Given the multidisciplinary perspectives of Public Health Law Research (PHLR) and the wide range of topics included in PHLR, the use of commonly-understood pictures to illustrate the ways in which law and health interact can be invaluable (Burris et al., 2010). Ranging from laws that prohibit individual behaviors, to laws that provide authority to act, to laws that regulate organizational practices, PHLR seeks to understand the mechanisms by which laws can improve health; visualizing these mechanisms in diagrams is an important tool for achieving such an understanding. The purpose of this monograph is to review some basic conventions used to create visual models, evaluate relevant examples of models in published PHLR studies, and offer recommendations for constructing clear and informative models.

Causal diagrams can do important work in PHLR, insofar as they answer several kinds of questions. They can help to describe ('how things are now'), classify ('why things go together'), explain ('how things really work'), predict ('what will happen if'), and decide ('what you should do now') As conceptual models, CDs not only map the steps by which law may impact health, but also allow a researcher to more carefully consider the set of measures to be used in developing a methodologically rigorous study. Models that exhibit valid correspondence and are appropriately complex yet clear will help PHLR researchers plan and carry out their work. Images that accurately represent the topic at hand may also be useful for policymakers in understanding new evidence for the many ways that laws may improve population health.

You may use Structural Equation approach, e.g. path analysis to deal with it. attached is for your reference

Another ref

A more technical ref

A directed acyclic graphs approach may help, this paper gives an introduction to the theoretical background:

Reducing bias through directed acyclic graphs, I Shrier & RW Platt

BMC Medical Research Methodology 2008, 8:70 doi:10.1186/1471-2288-8-

http://www.biomedcentral.com/1471-2288/8/70/

this site has software for practical implementation

http://www.dagitty.net/

http://en.wikipedia.org/wiki/Path_analysis_(statistics)

http://finzi.psych.upenn.edu/R/library/sem/html/00Index.html

Thank you for your comments.

More than 1500 variables is a lot, but I can support ‘Structural Equation Modeling (SEM)’ and maybe in combination with multilevel modelling. There are a lot of papers on the website of Mplus

(URL: www.statmodel.com).

Structural Equation Modeling (also known as path analysis, causal analysis, and other names) is a good way to formally model and test relations between variables with the benefit of a nice graphical representation of dependencies. However, SEM is typically restricted to linear relations between variables. If I understand you correctly, you don't believe in linear relations between your variables. This is the point where you should carefully think about why you don't believe in these and, then, gather all evidence for the type of interdependency that you assume or wish to model. Choosing a model is choosing a more abstract level of representation for your data. If you choose a model or a way of modeling that does not answer your research question, this might lead to some degree of disappointment.

Another way of modeling dependencies of variables in a acyclic graph are Bayesian Networks that model conditional (in)dependencies between variables.

Modeling 1500 variables at a time might become problematic for some SEM packages because, in that case, inference requires repeated inversions of a 1500x1500 covariance matrix, which is computationally expensive. You might want to start with smaller models and expand them successively.