Quantile Structural Equation Modeling: Testing a Novel Spatially-Weighted Approach

Quantile-sensitive methodologies have gained traction in recent years, with researchers leveraging these approaches to conduct more in-depth analyses than are capable with traditional mean-centered approaches. These approaches have been used widely for regression and correlational-based approaches, finding evidence of heterogeneous effects based on the portion of the distribution analyzed. However, the methodologies for conducting quantile-sensitive work using more complex designs are limited, and extending this work into structural equation modeling (SEM) approaches was our primary aim. We conducted our study using a series of Monte-Carlo simulations, each representing data where SEM models with varying structures and values fit best depending on the portion of the distributions analyzed. A novel distance-based method (DSW), was developed and applied to the simulated datasets, observing its average and range of effectiveness to detect the heterogeneous SEM models and effects that underlie the datasets throughout their distributions. Two other methods were also tested, but have known limitations and instead were meant to serve as references for this approach, highlighting the advantages of the DSW method and the ways it addressed their limitations. Results found that the DSW approach was highly effective in detecting heterogeneous findings in regression models, latent growth curves, and factor-analytic models (both nested and non-nested models), accurately detecting the modeled differences in varying latent factor structures and other effect sizes and significantly outperforming the other approaches. Limitations and future directions for this work are discussed, highlighting the new areas of work this method opens up and its potential areas of extension.