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Journal articles on the topic 'Nonlinear mixed-effects model'

Author: Grafiati

Published: 4 June 2021

Last updated: 5 February 2022

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1

Craig, B. A., and A. P. Schinckel. "Nonlinear Mixed Effects Model for Swine Growth." Professional Animal Scientist 17, no. 4 (December 2001): 256–60. http://dx.doi.org/10.15232/s1080-7446(15)31637-5.

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2

Harring, Jeffrey R. "A Nonlinear Mixed Effects Model for Latent Variables." Journal of Educational and Behavioral Statistics 34, no. 3 (September 2009): 293–318. http://dx.doi.org/10.3102/1076998609332750.

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The nonlinear mixed effects model for continuous repeated measures data has become an increasingly popular and versatile tool for investigating nonlinear longitudinal change in observed variables. In practice, for each individual subject, multiple measurements are obtained on a single response variable over time or condition. This structure can be adapted to examine the change in latent variables rather than modeling change in manifest variables. This article considers a nonlinear mixed effects model for describing nonlinear change of a latent construct over time, where the latent construct of interest is measured by multiple indicators gathered at each measurement occasion. To accomplish this, the nonlinear mixed effects model is modified to include a measurement model that explicitly expresses the relationship of the observed variables to the latent constructs. A method for marginal maximum likelihood estimation of this model is presented and discussed. An example using education data is provided to illustrate the utility of the model.

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3

Funatogawa, Ikuko, and Takashi Funatogawa. "Fundamentals in Population Pharmacokinetics: Mathematics in Linear Mixed Effects Model and Nonlinear Mixed Effects Model." Japanese Journal of Biometrics 36, Special_Issue (2015): S33—S48. http://dx.doi.org/10.5691/jjb.36.s33.

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4

Li, Yao Xiang, and Li Chun Jiang. "Fitting Growth Model Using Nonlinear Regression with Random Parameters." Key Engineering Materials 480-481 (June 2011): 1308–12. http://dx.doi.org/10.4028/www.scientific.net/kem.480-481.1308.

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Mixed Effect models are flexible models to analyze grouped data including longitudinal data, repeated measures data, and multivariate multilevel data. One of the most common applications is nonlinear growth data. The Chapman-Richards model was fitted using nonlinear mixed-effects modeling approach. Nonlinear mixed-effects models involve both fixed effects and random effects. The process of model building for nonlinear mixed-effects models is to determine which parameters should be random effects and which should be purely fixed effects, as well as procedures for determining random effects variance-covariance matrices (e.g. diagonal matrices) to reduce the number of the parameters in the model. Information criterion statistics (AIC, BIC and Likelihood ratio test) are used for comparing different structures of the random effects components. These methods are illustrated using the nonlinear mixed-effects methods in S-Plus software.

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5

Aggrey, S. E. "Logistic nonlinear mixed effects model for estimating growth parameters." Poultry Science 88, no. 2 (February 2009): 276–80. http://dx.doi.org/10.3382/ps.2008-00317.

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6

Elmi, Angelo, Sarah J. Ratcliffe, Samuel Parry, and Wensheng Guo. "A B-Spline Based Semiparametric Nonlinear Mixed Effects Model." Journal of Computational and Graphical Statistics 20, no. 2 (January 2011): 492–509. http://dx.doi.org/10.1198/jcgs.2010.09001.

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7

Davidian, Marie, and David M. Giltinan. "Some general estimation methods for nonlinear mixed-effects model." Journal of Biopharmaceutical Statistics 3, no. 1 (January 1, 1993): 23–55. http://dx.doi.org/10.1080/10543409308835047.

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8

DAVIDIAN, MARIE, and A. RONALD GALLANT. "The nonlinear mixed effects model with a smooth random effects density." Biometrika 80, no. 3 (1993): 475–88. http://dx.doi.org/10.1093/biomet/80.3.475.

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9

Williams, Donald R., Daniel R. Zimprich, and Philippe Rast. "A Bayesian nonlinear mixed-effects location scale model for learning." Behavior Research Methods 51, no. 5 (May 8, 2019): 1968–86. http://dx.doi.org/10.3758/s13428-019-01255-9.

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10

Frutos, G., and M. C. Ruiz de Villa. "Nonlinear mixed-effects model for the dissolution assays of drugs." Journal of Controlled Release 94, no. 2-3 (February 2004): 381–89. http://dx.doi.org/10.1016/j.jconrel.2003.10.017.

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11

Blozis, Shelley A., and Robert Cudeck. "Conditionally Linear Mixed-Effects Models With Latent Variable Covariates." Journal of Educational and Behavioral Statistics 24, no. 3 (September 1999): 245–70. http://dx.doi.org/10.3102/10769986024003245.

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A version of the nonlinear mixed-effects model is presented that allows random effects only on the linear coefficients. Nonlinear parameters are not stochastic. In nonlinear regression, this kind of model has been called conditionally linear. As a mixed-effects model, this structure is more flexible than the popular linear mixed-effects model, while being nearly as straightforward to estimate. In addition to the structure for the repeated measures, a latent variable model ( Browne, 1993 ) is specified for a distinct set of covariates that are related to the random effects in the second level. Unbalanced data are allowed on the repeated measures, and data that are missing at random are allowed on the repeated measures or on the observed variables of the factor analysis sub-model. Features of the model are illustrated by two examples.

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12

Strathe, A. B., A. Danfær, H. Sørensen, and E. Kebreab. "A multilevel nonlinear mixed-effects approach to model growth in pigs1." Journal of Animal Science 88, no. 2 (February 1, 2010): 638–49. http://dx.doi.org/10.2527/jas.2009-1822.

