The presence of unobserved node-specific heterogeneity in exponential random graph models (ERGM) is a general concern, both with respect to model validity as well as estimation instability. We, therefore, include node-specific random effects in the ERGM that account for unobserved heterogeneity in the network. This leads to a mixed model with parametric as well as random coefficients, labelled as mixed ERGM. Estimation is carried out by iterating between approximate pseudolikelihood estimation for the random effects and maximum likelihood estimation for the remaining parameters in the model. This approach provides a stable algorithm, which allows to fit nodal heterogeneity effects even for large scale networks. We also propose model selection based on the Akaike Information Criterion to check for node-specific heterogeneity.

While logistic regression models are easily accessible to researchers, when applied to network data there are unrealistic assumptions made about the dependence structure of the data. For temporal networks measured in discrete time, recent work has made good advances (Almquist & Butts, 2014), but there is still the assumption that the dyads are conditionally independent given the edge histories. This assumption can be quite strong and is sometimes difficult to justify. If time steps are rather large, one would typically expect not only the existence of temporal dependencies among the dyads across observed time points but also the existence of simultaneous dependencies affecting how the dyads of the network co-evolve. We propose a general observation-driven model for dynamic networks that overcomes this problem by modeling both the mean and the covariance structures as functions of the edge histories using a flexible autoregressive approach. This approach can be shown to fit into a generalized linear mixed model framework. We propose a visualization method that provides evidence concerning the existence of simultaneous dependence. We describe a simulation study to determine the method's performance in the presence and absence of simultaneous dependence, and we analyze both a proximity network from conference attendees and a world trade network. We also use this last data set to illustrate how simultaneous dependencies become more prominent as the time intervals become coarser.

Statistical analysis is increasingly used in seed germination/viability studies across different disciplines. The objective of this opinion piece is to assess current trends in statistical analysis of such data, and draw attention of readers to the limitations of the usual inferential statistics in controlling error rates. The assessments are based on a survey of 429 papers published in 139 peer-reviewed journals in the past 11 years. My intention is to identify areas of concern across a wide range of studies. Accordingly, the areas of greatest concern found in the analysis of percentage seed germination and viability data were: (1) pseudoreplication and/or use of a few replicates; (2) ignoring assumptions of ANOVA and non-parametric tests (NPARTs); (3) uncritical data transformation; (4) arbitrary choice of multiple comparison tests; and (5) lack of emphasis on effect sizes. Given the prevalence of these problems, in my opinion we would be building a body of knowledge on a shaky ground. The discussions that follow will: (1) describe situations where germination data violate assumptions of ANOVA and NPARTs; (2) highlight the implications of the various problems to Type I and Type II error rates; and (3) indicate remedial measures based on the recent statistical literature.