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This thesis is about composite-based structural equation modeling. Structural equation modeling in general can be used to model both theoretical concepts and their relations to one another. In traditional factor-based structural equation modeling, 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 structural equation modeling, 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 some methodological advancements in the field of composite-based structural equation modeling. In all, this thesis is made up of seven chapters. Chapter 1 provides an overview of the underlying model, as well as explicating the meaning of the term composite-based structural equation modeling. Chapter 2 gives 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 structural equation modeling. These guidelines are illustrated by an example simulation study that investigates the finite sample behavior of partial least squares path modeling (PLS-PM) and consistent partial least squares (PLSc) estimates, particularly regarding the consequences of sample correlations between measurement errors on statistical inference. The third Chapter presents estimators of composite-based structural equation modeling that are robust in responding to outlier distortion. For this purpose, estimators of composite-based structural equation modeling, PLS-PM and PLSc, are adapted. Unlike the original estimators, these adjustments can avoid distortion that could arise from random outliers in samples, as is demonstrated through a simulation study. Chapter 4 presents an approach to performing 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. The prediction performance is evaluated by means of a simulation study. In addition, the chapter gives guidelines on how to perform such predictions using the R package “cSEM”. This is demonstrated by means of an empirical example. Chapter 5 introduces confirmatory composite analysis (CCA) for research in “Human Development”. Using CCA, composite models can be estimated and assessed. This chapter uses the Henseler-Ogasawara specification for composite models, allowing, for example, the maximum likelihood method to be used for parameter estimation. Since the maximum likelihood estimator based on the Henseler-Ogasawara specification has limitations, Chapter 6 presents another specification of the composite model by means of which composite models can be estimated with the maximum likelihood method. The results of this maximum likelihood estimator are compared with those of PLS-PM, thus showing that this maximum likelihood estimator gives valid results even in finite samples. 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.

This dissertation deals with composite-based methods for structural equation models with latent variables and their enhancement. It comprises five chapters. Besides a brief introduction in the first chapter, the remaining chapters consisting of four essays cover the results of my PhD studies.Two of the essays have already been published in an international journal.
The first essay considers an alternative way of construct modeling in structural equation modeling.While in social and behavioral sciences theoretical constructs are typically modeled as common factors, in other sciences the common factor model is an inadequate way construct modeling due to its assumptions. This essay introduces the confirmatory composite analysis (CCA) analogous to confirmatory factor analysis (CFA). In contrast to CFA, CCA models theoretical constructs as composites instead of common factors. Besides the theoretical presentation of CCA and its assumptions, a Monte Carlo simulation is conducted which demonstrates that misspecifications of the composite model can be detected by the introduced test for overall model fit.
The second essay rises the question of how parameter differences can be assessed in the framework of partial least squares path modeling. Since the standard errors of the estimated parameters have no analytical closed-form, the t- and F-test known from regression analysis cannot be directly used to test for parameter differences. However, bootstrapping provides a solution to this problem. It can be employed to construct confidence intervals for the estimated parameter differences, which can be used for making inferences about the parameter difference in the population. To guide practitioners, guidelines were developed and demonstrated by means of empirical examples.
The third essay answers the question of how ordinal categorical indicators can be dealt with in partial least squares path modeling. A new consistent estimator is developed which combines the polychoric correlation and partial least squares path modeling to appropriately deal with the qualitative character of ordinal categorical indicators. The new estimator named ordinal consistent partial least squares combines consistent partial least squares with ordinal partial least squares. Besides its derivation, a Monte Carlo simulation is conducted which shows that the new estimator performs well in finite samples. Moreover, for illustration, an empirical example is estimated by ordinal consistent partial least squares.
The last essay introduces a new consistent estimator for polynomial factor models.
Similarly to consistent partial least squares, weights are determined to build stand-ins for the latent variables, however a non-iterative approach is used.
A Monte Carlo simulation shows that the new estimator behaves well in finite samples.