• Communications for Statistical Applications and Methods
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• v.27 no.6
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• pp.701-714
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• 2020

Quantitative high throughput screening (qHTS) assays are used to assess toxicity for many chemicals in a short period by collectively analyzing them at several concentrations. Data are routinely analyzed using nonlinear regression models; however, we propose a new method to analyze qHTS data using a nonlinear mixed effects model. qHTS data are generated by repeating the same experiment several times for each chemical; therefor, they can be viewed as if they are repeated measures data and hence analyzed using a nonlinear mixed effects model which accounts for both intra- and inter-individual variabilities. Furthermore, we apply a one-step approach incorporating robust estimation methods to estimate fixed effect parameters and the variance-covariance structure since outliers or influential observations are not uncommon in qHTS data. The toxicity of chemicals from a qHTS assay is classified based on the significance of a parameter related to the efficacy of the chemicals using the proposed method. We evaluate the performance of the proposed method in terms of power and false discovery rate using simulation studies comparing with one existing method. The proposed method is illustrated using a dataset obtained from the National Toxicology Program.

• Journal of the Korean Data and Information Science Society
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• v.20 no.2
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• pp.445-452
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• 2009

Credibility models are actuarial tools to distribute premiums fairly among a heterogeneous group of policyholders. Many existing credibility models can be expressed as special cases of linear mixed effects models. In this paper we propose a nonlinear credibility regression model by reforming the linear mixed effects model through kernel machine. The proposed model can be seen as prediction method applicable in any setting where repeated measures are made for subjects with different risk levels. Experimental results are then presented which indicate the performance of the proposed estimating procedure.

• Computers and Concrete
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• v.4 no.2
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• pp.135-156
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• 2007

Three 3D nonlinear finite-element models are developed to study the behavior of concrete beams and plates with and without external reinforcement by fibre-reinforced plastic (FRP). All three models are formulated based upon the 3D theory of elasticity. The stress model is modified from the element developed by Ramtekkar, et al. (2002) to incorporate material nonlinearity in the formulation. Both transverse stress and displacement components are used as nodal degrees-of-freedom to ensure the continuity of both stress and displacement components between the elements. The displacement model uses only displacement components as nodal degrees-of-freedom. The transition model has both stress and displacement components as nodal degrees-of-freedom on one surface, and only displacement components as nodal degrees-of-freedom on the opposite surface. The transition model serves as a connector between the stress and the displacement models. The developed models are validated by comparing the results of the analyses with an existing experimental result. Parametric studies of the effects of the externally reinforced FRP on the load capacity of reinforced concrete (RC) beams and concrete plates are performed to demonstrate the practicality and the efficiency of the proposed models.

• 대한임상약리학회:학술대회논문집
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• 2006.11a
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• pp.37-38
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• 2006

• The Korean Journal of Applied Statistics
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• v.31 no.1
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• pp.123-137
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• 2018

A nonlinear mixed effects model is mainly used to analyze repeated measurement data in various fields. A nonlinear mixed effects model consists of two stages: the first-stage individual-level model considers intra-individual variation and the second-stage population model considers inter-individual variation. The individual-level model, which is the first stage of the nonlinear mixed effects model, estimates the parameters of the nonlinear regression model. It is the same as the general nonlinear regression model, and usually estimates parameters using the least squares estimation method. However, the least squares estimation method may have a problem that the estimated value of the parameters and standard errors become extremely large if the assumed nonlinear function is not explicitly revealed by the data. In this paper, a new estimation method is proposed to solve this problem by introducing the ridge regression method recently proposed in the nonlinear regression model into the first-stage individual-level model of the nonlinear mixed effects model. The performance of the proposed estimator is compared with the performance with the standard estimator through a simulation study. The proposed methodology is also illustrated using quantitative high throughput screening data obtained from the US National Toxicology Program.

• Animal Bioscience
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• v.35 no.5
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• pp.648-658
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• 2022

Objective: The identification of nonlinear mixed models that describe the growth trajectory of New Zealand rabbits was performed based on weight records and carcass measures obtained using ultrasonography. Methods: Phenotypic records of body weight (BW) and loin eye area (LEA) were collected from 66 animals raised in a didactic-productive module of cuniculture located in the southern Piaui state, Brazil. The following nonlinear models were tested considering fixed parameters: Brody, Gompertz, Logistic, Richards, Meloun 1, modified Michaelis-Menten, Santana, and von Bertalanffy. The coefficient of determination (R²), mean squared error, percentage of convergence of each model (%C), mean absolute deviation of residuals, Akaike information criterion (AIC), and Bayesian information criterion (BIC) were used to determine the best model. The model that best described the growth trajectory for each trait was also used under the context of mixed models, considering two parameters that admit biological interpretation (A and k) with random effects. Results: The von Bertalanffy model was the best fitting model for BW according to the highest value of R² (0.98) and lowest values of AIC (6,675.30) and BIC (6,691.90). For LEA, the Logistic model was the most appropriate due to the results of R² (0.52), AIC (783.90), and BIC (798.40) obtained using this model. The absolute growth rates estimated using the von Bertalanffy and Logistic models for BW and LEA were 21.51g/d and 3.16 cm², respectively. The relative growth rates at the inflection point were 0.028 for BW (von Bertalanffy) and 0.014 for LEA (Logistic). Conclusion: The von Bertalanffy and Logistic models with random effect at the asymptotic weight are recommended for analysis of ponderal and carcass growth trajectories in New Zealand rabbits. The inclusion of random effects in the asymptotic weight and maturity rate improves the quality of fit in comparison to fixed models.

