Author : Nicholas J. Rockwood
Publisher :
ISBN 13 :
Total Pages : 113 pages
Book Rating : 4.:/5 (115 download)
Book Synopsis Estimating Multilevel Structural Equation Models with Random Slopes for Latent Covariates by : Nicholas J. Rockwood
Download or read book Estimating Multilevel Structural Equation Models with Random Slopes for Latent Covariates written by Nicholas J. Rockwood and published by . This book was released on 2019 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 other random effects can be computed in closed-form. For most models implemented in practice, this method results in a function that typically requires less than four dimensions of numerical integration. Thus, the estimation routine I develop here allows for many models within the MSEM framework to be estimated that would otherwise be impractical to fit using currently implemented methods. In addition to developing this new ML estimation algorithm, three example MSEMs are fit to real-world datasets to demonstrate the generality of the MSEM framework. Further, I assess the performance of this estimation routine using three small-scale simulation studies based on the examples. Overall, the estimation routine appears to recover the true parameters well, highlighting the utility of this new method. I also discuss limitations of the proposed method, possible ways of extending the methodology to account for other types of data (e.g., categorical and count outcomes), and the importance of future research to assess the performance of the ML estimates for such models relative to other modeling frameworks.
