A Comparison of Estimation Methods for Nonlinear Mixed-Effects Models Under Model Misspecification and Data Sparseness: A Simulation Study

Harring, Jeffrey R.; Liu, Junhui

doi:10.22237/jmasm/1462076760

Cited by 9 publications

(9 citation statements)

References 37 publications

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“…Next, we used nonadaptive Gaussian quadrature to fit the nonlinear mixed-effects model (7) to the generated data sets. For this case, we repeated the above calculations to obtain the simulated relative bias of̂M L using (8). The simulations results, which are reported in Table 2, are very similar to those from the adaptive Gaussian quadrature, and the only difference is that the estimates of variance components show little bias under the correct random-effects distribution.…”

Section: The Impact On Estimationmentioning

confidence: 77%

“…in whicĥ * ML is the mean of maximum likelihood estimates obtained from the 500 replications. Then, for each simulation setting, we computed the simulated relative bias of̂M L according to (8). The simulations results are presented in Table 1.…”

Section: The Impact On Estimationmentioning

confidence: 99%

“…It has been shown that numerical approximations generally provide more accurate parameter estimates compared with the analytical approximations. In a recent paper, Harring and Liu showed, via extensive simulations, that Gauss‐Hermite quadrature outperforms both the first‐order expansion and the Laplace's approximation in terms of estimation accuracy. Furthermore, in their simulations with two random effects, they observed that Gauss‐Hermite quadrature and the first‐order expansion do not suffer from convergence issues, while the Laplace's approximation encounters convergence difficulty.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear mixed‐effects models with misspecified random‐effects distribution

Drikvandi

2019

Pharmaceutical Statistics

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Nonlinear mixed-effects models are being widely used for the analysis of longitudinal data, especially from pharmaceutical research. They use random effects which are latent and unobservable variables so the random-effects distribution is subject to misspecification in practice. In this paper, we first study the consequences of misspecifying the random-effects distribution in nonlinear mixed-effects models. Our study is focused on Gauss-Hermite quadrature, which is now the routine method for calculation of the marginal likelihood in mixed models. We then present a formal diagnostic test to check the appropriateness of the assumed random-effects distribution in nonlinear mixed-effects models, which is very useful for real data analysis. Our findings show that the estimates of fixed-effects parameters in nonlinear mixed-effects models are generally robust to deviations from normality of the random-effects distribution, but the estimates of variance components are very sensitive to the distributional assumption of random effects. Furthermore, a misspecified random-effects distribution will either overestimate or underestimate the predictions of random effects. We illustrate the results using a real data application from an intensive pharmacokinetic study.

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Section: The Impact On Estimationmentioning

confidence: 77%

Section: The Impact On Estimationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Nonlinear mixed‐effects models with misspecified random‐effects distribution

Drikvandi

2019

Pharmaceutical Statistics

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“…To determine the best trajectory for verbal ability in our motivating data, we first fit the six curves from Table 1 with a marginal nonlinear regression model (i.e., with no random effects) using Proc Nlin in SAS 9.4. We compared the mean square error (MSE) for each of these curves to inform which would be the best candidates for inclusion in the full nonlinear mixed effect model, especially because these models are notorious for their difficulties with computation and convergence (e.g., Harring & Liu, 2016).…”

Section: Motivating Datamentioning

confidence: 99%

Estimating New Quantities from Longitudinal Test Scores to Improve Forecasts of Future Performance

McNeish

Dumas

Grimm

2019

Multivariate Behavioral Research

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Psychometric models for longitudinal test scores typically estimate quantities associated with single-administration tests, like ability at each time-point. However, models for longitudinal tests have not considered opportunities to estimate new quantities that are unavailable from singleadministration tests. Specifically, we discuss dynamic measurement modelswhich combine aspects of longitudinal IRT, nonlinear growth models, and dynamic assessmentto directly estimate capacity, defined as the expected future score once the construct has fully developed. After discussing the history and connecting these areas into a single framework, we apply the model to verbal test scores from the Intergenerational Studies, which follow 494 people from 3 to 72 years old. The goal is to predict adult verbal scores (Age ≥ 34) from adolescent scores (Age ≤ 20). We held-out the adult data for prediction and compared predictions from traditional longitudinal IRT ability scores and proposed dynamic measurement capacity scores from models fit to the adolescent data. Results showed that the R 2 from capacity scores were 2.5 times larger than the R 2 from longitudinal IRT ability scores (43% vs. 16%), providing some evidence that exploring new quantities available from longitudinal testing could be worthwhile when an interest in testing is forecasting future performance.

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“…In the process, the true bias and covariance of the retrieval errors can be determined. This approach and the underlying statistical model resemble simulation studies of nonlinear mixed effects (NLME) models [14,15]. In the remote sensing application, the inference objective focuses on the state, which would be considered the random effect in the NLME context.…”

mentioning

confidence: 99%

Simulation-Based Uncertainty Quantification for Estimating Atmospheric CO$_2$ from Satellite Data

Hobbs¹,

Braverman²,

Cressie³

et al. 2017

SIAM/ASA J. Uncertainty Quantification

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Remote sensing of the atmosphere has provided a wealth of data for analyses and inferences in earth science. Satellite observations can provide information on the atmospheric state at fine spatial and temporal resolution while providing substantial coverage across the globe. For example, this capability can greatly enhance the understanding of the space-time variation of the greenhouse gas, carbon dioxide (CO2), since ground-based measurements are limited. NASA's Orbiting Carbon Observatory-2 (OCO-2) collects tens of thousands of observations of reflected sunlight daily, and the mission's retrieval algorithm processes these indirect measurements into estimates of atmospheric CO2. The retrieval is an inverse problem and consists of a physical forward model for the transfer of radiation through the atmosphere that includes absorption and scattering by gases, aerosols, and the surface. The model and other algorithm inputs introduce key sources of uncertainty into the retrieval problem. This article develops a computationally efficient surrogate model that is embedded in a simulation experiment for studying the impact of uncertain inputs on the distribution of the retrieval error. Abstract. Remote sensing of the atmosphere has provided a wealth of data for analyses and 5 inferences in Earth science. Satellite observations can provide information on the atmospheric state 6 at fine spatial and temporal resolution while providing substantial coverage across the globe. For 7 example, this capability can greatly enhance the understanding of the space-time variation of the 8 greenhouse gas, carbon dioxide (CO 2 ), since ground-based measurements are limited. NASA's Or-9 biting Carbon Observatory-2 (OCO-2) collects tens of thousands of observations of reflected sunlight 10 daily, and the mission's retrieval algorithm processes these indirect measurements into estimates of 11 atmospheric CO 2 . The retrieval is an inverse problem and consists of a physical forward model for 12 the transfer of radiation through the atmosphere that includes absorption and scattering by gases, 13 aerosols, and the surface. The model and other algorithm inputs introduce key sources of uncertainty 14 into the retrieval problem. This article develops a computationally efficient surrogate model that is 15 embedded in a simulation experiment for studying the impact of uncertain inputs on the distribution 16 of the retrieval error. 17

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A Comparison of Estimation Methods for Nonlinear Mixed-Effects Models Under Model Misspecification and Data Sparseness: A Simulation Study

Cited by 9 publications

References 37 publications

Nonlinear mixed‐effects models with misspecified random‐effects distribution

Nonlinear mixed‐effects models with misspecified random‐effects distribution

Estimating New Quantities from Longitudinal Test Scores to Improve Forecasts of Future Performance

Simulation-Based Uncertainty Quantification for Estimating Atmospheric CO$_2$ from Satellite Data

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