title: Estimation of the latent mediated effect with ordinal data using the limited-information and Bayesian full-information approaches.
abstract: It is common to encounter latent variables with ordinal data in social or behavioral research. Although a mediated effect of latent variables (latent mediated effect, or LME) with ordinal data may appear to be a straightforward combination of LME with continuous data and latent variables with ordinal data, the methodological challenges to combine the two are not trivial. This research covers model structures as complex as LME and formulates both point and interval estimates of LME for ordinal data using the Bayesian full-information approach. We also combine weighted least squares (WLS) estimation with the bias-corrected bootstrapping (BCB; Efron Journal of the American Statistical Association, 82, 171-185, 1987) method or the traditional delta method as the limited-information approach. We evaluated the viability of these different approaches across various conditions through simulation studies, and provide an empirical example to illustrate the approaches. We found that the Bayesian approach with reasonably informative priors is preferred when both point and interval estimates are of interest and the sample size is 200 or above.
authors.affiliation: Department of Psychology, Sun Yat-Sen University, Guangzhou, GD, China. jinsong.chen@live.com.
authors.forename: Jinsong
authors.initials: J
authors.lastname: Chen
authors.affiliation: Department of Educational Psychology, Rutgers, the State University of New Jersey, New Brunswick, NJ, USA.
authors.forename: Dake
authors.initials: D
authors.lastname: Zhang
authors.affiliation: Graduate School of Education and Human Development, George Washington University, Washington, DC, USA.
authors.forename: Jaehwa
authors.initials: J
authors.lastname: Choi
mesh_terms: D000465:Algorithms; D001499:Bayes Theorem; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D006801:Humans; D016018:Least-Squares Analysis; D008962:Models, Theoretical; D018401:Sample Size
keywords: Bayesian full information; Latent mediated effect; Limited information; Ordinal data; Structural equation model