROC analysis , 2006, Pattern Recognit. Lett..

[4]  D. Harville Matrix Algebra From a Statistician's Perspective , 1998 .

[5]  L. Michell,et al.  Girls, pecking order and smoking. , 1997, Social science & medicine.

[6]  J. Hintze,et al.  Violin plots : A box plot-density trace synergism , 1998 .

[7]  Willem E. Saris,et al.  The Detection and Correction of Specification Errors in Structural Equation Models , 1987 .

[8]  Stephen E. Fienberg,et al.  Testing Statistical Hypotheses , 2005 .

[9]  Stanley Wasserman,et al.  Social Network Analysis: Methods and Applications , 1994, Structural analysis in the social sciences.

[10]  Tom A. B. Snijders,et al.  Manual for SIENA version 2.1 , 2005 .

[11]  Peng Wang,et al.  Closure, connectivity and degree distributions: Exponential random graph (p*) models for directed social networks , 2009, Soc. Networks.

[12]  J. Lospinoso Statistical models for social network dynamics , 2012 .

[13]  Michael Michell Smoke Rings: social network analysis of friendship groups, smoking and drug-taking , 2000 .

[14]  René Veenstra,et al.  Network–Behavior Dynamics , 2013 .

[15]  Tom A. B. Snijders,et al.  Markov models for digraph panel data: Monte Carlo-based derivative estimation , 2007, Comput. Stat. Data Anal..

[16]  T. Snijders The statistical evaluation of social network dynamics , 2001 .

[17]  T. Snijders,et al.  Modeling the Coevolution of Networks and Behavior , 2007 .

[18]  T. Snijders,et al.  Bayesian inference for dynamic social network data , 2007 .

[19]  Tom A. B. Snijders,et al.  Introduction to stochastic actor-based models for network dynamics , 2010, Soc. Networks.

[20]  Joshua Alfred Lospinoso,et al.  Smoking Behavior and Friendship Formation: The Importance of Time Heterogeneity in Studying Social Network Dynamics , 2011, 2011 44th Hawaii International Conference on System Sciences.

[21]  P. Holland,et al.  Local Structure in Social Networks , 1976 .

[22]  D. Hunter,et al.  Goodness of Fit of Social Network Models , 2008 .

[23]  Per Block,et al.  Reciprocity, transitivity, and the mysterious three-cycle , 2015, Soc. Networks.

[24]  Eric D. Kolaczyk,et al.  Statistical Analysis of Network Data: Methods and Models , 2009 .

[25]  Tom A. B. Snijders,et al.  Stochastic Actor-Oriented Models for Network Dynamics , 2017 .

[26]  D. Kaplan Evaluating and Modifying Covariance Structure Models: A Review and Recommendation. , 1990, Multivariate behavioral research.

[27]  Tom A. B. Snijders,et al.  Assessing and accounting for time heterogeneity in stochastic actor oriented models , 2011, Adv. Data Anal. Classif..

[28]  Michael Schweinberger,et al.  MAXIMUM LIKELIHOOD ESTIMATION FOR SOCIAL NETWORK DYNAMICS. , 2010, The annals of applied statistics.

[29]  M. Schweinberger Statistical modelling of network panel data: goodness of fit. , 2012, The British journal of mathematical and statistical psychology.

[30]  C. Steglich,et al.  DYNAMIC NETWORKS AND BEHAVIOR: SEPARATING SELECTION FROM INFLUENCE: separating selection from influence , 2010 .

[31]  David Kaplan,et al.  On the modification and predictive validity of covariance structure models , 1991 .

[32]  D. Hunter,et al.  Inference in Curved Exponential Family Models for Networks , 2006 .

[33]  P. Pattison,et al.  New Specifications for Exponential Random Graph Models , 2006 .

[34]  Eric D. Kolaczyk,et al.  Statistical Analysis of Network Data , 2009 .