Two-Stage Limited-Information Estimation for Structural Equation Models of Round-Robin Variables

Terrence D. Jorgensen (), Aditi M. Bhangale and Yves Rosseel
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Terrence D. Jorgensen: Research Institute of Child Development and Education, University of Amsterdam, Nieuwe Achtergracht 127, 1018 WS Amsterdam, The Netherlands
Aditi M. Bhangale: Research Institute of Child Development and Education, University of Amsterdam, Nieuwe Achtergracht 127, 1018 WS Amsterdam, The Netherlands
Yves Rosseel: Center for Data Analysis and Statistical Science, Ghent University, Krijgslaan 281-S9, 9000 Gent, Belgium

Stats, 2024, vol. 7, issue 1, 1-34

Abstract: We propose and demonstrate a new two-stage maximum likelihood estimator for parameters of a social relations structural equation model (SR-SEM) using estimated summary statistics ( Σ ^ ) as data, as well as uncertainty about Σ ^ to obtain robust inferential statistics. The SR-SEM is a generalization of a traditional SEM for round-robin data, which have a dyadic network structure (i.e., each group member responds to or interacts with each other member). Our two-stage estimator is developed using similar logic as previous two-stage estimators for SEM, developed for application to multilevel data and multiple imputations of missing data. We demonstrate out estimator on a publicly available data set from a 2018 publication about social mimicry. We employ Markov chain Monte Carlo estimation of Σ ^ in Stage 1, implemented using the R package rstan. In Stage 2, the posterior mean estimates of Σ ^ are used as input data to estimate SEM parameters with the R package lavaan. The posterior covariance matrix of estimated Σ ^ is also calculated so that lavaan can use it to calculate robust standard errors and test statistics. Results are compared to full-information maximum likelihood (FIML) estimation of SR-SEM parameters using the R package srm. We discuss how differences between estimators highlight the need for future research to establish best practices under realistic conditions (e.g., how to specify empirical Bayes priors in Stage 1), as well as extensions that would make 2-stage estimation particularly advantageous over single-stage FIML.

Keywords: structural equation model; social relations model; social network data; round-robin design; maximum likelihood estimation; two-stage estimation; Markov chain Monte Carlo estimation (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2024
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