A general two-level latent variable model is developed to provide a comprehensive framework for model comparison of various submodels. Nonlinear relationships among the latent variables in the structural equations at ...
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A general two-level latent variable model is developed to provide a comprehensive framework for model comparison of various submodels. Nonlinear relationships among the latent variables in the structural equations at both levels, as well as the effects of fixed covariates in the measurement and structural equations at both levels, can be analyzed within the framework. Moreover, the methodology can be applied to hierarchically mixed continuous, dichotomous, and polytomous data. A Monte Carlo EM algorithm is implemented to produce the maximum likelihood estimate. The E-step is completed by approximating the conditional expectations through observations that are simulated by Markov chain Monte Carlo methods, while the M-step is completed by conditional maximization. A procedure is proposed for computing the complicated observed-data log likelihood and the BIC for model comparison. The methods are illustrated by using a real data set.
Finite mixture of structural equation models is very useful to analyze data from heterogeneous populations. In this article, we present a feasible procedure to assess local influence of minor perturbations for identif...
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Finite mixture of structural equation models is very useful to analyze data from heterogeneous populations. In this article, we present a feasible procedure to assess local influence of minor perturbations for identifying influential aspects on the maximum likelihood estimation of a finite mixture of structural equation models. A Monte Carlo EM algorithm which treats both latent variables and allocation variables as hypothetical missing data is implemented. The local influence measures are developed on the basis of a Q-displacement function at the E-step of the algorithm. The diagnostic measures are based on the conformal normal curvature that can be computed easily. Building blocks of the diagnostic measures are derived, and they are evaluated via observations simulated by the Gibbs sampler from the appropriate conditional distributions. A number of interesting and novel perturbations are considered. The methodology is illustrated with a real example.
Recently, it is recognized that nonlinear relationships among latent variables in a structural equation model are important. In this article, maximum likelihood (ML) analysis of a general nonlinear structural equation...
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Recently, it is recognized that nonlinear relationships among latent variables in a structural equation model are important. In this article, maximum likelihood (ML) analysis of a general nonlinear structural equation model that contains fixed covariates in the measurement equation and the nonlinear structural equation is investigated. A mcem algorithm is implemented to obtain the ML estimates, in which the E-step is completed with the help of a hybrid algorithm that combines the Gibbs sampler and the Metropolis-Hastings algorithm whilst the M-step is completed by conditional maximization. The importance sampling is employed to compute the observed-data likelihood in the Bayesian Information Criterion for model comparison. The methodology is illustrated with a simulation study and a real example. (C) 2002 Elsevier B.V. All rights reserved.
The objective of this paper is to develop the maximum likelihood approach for analyzing a finite mixture of structural equation models with missing data that are missing at random. A Monte Carlo EM algorithm is propos...
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The objective of this paper is to develop the maximum likelihood approach for analyzing a finite mixture of structural equation models with missing data that are missing at random. A Monte Carlo EM algorithm is proposed for obtaining the maximum likelihood estimates. A well-known statistic in model comparison, namely the Bayesian Information Criterion (BIC), is used for model comparison. With the presence of missing data, the computation of the observed-data likelihood function value involved in the BIC is not straightforward. A procedure based on path sampling is developed to compute this function value. It is shown by means of simulation studies that ignoring the incomplete data with missing entries gives less accurate ML estimates. An illustrative real example is also presented.
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...
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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.
We present a maximum likelihood estimation procedure for the multivariate frailty model. The estimation is based on a Monte Carlo EM algorithm. The expectation step is approximated by averaging over random samples dra...
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We present a maximum likelihood estimation procedure for the multivariate frailty model. The estimation is based on a Monte Carlo EM algorithm. The expectation step is approximated by averaging over random samples drawn from the posterior distribution of the frailties using rejection sampling. The maximization step reduces to a standard partial likelihood maximization. We also propose a simple rule based on the relative change in the parameter estimates to decide on sample size in each iteration and a stopping time for the algorithm. An important new concept is acquiring absolute convergence of the algorithm through sample size determination and an efficient sampling technique. The method is illustrated using a rat carcinogenesis dataset and data on vase lifetimes of cut roses. The estimation results are compared with approximate inference based on penalized partial likelihood using these two examples. Unlike the penalized partial likelihood estimation, the proposed full maximum likelihood estimation method accounts for all the uncertainty while estimating standard errors for the parameters.
In reliability studies, often we only have one failure data recorded in a life testing experiment. If there are two parameters in the reliability model, such as the model using Weibull distribution, then maximum likel...
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