Doctor of Philosophy, The Ohio State University, 2019, Psychology
Multilevel structural equation modeling (MSEM) is an emerging statistical framework for the analysis of hierarchically structured data, such as data corresponding to students nested within classrooms or repeated measurements nested within individuals. The MSEM framework provides several advantages over the traditional multilevel modeling (MLM) and structural equation modeling (SEM) frameworks, including the ability to model multivariate responses, level-2 response variables, measurement error via factor models, and structural relations (e.g., regressions) among the random effects/latent variables. Although several formulations of the MSEM have been presented (see, e.g., Liang & Bentler, 2004; Rabe-Hesketh, Skrondal, & Pickles, 2004; Mehta & Neale, 2005), the framework of B. Muthen and Asparouhov (2008) as implemented in Mplus (L. K. Muthen & Muthen, 2017) has the advantage that the relationship between lower-level (i.e., level-1) latent variables can be modeled as randomly varying across upper-level (i.e., level-2) units. Unfortunately, maximum likelihood (ML) estimation of the parameters for such models, as implemented in Mplus, is computationally demanding due to the likelihood function having to be approximated, as the function cannot be computed in closed-form. Mplus numerically integrates over all of the random effects/latent variables using quadrature-based methods. This approach is not feasible for high-dimensional latent variable models, which reduces the potential models that can practically be fit. In this dissertation, I develop a more computationally efficient and accurate ML estimation routine for MSEMs with random slopes for latent variables. The method relies on a reformulation of the likelihood function so that some of the integrals can be computed analytically, reducing the dimension of numerical integration required. Specifically, only the random slopes for latent variables need to be numerically integrated, as the integrals corresponding to the ot (open full item for complete abstract)
Committee: Andrew Hayes Ph.D. (Advisor); Paul De Boeck Ph.D. (Committee Member); Jolynn Pek Ph.D. (Committee Member)
Subjects: Education; Educational Tests and Measurements; Psychology; Quantitative Psychology; Statistics