Bias Analysis and SIMEX Approach in Generalized Linear Mixed Measurement Error Models

Wang, Naisyin; Lin, Xihong; Gutierrez, Roberto G.; Carroll, Raymond J.

doi:10.2307/2669621

Cited by 66 publications

(84 citation statements)

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“…Many issues, however, merit further research. For instance, the SAEM algorithm could be applied to problems of missing τ k 2 (blue line) at each iteration; (d) σ k 1 (red line) and σ k 2 (blue line) at each iteration data, such as those found in generalized linear mixed measurement error models (Wang et al, 1998), parametric regression models with missing covariates (Horton and Laird, 1998), and generalized nonparametric mixed effects models (Karcher and Wang, 2001). The SAEM algorithm should provide an efficient algorithm for finding the maximum likelihood estimate of those models for missing data.…”

Section: Discussionmentioning

confidence: 99%

Maximum likelihood from spatial random effects models via the stochastic approximation expectation maximization algorithm

Zhu

Peterson

2007

Stat Comput

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We introduce a class of spatial random effects models that have Markov random fields (MRF) as latent processes. Calculating the maximum likelihood estimates of unknown parameters in SREs is extremely difficult, because the normalizing factors of MRFs and additional integrations from unobserved random effects are computationally prohibitive. We propose a stochastic approximation expectation-maximization (SAEM) algorithm to maximize the likelihood functions of spatial random effects models. The SAEM algorithm integrates recent improvements in stochastic approximation algorithms; it also includes components of the Newton-Raphson algorithm and the expectation-maximization (EM) gradient algorithm. The convergence of the SAEM algorithm is guaranteed under some mild conditions. We apply the SAEM algorithm to three examples that are representative of real-world applications: a state space model, a noisy Ising model, and segmenting magnetic resonance images (MRI) of the human brain. The SAEM algorithm gives satisfactory results in finding the maximum likelihood estimate of spatial random effects models in each of these instances.

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Section: Discussionmentioning

confidence: 99%

Maximum likelihood from spatial random effects models via the stochastic approximation expectation maximization algorithm

Zhu

Peterson

2007

Stat Comput

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“…This makes the estimation of the multilevel model very demanding, especially considering that a measurement error correction should be implemented. The SIMEX method can be applied to multilevel models (see, e.g., Wang, Lin, Gutierrez, & Carroll, 1998), but further study is necessary to clarify how to obtain random effects estimates, which are of primary interest in this context. On the contrary, the procedure proposed in this paper is quite simple and it is also reasonably effective even for small sample sizes, as shown by the simulations presented in Section 4.…”

Section: Discussionmentioning

confidence: 99%

Reducing Measurement Error in Student Achievement Estimation

2007

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“…Thus, the GLMM can be specified to accommodate outcome variables conditional on mixtures of possibly correlated random and fixed effects (Breslow and Clayton 1993;Buonaccorsi 1996;Wang et al 1998;Wolfinger and O'Connell 1993). Details of such models, covering both statistical inferences and computational methods, can be found in the texts by McCulloch and Searle (2001) and Jiang (2007).…”

Section: Introductionmentioning

confidence: 99%