Cause for concern: Omitted cross-loadings in measurement models of nonlinear structural equation models

Cross-loadings on non-target factors in measurement models of linear structural equation models (SEM) are often observed in empirical research but frequently disregarded. Previous research on linear SEM has already shown that omitted positive cross-loadings result in overestimated covariances of the latent predictor variables and distorted linear effects. For nonlinear SEM with interaction and quadratic effects, omitting cross-loadings has not been investigated. This study examines the consequences of omitted cross-loadings in both linear and nonlinear SEM using a single empirical dataset and a small simulation study. We focus on the bias patterns that emerge when cross-loadings-reflecting the multidimensionality of items-are either positive or negative and assess how these biases vary with the level of the latent predictor covariance. The empirical analysis reveals that constraining theoretically justified cross-loadings to zero results in systematic over- and underestimation of factor loadings and structural parameters, with more pronounced effects in the nonlinear component of the model, thereby altering the functional form of the relationships between the latent variables. The simulation study further illustrates that the direction and magnitude of bias in both linear and nonlinear SEM depend jointly on the sign of the cross-loadings and the level of the latent predictor covariance. These findings underscore the critical importance of incorporating cross-loadings only theory-driven to maintain an accurate representation of the functional relationships between latent constructs. Practical implications and challenges of including cross-loadings in the model are discussed.