• Journal of Korean Society of Forest Science
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• v.111 no.1
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• pp.136-149
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• 2022

In this study, the performance of a nonlinear mixed-effects (NLME) model used to estimate the stem taper of Pinus densiflora in Gangwon Province was compared with that of a nonlinear fixed-effects (NLFE) model using several performance measures. For the diameters of whole tree stems, the NLME model improved on the performance of the NLFE model by 26.4%, 42.9%, 43.1%, and 0.9% in terms of BIAS, MAB, RMSE, and FI, respectively. For the cross-section areas of whole tree stems, the NLME model improved on the performance of the NLFE model by 67.7%, 44.7%, 45.8%, and 1.0% in terms of BIAS, MAB, RMSE, and FI, respectively. Based on the analysis of 12 relative height classes of tree stems, stem taper estimation performance was also reasonably improved by the NLME model, which showed better MAB, RMSE, and FI at every relative height class compared with those of the NLFE model. In some classes, the NLFE model had better BIAS than the NLME model (stem diameter: 0.05, 0.2, 0.3, and 0.8; stem cross-section area: 0.05, 0.3, 0.5, 0.6, and 1.0). However, the NLME model enhanced the performance of stem diameter and cross-section area estimations at the lowest stem part (0.2 m from the ground). Improvements for stem diameter in terms of BIAS, MAB, RMSE, and FI were 84.2%, 69.8%, 68.7%, and 3.1%, respectively. For stem cross-section areas, the improvements in BIAS, MAB, RMSE, and FI were 98.5%, 70.1%, 68.7%, and 3.1%, respectively. The cross-section area at 0.2 m from the ground occupied 22.7% of total cross-section area. Improvements in estimation of cross-section area at the lowest stem part indicate that stem volume estimation performance could also be enhanced. Although NLME models are more difficult to fit than NLFE models, the use of NLME models as a standard method for the estimating the parameters of stem taper equations should be considered.

• Advances in nano research
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• v.6 no.2
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• pp.163-182
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• 2018

Based on the Reissner mixed variational theorem (RMVT), the authors present a nonlocal Timoshenko beam theory (TBT) for the nonlinear free vibration analysis of multi-walled carbon nanotubes (MWCNT) embedded in an elastic medium. In this formulation, four different edge conditions of the embedded MWCNT are considered, two different models with regard to the van der Waals interaction between each pair of walls constituting the MWCNT are considered, and the interaction between the MWCNT and its surrounding medium is simulated using the Pasternak-type foundation. The motion equations of an individual wall and the associated boundary conditions are derived using Hamilton's principle, in which the von $K{\acute{a}}rm{\acute{a}}n$ geometrical nonlinearity is considered. Eringen's nonlocal elasticity theory is used to account for the effects of the small length scale. Variations of the lowest frequency parameters with the maximum modal deflection of the embedded MWCNT are obtained using the differential quadrature method in conjunction with a direct iterative approach.

• Journal of Applied Reliability
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• v.18 no.1
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• pp.33-39
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• 2018

Purpose: Accelerated degradation tests can be effective in assessing product reliability when degradation leading to failure can be observed. This article proposes an accelerated degradation test model for highly reliable solid state drives (SSDs). Methods: We suggest a nonlinear mixed-effects (NLME) model to degradation data for SSDs. A Monte Carlo simulation is used to estimate lifetime distribution in accelerated degradation testing data. This simulation is performed by generating random samples from the assumed NLME model. Conclusion: We apply the proposed method to degradation data collected from SSDs. The derived power model is shown to be much better at fitting the degradation data than other existing models. Finally, the Monte Carlo simulation based on the NLME model provides reasonable results in lifetime estimation.

• Asian-Australasian Journal of Animal Sciences
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• v.24 no.1
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• pp.17-27
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• 2011

A selection experiment for reduced residual feed intake (RFI) in Yorkshire pigs consisted of a line selected for lower RFI (LRFI) and a random control line (CTRL). Longitudinal measurements of daily feed intake (DFI) and body weight (BW) from generation 5 of this experiment were used. The objectives of this study were to evaluate the use of random regression (RR) and nonlinear mixed models to predict DFI and BW for individual pigs, accounting for the substantial missing information that characterizes these data, and to evaluate the effect of selection for RFI on BW and DFI curves. Forty RR models with different-order polynomials of age as fixed and random effects, and with homogeneous or heterogeneous residual variance by month of age, were fitted for both DFI and BW. Based on predicted residual sum of squares (PRESS) and residual diagnostics, the quadratic polynomial RR model was identified to be best, but with heterogeneous residual variance for DFI and homogeneous residual variance for BW. Compared to the simple quadratic and linear regression models for individual pigs, these RR models decreased PRESS by 1% and 2% for DFI and by 42% and 36% for BW on boars and gilts, respectively. Given the same number of random effects as the polynomial RR models, i.e., two for BW and one for DFI, the non-linear Gompertz model predicted better than the polynomial RR models but not as good as higher order polynomial RR models. After five generations of selection for reduced RFI, the LRFI line had a lower population curve for DFI and BW than the CTRL line, especially towards the end of the growth period.