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

Abstract

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.

ANCOVA versus Change Score for the Analysis of Nonexperimental Two-Wave Data: A Structural Modeling Perspective

“…By clarifying the causal assumptions of these two widely used approaches, we hope to support researchers in utilizing the strength of longitudinal data and, at the same time, we hope to raise the awareness of the strong assumptions that are needed for making causal conclusions. This is also in line with recent prominent calls in psychology that nonexperimental research should begin to talk more openly about causal assumptions and causal effects because causal questions are central to most psychological theories (e.g., Brick & Bailey, 2020;Foster, 2010;Grosz, Rohrer, & Thoemmes, 2020;Quynh Nguyen, Schmid, & Stuart, 2020).…”

Academic Achievement and Economic Attainment: Reexamining Associations Between Test Scores and Long-Run Earnings

“…If such a projection is based on the unadjusted correlation between test scores and earnings (or even a correlation adjusted for demographic characteristics), then the evaluator is betting that the educational program in question also affected a host of unmeasured characteristics of the child that also influence the association between test scores and earnings. The validity of such assumptions likely depends on the specific features of the program in question (Brick & Bailey, 2020). Thus, the field sorely needs more longitudinal research of experimentally evaluated educational programs to better understand how short-term impacts translate to longer-term effects (see Athey et al, 2019; Watts et al, 2019).…”

Changes in Size and Interpretation of Parameter Estimates in Within-Person Models in the Presence of Time-Invariant and Time-Varying Covariates

“…Whether to include a TVC or not in a given analysis can be difficult to decide beforehand, as there might be multiple plausible causal models (Rohrer and Lucas, 2020 ). In such cases, it might be worthwhile to consider and contrast a range of plausible model specifications (Del Giudice and Gangestad, 2021 ) and to make explicit the assumptions underlying these models using a directed acyclic graph (Elwert and Winship, 2014 ) or matrices of implied causation (Brick and Bailey, 2020 ). Based on these explicit causal assumptions, researchers can take an informed decision and argue for the theoretically most meaningful model and flesh out the causal chains (Rohrer and Lucas, 2020 ).…”

“…As a consequence, researchers should report or document all model results with and without covariates included (see also Simmons et al, 2011 ; Asendorpf et al, 2013 ). Finally, when possible, as many assumptions as possible about the variables included in a model should be tested (Elwert and Winship, 2014 ; Brick and Bailey, 2020 ). For example, whether an observed TIC has constant or varying effects is a straightforward assumption to test (Johnson et al, 2016 ; Mulder and Hamaker, 2021 ).…”