Philippa Pattison

Logit models and logistic regressions for social networks: I. An introduction to Markov graphs andp

Spanning nearly sixty years of research, statistical network analysis has passed through (at least) two generations of researchers and models. Beginning in the late 1930s, the first generation of research dealt with the distribution of various network statistics, under a variety of null models. The second generation, beginning in the 1970s and continuing into the 1980s, concerned models, usually for probabilities of relational ties among very small subsets of actors, in which various simple substantive tendencies were parameterized. Much of this research, most of which utilized log linear models, first appeared in applied statistics publications.But recent developments in social network analysis promise to bring us into a third generation. The Markov random graphs of Frank and Strauss (1986) and especially the estimation strategy for these models developed by Strauss and Ikeda (1990; described in brief in Strauss, 1992), are very recent and promising contributions to this field. Here we describe a large class of models that can be used to investigate structure in social networks. These models include several generalizations of stochastic blockmodels, as well as models parameterizing global tendencies towards clustering and centralization, and individual differences in such tendencies. Approximate model fits are obtained using Strauss and Ikedas (1990) estimation strategy.In this paper we describe and extend these models and demonstrate how they can be used to address a variety of substantive questions about structure in social networks.

New Specifications for Exponential Random Graph Models

The most promising class of statistical models for expressing structural properties of social networks observed at one moment in time is the class of exponential random graph models (ERGMs), also known as p* models. The strong point of these models is that they can represent a variety of structural tendencies, such as transitivity, that define complicated dependence patterns not easily modeled by more basic probability models. Recently, Markov chain Monte Carlo (MCMC) algorithms have been developed that produce approximate maximum likelihood estimators. Applying these models in their traditional specification to observed network data often has led to problems, however, which can be traced back to the fact that important parts of the parameter space correspond to nearly degenerate distributions, which may lead to convergence problems of estimation algorithms, and a poor fit to empirical data. This paper proposes new specifications of exponential random graph models. These specifications represent structural properties such as transitivity and heterogeneity of degrees by more complicated graph statistics than the traditional star and triangle counts. Three kinds of statistics are proposed: geometrically weighted degree distributions, alternating k-triangles, and alternating independent two-paths. Examples are presented both of modeling graphs and digraphs, in which the new specifications lead to much better results than the earlier existing specifications of the ERGM. It is concluded that the new specifications increase the range and applicability of the ERGM as a tool for the statistical analysis of social networks.

Emotion recognition via facial expression and affective prosody in schizophrenia: a methodological review.

Disturbances in affect recognition may be one of the most pervasive and serious aspects of the schizophrenic patients interpersonal problems. Interest in the decoding of emotional information in schizophrenia has focused on facial affect recognition with 29 experimental papers on that topic published since 1987. A smaller literature exists on the topic of recognition of affect in speech and there are at least seven studies, which have examined both face and voice perception in the same individuals with schizophrenia. This paper includes a comprehensive analysis of the schizophrenia facial affect recognition research over the past decade and the schizophrenia literature on affective prosody, and provides the first review of the schizophrenia literature on multichannel emotion recognition research. The weight of evidence would suggest that individuals with schizophrenia experience problems in the perception of emotional material; however, the specificity, extent, and nature of the deficits are unclear. Emotion recognition research in schizophrenia should be informed by the general literature on emotion recognition with serious attention paid to methodological issues.

Recent developments in exponential random graph (p*) models for social networks

This article reviews new specifications for exponential random graph models proposed by Snijders et al. [Snijders, T.A.B., Pattison, P., Robins, G.L., Handcock, M., 2006. New specifications for exponential random graph models. Sociological Methodology] and demonstrates their improvement over homogeneous Markov random graph models in fitting empirical network data. Not only do the new specifications show improvements in goodness of fit for various data sets, but they also help to avoid the problem of neardegeneracy that often afflicts the fitting of Markov random graph models in practice, particularly to network data exhibiting high levels of transitivity. The inclusion of a new higher order transitivity statistic allows estimation of parameters of exponential graph models for many (but not all) cases where it is impossible to estimate parameters of homogeneous Markov graph models. The new specifications were used to model a large number of classical small-scale network data sets and showed a dramatically better performance than Markov graph models. We also review three current programs for obtaining maximum likelihood estimates of model parameters and we compare these Monte Carlo maximum likelihood estimates with less accurate pseudo-likelihood estimates. Finally, we discuss whether homogeneous Markov random graph models may be superseded by the new specifications, and how additional elaborations may further improve model performance.

Facial affect and affective prosody recognition in first-episode schizophrenia.

Individuals with schizophrenia experience problems in the perception of emotional material; however, the specificity, extent, and nature of the deficits are unclear. Facial affect and affective prosody recognition were examined in representative samples of individuals with first-episode psychosis, assessed as outpatients during the early recovery phase of illness, and non-patients. Perception tasks were selected to allow examination of emotion category results across face and voice modalities. Facial tasks were computerised modifications of the Feinberg et al. procedure (Feinberg, T.E., Rifkin, A., Schaffer, C., Walker, E., 1986. Arch. Gen. Psychiatry 43, 276--279). Prosody tasks were developed using four professional actors, and item selections were based on responses of undergraduates. Participant groups did not differ in their understanding of the words used to describe emotions. Findings supported small but consistent deficits in recognition of fear and sadness across both communication channels for the combined schizophrenia (n=29) and other psychotic disorders (n=28) groups as compared to the affective psychoses (n=23) and non-patients (n=24). A diagnostic effect was evident that was independent of the contribution of intelligence. The detection of emotion recognition impairments in first-episode schizophrenia suggests a trait deficit. The pattern of results is consistent with amygdala dysfunction in schizophrenia and related psychoses.

