Structural equation modeling (SEM) and path analysis using composite-scores are distinct classes of methods for modeling the relationship of theoretical constructs. The two classes of methods are integrated in the partial-least-squares approach to structural equation modeling (PLS-SEM), which systematically generates weighted composites and uses them to conduct path analysis of the structural model via the least-squares method. However, the goodness of PLS-SEM depends on the statistical properties of the composites, which are further determined by the formulations of the weights. This article studies how the formulations of PLS-SEM composites are affected by model specification, with focus on the sensitivity of the weights to common specification errors. Results indicate that the weights under PLS SEM mode A are not affected by within-block error-covariances but those under mode B are. While between-block error-covariances and cross-loadings only affect the weights of the involved items under both PLS-SEM modes A and B, the weights under mode B are much more sensitive than those under mode A. In contrast, the weights under a recently proposed transformed mode (denoted as BA) are a compromise between those of modes A and B. The findings not only advance the understanding of the PLS-SEM methodology but also facilitate model diagnostics. Empirical applications of the results are illustrated via the analysis of a real dataset. [This paper was published in "Structural Equation Modeling" v30 n1 p53-69 2023.]