Harrison White and several anonymous reviewers for valuable comments on the work. 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 semi-paths. We argue that this class of models holds new promise for the development of empirically plausible models for networks and network-based processes. 2 1.

The “numerical method ” in medicine goes back to Pierre Louis ’ study of pneumonia (1835), and John Snow’s book on the epidemiology of cholera (1855). Snow took advantage of natural experiments and used convergent lines of evidence to demonstrate that cholera is a waterborne infectious disease. More recently, investigators in the social and life sciences have used statistical models and significance tests to deduce cause-and-effect relationships from patterns of association; an early example is Yule’s study on the causes of poverty (1899). In my view, this modeling enterprise has not been successful. Investigators tend to neglect the difficulties in establishing causal relations, and the mathematical complexities obscure rather than clarify the assumptions on which the analysis is based. Formal statistical inference is, by its nature, conditional. If maintained hypotheses A, B, C,... hold, then H can be tested against the data. However, if A, B, C,... remain in doubt, so must inferences about H. Careful scrutiny of maintained hypotheses should therefore be a critical part of empirical work—a principle honored more often in the breach than the observance. Snow’s work on cholera will be contrasted with modern studies that depend on statistical models and tests of significance. The examples may help to clarify the limits of current statistical techniques for making causal inferences from patterns of association. 1.

This paper (which is mainly expository) sets up graphical models for causation, having a bit less than the usual complement of hypothetical counterfactuals. Assuming the invariance of error distributions may be essential for causal inference, but the errors themselves need not be invariant. Graphs can be interpreted using conditional distributions, so that we can better address connections between the mathematical framework and causality in the world. The identification problem is posed in terms of conditionals. As will be seen, causal relationships cannot be inferred from a data set by running regressions unless there is substantial prior knowledge about the mechanisms that generated the data. There are few successful applications of graphical models, mainly because few causal pathways can be excluded on a priori grounds. The invariance conditions themselves remain to be assessed.

Experiments offer more reliable evidence on causation than observational studies, which is not to gainsay the contribution to knowledge from observation. Experiments should be analyzed as experiments, not as observational studies. A simple comparison of rates might be just the right tool, with little value added by “sophisticated” models. This article discusses current models for causation, as applied to experimental and observational data. The intention-to-treat principle and the effect of treatment on the treated will also be discussed. Flaws in per-protocol and treatment-received estimates will be demonstrated.

The "salt hypothesis" is that higher levels of salt in the diet lead to higher levels of blood pressure, with attendant risk of cardiovascular disease. Intersalt was designed to test the hypothesis, with a cross-sectional study of salt levels and blood pressures in 52 populations. The study is often cited to support the salt hypothesis, but the data are somewhat contradictory. Thus, four of the populations (Kenya, Papua, and two Indian tribes in Brazil) have very low levels of salt and blood pressure. Across the other 48 populations, however, blood pressures go down as salt levels go up---contradicting the salt hypothesis. Regressions of blood pressure on age indicate that for young people, blood pressure is inversely related to salt intake---another paradox. This paper discusses the Intersalt data and study design, looking at some of the statistical issues and identifying respects in which the study failed to follow its own protocol. Also considered are human experiments bearing on t...

Increased interest in longitudinal social networks and the recognition that visualization fosters theoretical insight create a need for dynamic network visualizations, or network “movies. ” This article confronts theoretical questions surrounding the temporal representations of social networks and technical questions about how best to link network change to changes in the graphical representation. The authors divide network movies into (1) static flip books, where node position remains constant but edges cumulate over time, and (2) dynamic movies, where nodes move as a function of changes in relations. Flip books are particularly useful in contexts where relations are sparse. For more connected networks, movies are often more appropriate. Three empirical examples demonstrate the advantages of different movie styles. A new software program for creating network movies is discussed in the appendix.

Regression models are often used to infer causation from association. For instance, Yule [79] showed – or tried to show – that welfare was a cause of poverty. Path models and structural equation models are later

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Acknowledgments: This paper has benefited from participation in the SFI seminar on