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Article

Evaluating the Observed Log-Likelihood Function in Two-Level Structural Equation Modeling with Missing Data: From Formulas to R Code

by
Yves Rosseel
Department of Data Analysis, Ghent University, Henri Dunantlaan 1, B-9000 Ghent, Belgium
Psych 2021, 3(2), 197-232; https://doi.org/10.3390/psych3020017
Submission received: 30 April 2021 / Revised: 3 June 2021 / Accepted: 4 June 2021 / Published: 7 June 2021
(This article belongs to the Special Issue Computational Aspects, Statistical Algorithms and Software in Psychometrics)
Versions Notes

Abstract

This paper discusses maximum likelihood estimation for two-level structural equation models when data are missing at random at both levels. Building on existing literature, a computationally efficient expression is derived to evaluate the observed log-likelihood. Unlike previous work, the expression is valid for the special case where the model implied variance–covariance matrix at the between level is singular. Next, the log-likelihood function is translated to R code. A sequence of R scripts is presented, starting from a naive implementation and ending at the final implementation as found in the lavaan package. Along the way, various computational tips and tricks are given.
Keywords: structural equation modeling; multilevel; missing data; observed loglikelihood; R code structural equation modeling; multilevel; missing data; observed loglikelihood; R code

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MDPI and ACS Style

Rosseel, Y. Evaluating the Observed Log-Likelihood Function in Two-Level Structural Equation Modeling with Missing Data: From Formulas to R Code. Psych 2021, 3, 197-232. https://doi.org/10.3390/psych3020017

AMA Style

Rosseel Y. Evaluating the Observed Log-Likelihood Function in Two-Level Structural Equation Modeling with Missing Data: From Formulas to R Code. Psych. 2021; 3(2):197-232. https://doi.org/10.3390/psych3020017

Chicago/Turabian Style

Rosseel, Yves. 2021. "Evaluating the Observed Log-Likelihood Function in Two-Level Structural Equation Modeling with Missing Data: From Formulas to R Code" Psych 3, no. 2: 197-232. https://doi.org/10.3390/psych3020017

APA Style

Rosseel, Y. (2021). Evaluating the Observed Log-Likelihood Function in Two-Level Structural Equation Modeling with Missing Data: From Formulas to R Code. Psych, 3(2), 197-232. https://doi.org/10.3390/psych3020017

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