Composite-based Methods in Structural Equation Modeling

Abstract

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.