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Abstract:
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Tracing pathways of dependence to understand development was a main aim of geneticist Sewell Wright when he formulated - a century ago - linear generating processes, represented them by directed graphs and evaluated the fit to his data. This approach started to be generalized with graphical Markov models in the 1970th, permitting variables of any type, by using the concept of conditional independence and by combining directed with undirected graphs. We have now a most suitable subclass, named `traceable regressions', to model development in ordered single and joint responses together with a set of context variables. A main difficulty was to find special, testable properties of the generated distributions which are needed to concentrate on conditional dependences, in addition to Markov structure. Traceable regression include, among others, linear regressions, generalized linear models, subclasses of structural equations for longitudinal studies as well as models for planned and for only virtual interventions. Here, we use several examples of studies to illustrate and summarize the now available features of traceable regressions and to point at open research questions.
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