Social Indicators III: Selected Data on Social Conditions and Trends in the United States.

Wainer, Howard; Census, U.S.

doi:10.2307/2288666

Cited by 7 publications

(1 citation statement)

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“…The following example is derived from information on a social survey, [93]. It shows how conditioning on the inner node of a sink V induces a conditional dependence.…”

Section: Parent Graphs and Three Vsmentioning

confidence: 99%

GraphicalMarkov Models, Unifying Results and Their Interpretation

Wermuth

2015

Wiley StatsRef: Statistics Reference Online

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Graphical Markov models combine conditional independence constraints with graphical representations of stepwise data generating processes. The models started to be formulated about 40 years ago and vigorous development is ongoing. Longitudinal observational studies as well as intervention studies are best modelled via a subclass called regression graph models and, especially traceable regressions. Regression graphs include two types of undirected graph and directed acyclic graphs in ordered sequences of joint responses. Response components may correspond to discrete or continuous random variables or to both types and may depend exclusively on variables which have been generated earlier. These aspects are essential when causal hypothesis are the motivation for the planning of empirical studies.To turn the graphs into useful tools for tracing pathways of dependence, for understanding development over time and for predicting structure in alternative models, the generated distributions have to mimic some properties of joint Gaussian distributions. Here, relevant results concerning these aspects are spelled out and illustrated by examples. With regression graph models, it becomes feasible, for the first time, to derive structural effects of (1) ignoring some of the variables, of (2) selecting subpopulations via fixed levels of some other variables or of (3) changing the order in which the variables might get generated. Thus, the most important future applications of these models will aim at the best possible integration of knowledge from related studies.

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“…The following example is derived from information on a social survey, [93]. It shows how conditioning on the inner node of a sink V induces a conditional dependence.…”

Section: Parent Graphs and Three Vsmentioning

confidence: 99%