LOGIT MODELS AND LOGISTIC REGRESSIONS FOR SOCIAL NETWORKS : II. MULTIVARIATE RELATIONS

The research described here builds on our previous work by generalizing the univariate models described there to models for multivariate relations. This family, labelled p*, generalizes the Markov random graphs of Frank and Strauss, which were further developed by them and others, building on Besags ideas on estimation. These models were first used to model random variables embedded in lattices by Ising, and have been quite common in the study of spatial data. Here, they are applied to the statistical analysis of multigraphs, in general, and the analysis of multivariate social networks, in particular. In this paper, we show how to formulate models for multivariate social networks by considering a range of theoretical claims about social structure. We illustrate the models by developing structural models for several multivariate networks.

Closure, connectivity and degree distributions : Exponential random graph (p*) models for directed social networks

Abstract The new higher order specifications for exponential random graph models introduced by Snijders et al. [Snijders, T.A.B., Pattison, P.E., Robins G.L., Handcock, M., 2006. New specifications for exponential random graph models. Sociological Methodology 36, 99–153] exhibit substantial improvements in model fit compared with the commonly used Markov random graph models. Snijders et al., however, concentrated on non-directed graphs, with only limited extensions to directed graphs. In particular, they presented a transitive closure parameter based on path shortening. In this paper, we explain the theoretical and empirical advantages in generalizing to additional closure effects. We propose three new triadic-based parameters to represent different versions of triadic closure: cyclic effects; transitivity based on shared choices of partners; and transitivity based on shared popularity. We interpret the last two effects as forms of structural homophily, where ties emerge because nodes share a form of localized structural equivalence. We show that, for some datasets, the path shortening parameter is insufficient for practical modeling, whereas the structural homophily parameters can produce useful models with distinctive interpretations. We also introduce corresponding lower order effects for multiple two-path connectivity. We show by example that the in- and out-degree distributions may be better modeled when star-based parameters are supplemented with parameters for the number of isolated nodes, sources (nodes with zero in-degrees) and sinks (nodes with zero out-degrees). Inclusion of a Markov mixed star parameter may also help model the correlation between in- and out-degrees. We select some 50 graph features to be investigated in goodness of fit diagnostics, covering a variety of important network properties including density, reciprocity, geodesic distributions, degree distributions, and various forms of closure. As empirical illustrations, we develop models for two sets of organizational network data: a trust network within a training group, and a work difficulty network within a government instrumentality.

Small and Other Worlds: Global Network Structures from Local Processes1

Using simulation, we contrast global network structures—in particular, small world properties—with the local patterning that generates the network. We show how to simulate Markov graph distributions based on assumptions about simple local social processes. We examine the resulting global structures against appropriate Bernoulli graph distributions and provide examples of stochastic global “worlds,” including small worlds, long path worlds, and nonclustered worlds with many four‐cycles. In light of these results we suggest a locally specified social process that produces small world properties. In examining movement from structure to randomness, parameter scaling produces a phase transition at a “temperature” where regular structures “melt” into stochastically based counterparts. We provide examples of “frozen” structures, including “caveman” graphs, bipartite structures, and cyclic structures.

Neighborhood–Based Models For Social Networks

We argue that social networks can be modeled as the outcome of processes that occur in overlapping local regions of the network, termed local social neighborhoods. Each neighborhood is conceived as a possible site of interaction and corresponds to a subset of possible network ties. In this paper, we discuss hypotheses about the form of these neighborhoods, and we present two new and theoretically plausible ways in which neighborhood-based models for networks can be constructed. In the first, we introduce the notion of a setting structure, a directly hypothesized (or observed) set of exogenous constraints on possible neighborhood forms. In the second, we propose higher-order neighborhoods that are generated, in part, by the outcome of interactive network processes themselves. Applications of both approaches to model construction are presented, and the developments are considered within a general conceptual framework of locale for social networks. We show how assumptions about neighborhoods can be cast within a hierarchy of increasingly complex models; these models represent a progressively greater capacity for network processes to “reach” across a network through long cycles or semipaths. We argue that this class of models holds new promise for the development of empirically plausible models for networks and network-based processes.

Network models for social selection processes

Abstract We present network models for social selection processes, based on the p∗ class of models. Social selection occurs when individuals form social relationships on the basis of certain characteristics they possess. Similarity is a common hypothesis for selection processes, but one that is usually framed dyadically. Structural balance approaches move beyond dyadic conceptualizations and require more sophisticated modeling. The two-block chain graph approach of p∗ social influence models is adapted to allow individual attribute variables to be predictors of network ties. Using a range of dependence assumptions, we present a hierarchy of increasingly complex selection models, including models for continuous attribute measures, which in their simplest form may be assumed to be linear. The models have scope, however, for more complex functional formulations so that more specific hypotheses may be investigated by postulating a particular functional form. Our empirical examples illustrate how dyadic selection may be transmuted into structural effects, and how the absence of dyadic selection may still mask a subtle higher order selection effect as individuals “position” themselves within a wider social environment. In conclusion, we discuss the links between social influence and social selection models.