Scientist’s guide to developing explanatory statistical models using causal analysis principles

Abstract

Recent discussions of model selection and multimodel inference highlight a general challenge for researchers: how to convey the explanatory content of a hypothesized model or set of competing models clearly. The advice from statisticians for scientists employing multimodel inference is to develop a well‐thought‐out set of candidate models for comparison, though precise instructions for how to do that are typically not given. A coherent body of knowledge, which falls under the general term causal analysis, now exists for examining the explanatory scientific content of candidate models. Much of the literature on causal analysis has been recently developed, and we suspect may not be familiar to many ecologists. This body of knowledge comprises a set of graphical tools and axiomatic principles to support scientists in their endeavors to create “well‐formed hypotheses,” as statisticians are asking them to do. Causal analysis is complementary to methods such as structural equation modeling, which provides the means for evaluation of proposed hypotheses against data. In this paper, we summarize and illustrate a set of principles that can guide scientists in their quest to develop explanatory hypotheses for evaluation. The principles presented in this paper have the capacity to close the communication gap between statisticians, who urge scientists to develop well‐thought‐out coherent models, and scientists, who would like some practical advice for exactly how to do that.

Benefits and tradeoffs of reduced tillage and manure application methods in a Zea mays silage system

“…To examine direct and indirect effects of management practices and hypothesized drivers of soil N and daily GHG emissions, we developed and compared structural equation models. Classical statistical techniques do not permit the investigation of causal relationships; however, the use of structural equation models develops causal understanding from data by testing networks of causal relationships (Figure 1) (Eisenhauer, Bowker, Grace, & Powell, 2015; Grace & Irvine, 2020; Grace et al., 2012). While relying on some correlative information, structural equation model approaches causal understanding (as in Shipley, 2002) by fitting data to models that represent alternative causal hypotheses (e.g., Supplemental Figure S1) and by testing and comparing model fit (based on model‐implied vs. observed covariance matrices; Eisenhauer et al., 2015; Grace et al., 2006, 2012).…”

Forecasting community reassembly using climate‐linked spatio‐temporal ecosystem models

“…For example, structural equation modelling (Kaplan 2001) would define this covariance via a set of hypothesized causal relationships, e.g. where the dependency of biological variables upon changes in specific physical variables could be estimated and used to predict future counterfactual changes (Grace and Irvine 2020). This allows a joint model (where biological and physical variables are both treated as response variables as done here) to still support inference similar to a conventional linear model (where physical variables are treat as ‘independent' and biological variables ‘dependent'), although we do not pursue the topic further here.…”

“…For example, structural equation modelling (Kaplan 2001) would define this covariance via a set of hypothesized causal relationships, e.g. where the dependency of biological variables upon changes in specific physical variables could be estimated and used to predict future counterfactual changes (Grace and Irvine 2020).…”

Impacts ofSpartina alterniflorainvasion on soil inorganic carbon in coastal wetlands in China

“…In the case of the invasion-soil concept, SIC and S. alterniflora invasion can be linked through the analysis of multiple soil processes or functions, which control SIC and response to invasion. SEM is designed to evaluate the empirical support for proposed explanatory hypotheses, such as the ones proposed here (Grace & Irvine, 2019).…”