We have used path analysis for differentiating between direct and indirect effects of various factors on the target variables, and for quantifying the relative contributions of controlling factors in a recent publication in Ecology and Evolution under the topic "Relating microbial community structure to functioning in forest soil organic carbon transformation and turnover". This was done by developing first a Structure Equation Model (SEM) based on prior (or emperical) knowledge or hypothetical linkage among the variables concerned and then putting all categorical data through the analysis. The article can be downloaded from my RG site if you are interested in this topic. Hope it may help.
I think expert knowledge still is and will be important in determining causal relationship and distinguishing controlling factors. One example is Species distribution modelling. Frequently some factors are strongly predicting species distribution whereas they are not in causal relationship. In other example is study of diversity distribution along a gradient. For example monotonic decrease of species diversity along an elevation is most strongly associated with altitude however altitude is not per-see the factor determining the relationship. Statistical methods usually give stronger weight to altitude and only expert can decide whither other controlling factors are important or not. Probably these issue is more important in medicine
Hi, one approach is to use cognitive mapping in which causal relationships are represented explicitly as a graph (in the technical sense of "graph" as a network of nodes and edges). The information elicited is subjective and inferences arising from using the elicited causal relationships must be used with caution in light of that, but it is a useful method for making progress in areas where there are few data on which to base formal models. There area couple of chapters in this book edited by Michael Glykas, which are available for download from my public ResearchGate profile: