Computationally Efficient Estimation of Multilevel High-Dimensional Latent Variable Models
نویسندگان
چکیده
Multilevel analysis often leads to modeling with multiple latent variables on several levels. While this is less of a problem with Gaussian observed variables, maximum-likelihood (ML) estimation with categorical outcomes presents computational problems due to multidimensional numerical integration. We describe a new method that compared to ML is both computationally efficient and has similar MSE. The method is an extension of the Muthen (1984) weighted least squares (WLS) estimation method to multilevel multivariate latent variable models for any combination of categorical, censored, and normal observed variables. Using a new version of the Mplus program, we compare MSE and the computational time for the ML and WLS estimators in a simulation study.
منابع مشابه
High Dimensional Expectation-Maximization Algorithm: Statistical Optimization and Asymptotic Normality
We provide a general theory of the expectation-maximization (EM) algorithm for inferring high dimensional latent variable models. In particular, we make two contributions: (i) For parameter estimation, we propose a novel high dimensional EM algorithm which naturally incorporates sparsity structure into parameter estimation. With an appropriate initialization, this algorithm converges at a geome...
متن کاملHigh Dimensional EM Algorithm: Statistical Optimization and Asymptotic Normality
We provide a general theory of the expectation-maximization (EM) algorithm for inferring high dimensional latent variable models. In particular, we make two contributions: (i) For parameter estimation, we propose a novel high dimensional EM algorithm which naturally incorporates sparsity structure into parameter estimation. With an appropriate initialization, this algorithm converges at a geome...
متن کاملTensor decompositions for learning latent variable models
This work considers a computationally and statistically efficient parameter estimation method for a wide class of latent variable models—including Gaussian mixture models, hidden Markov models, and latent Dirichlet allocation—which exploits a certain tensor structure in their low-order observable moments (typically, of secondand third-order). Specifically, parameter estimation is reduced to the...
متن کاملHigh-Dimensional Variance-Reduced Stochastic Gradient Expectation-Maximization Algorithm
We propose a generic stochastic expectationmaximization (EM) algorithm for the estimation of high-dimensional latent variable models. At the core of our algorithm is a novel semi-stochastic variance-reduced gradient designed for the Qfunction in the EM algorithm. Under a mild condition on the initialization, our algorithm is guaranteed to attain a linear convergence rate to the unknown paramete...
متن کاملEstimation of Contextual Effects through Nonlinear Multilevel Latent Variable Modeling with a Metropolis-Hastings Robbins-Monro Algorithm
The main purpose of this study is to improve estimation efficiency in obtaining fullinformation maximum likelihood (FIML) estimates of contextual effects in the framework of nonlinear multilevel latent variable model by adopting the Metropolis-Hastings Robbins-Monro algorithm (MH-RM; Cai, 2008, 2010a, 2010b). Results indicate that the MH-RM algorithm can produce FIML estimates and their standar...
متن کامل