This thesis is about composite-based structural equation modeling (SEM). In traditional factor-based SEM, these theoretical concepts are modeled as common factors, i.e., as latent variables which explain the covariance structure of their observed variables. In contrast, in composite-based SEM, the theoretical concepts can be modeled both as common factors and as composites, i.e., as linear combinations of observed variables that convey all the information between their observed variables and all other variables in the model. This thesis presents methodological advancements in the field of composite-based SEM. In specific, Chapter 1 provides an overview of the underlying model, as well as a definition of the term composite-based SEM. Chapter 2 provides guidelines on how to perform Monte Carlo simulations in the statistic software R using the package “cSEM” with various estimators in the context of composite based SEM. The third Chapter presents estimators of composite-based SEM, which are adaptions of partial least squares path modeling (PLS-PM) and consistent partial least squares (PLSc), which are robust in responding to outlier distortion. These adjustments can avoid distortion that could arise from random outliers in samples. Chapter 4 presents an approach to performing out-of-sample predictions based on models estimated with ordinal partial least squares and ordinal consistent partial least squares. Here, the observed variables lie on an ordinal categorical scale which is explicitly taken into account in both estimation and prediction. Chapter 5 introduces confirmatory composite analysis (CCA) for research in “Human Development”. This chapter uses the Henseler-Ogasawara specification for composite models, allowing, for example, the maximum likelihood method to be used for parameter estimation. As an alternative, Chapter 6 presents another specification of the composite model by means of which composite models can be estimated with the maximum likelihood method. The last chapter, Chapter 7, gives an overview of the development and different strands of composite-based structural equation modeling. Additionally, here I examine the contribution the previous chapters make to the wider distribution of composite-based structural equation modeling.