Maximum likelihood estimation for nonlinear structural equation models with normal latent variables

2010 ◽  
Vol 5 (2) ◽  
pp. 137-147
Author(s):  
Yan D. Zhao ◽  
Dewi Rahardja
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Latent Variables ◽  
Structural Equation ◽  
Structural Equation Models ◽  
Likelihood Estimation ◽  
Nonlinear Structural ◽  
Nonlinear Structural Equation

Maximum Likelihood Estimation of Nonlinear Structural Equation Models with Ignorable Missing Data

2003 ◽  
Vol 28 (2) ◽  
pp. 111-134 ◽  
Author(s):  
Sik-Yum Lee ◽  
Xin-Yuan Song ◽  
John C. K. Lee
Keyword(s):  
Missing Data ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Latent Variables ◽  
Structural Equation ◽  
Likelihood Estimation ◽  
Maximum Likelihood Estimates ◽  
Equation Modeling ◽  
Nonlinear Structural ◽  
Nonlinear Structural Equation

The existing maximum likelihood theory and its computer software in structural equation modeling are established on the basis of linear relationships among latent variables with fully observed data. However, in social and behavioral sciences, nonlinear relationships among the latent variables are important for establishing more meaningful models and it is very common to encounter missing data. In this article, an EM type algorithm is developed for maximum likelihood estimation of a general nonlinear structural equation model with ignorable missing data, which are missing at random with an ignorable mechanism. To avoid computation of the complicated multiple integrals involved in the conditional expectations, the E-step is completed by a hybrid algorithm that combines the Gibbs sampler and the Metropolis-Hastings algorithm; while the M-step is completed efficiently by conditional maximization. Standard errors of the maximum likelihood estimates are obtained via Louis’s formula. The methodology is illustrated with results obtained from a simulation study and a real data set with rather complicated missing patterns and a large number of missing entries.

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