Rock the MIC: The Matrix of Implied Causation, a Tool for Experimental Design and Model Checking

Path modeling and the extended structural equation modeling framework are in increasingly common use for statistical analysis in modern behavioral science. Path modeling, including structural equation modeling, provides a flexible means of defining complex models in a way that allows them to be easily visualized, specified, and fitted to data. Although causality cannot be determined simply by fitting a path model, researchers often use such models as representations of underlying causal-process models. Indeed, causal implications are a vital characteristic of a model's explanatory value, but these implications are rarely examined directly. When models are hypothesized to be causal, they can be differentiated from one another by examining their causal implications as defined by a combination of the model assumptions, data, and estimation procedure. However, the implied causal relationships may not be immediately obvious to researchers, especially for intricate or long-chain causal structures (as in longitudinal panel designs). We introduce the matrix of implied causation (MIC) as a tool for easily understanding and reporting a model's implications for the causal influence of one variable on another. With examples from the literature, we illustrate the use of MICs in model checking and experimental design. We argue that MICs should become a routine element of interpretation when models with complex causal implications are examined, and that they may provide an additional tool for differentiating among models with otherwise similar fit.