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13

Schumacher, Fernanda L., Clécio S. Ferreira, Marcos O. Prates, Alberto Lachos, and Victor H. Lachos. "A robust nonlinear mixed-effects model for COVID-19 death data." Statistics and Its Interface 14, no. 1 (2021): 49–57. http://dx.doi.org/10.4310/20-sii637.

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14

Sun, Huihui, and Qiang Liu. "Local influence of nonlinear mixed effects model based on M-estimation." Communications in Statistics - Theory and Methods 49, no. 21 (May 30, 2019): 5342–55. http://dx.doi.org/10.1080/03610926.2019.1618474.

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15

Denti, Paolo, Alessandra Bertoldo, Paolo Vicini, and Claudio Cobelli. "IVGTT glucose minimal model covariate selection by nonlinear mixed-effects approach." American Journal of Physiology-Endocrinology and Metabolism 298, no. 5 (May 2010): E950—E960. http://dx.doi.org/10.1152/ajpendo.00656.2009.

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Population approaches, traditionally employed in pharmacokinetic-pharmacodynamic studies, have shown value also in the context of glucose-insulin metabolism models by providing more accurate individual parameters estimates and a compelling statistical framework for the analysis of between-subject variability (BSV). In this work, the advantages of population techniques are further explored by proposing integration of covariates in the intravenous glucose tolerance test (IVGTT) glucose minimal model analysis. A previously published dataset of 204 healthy subjects, who underwent insulin-modified IVGTTs, was analyzed in NONMEM, and relevant demographic information about each subject was employed to explain part of the BSV observed in parameter values. Demographic data included height, weight, sex, and age, but also basal glycemia and insulinemia, and information about amount and distribution of body fat. On the basis of nonlinear mixed-effects modeling, age, visceral abdominal fat, and basal insulinemia were significant predictors for SI (insulin sensitivity), whereas only age and basal insulinemia were significant for P2 (insulin action). The volume of distribution correlated with sex, age, percentage of total body fat, and basal glycemia, whereas no significant covariate was detected to explain variability in SG (glucose effectiveness). The introduction of covariates resulted in a significant shrinking of the unexplained BSV, especially for SI and P2 and considerably improved the model fit. These results offer a starting point for speculation about the physiological meaning of the relationships detected and pave the way for the design of less invasive and less expensive protocols for epidemiological studies of glucose-insulin metabolism.

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16

Davidian, Marie, and David M. Giltinan. "Analysis of repeated measurement data using the nonlinear mixed effects model." Chemometrics and Intelligent Laboratory Systems 20, no. 1 (August 1993): 1–24. http://dx.doi.org/10.1016/0169-7439(93)80017-c.

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17

Blouin, David C., Eric P. Webster, and Wei Zhang. "Analysis of Synergistic and Antagonistic Effects of Herbicides Using Nonlinear Mixed-Model Methodology." Weed Technology 18, no. 2 (June 2004): 464–72. http://dx.doi.org/10.1614/wt-03-047r1.

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When herbicides are applied in mixture, and infestation by weeds is less than expected compared with when herbicides are applied alone, a synergistic effect is said to exist. The inverse response is described as being antagonistic. However, if the expected response is defined as a multiplicative, nonlinear function of the means for the herbicides when applied alone, then standard linear model methodology for tests of hypotheses does not apply directly. Consequently, nonlinear mixed-model methodology was explored using the nonlinear mixed-model procedure (PROC NLMIXED) of SAS System®. Generality of the methodology is illustrated using data from a randomized block design with repeated measures in time. Nonlinear mixed-model estimates and tests of synergistic and antagonistic effects were more sensitive in detecting significance, and PROC NLMIXED was a versatile tool for implementation.

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18

Gallop, Robert J., Sona Dimidjian, David C. Atkins, and Vito Muggeo. "Quantifying Treatment Effects When Flexibly Modeling Individual Change in a Nonlinear Mixed Effects Model." Journal of Data Science 9, no. 2 (April 5, 2021): 221–41. http://dx.doi.org/10.6339/jds.201104_09(2).0006.

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19

Zhao, Dehai, Machelle Wilson, and Bruce E. Borders. "Modeling response curves and testing treatment effects in repeated measures experiments: a multilevel nonlinear mixed-effects model approach." Canadian Journal of Forest Research 35, no. 1 (January 1, 2005): 122–32. http://dx.doi.org/10.1139/x04-163.

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A multilevel nonlinear mixed-effects modeling approach is used to model loblolly pine (Pinus taeda L.) stand volume growth in conjunction with four silvicultural treatments. Comparisons of treatment effects over time are integrated with the model-building process. Three-level random effects are introduced into a modified Richards growth model. Within-plot heterogeneity and correlation still occur, which are described by the exponential variance function and a first-order autoregressive model. The combination of complete vegetation control with fertilization results in the largest growth response; annual fertilization has the next largest growth response, with the exception that at very early stages the response is lower than that of vegetation control only; the control has the lowest growth response. The advantages of the multilevel nonlinear mixed effects model include its ability to handle unbalanced and incomplete repeated measures data, its flexibility to model multiple sources of heterogeneity and complex patterns of correlation, and its higher power to make treatment comparisons. We address in detail a general strategy of multilevel nonlinear mixed effects model building.

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20

Zou, Qingming, and Zhongyi Zhu. "Testing the Correlation and Heterogeneity for Hierarchical Nonlinear Mixed-Effects Models." Advances in Decision Sciences 2011 (August 16, 2011): 1–16. http://dx.doi.org/10.1155/2011/976823.

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Nonlinear mixed-effects models are very useful in analyzing repeated-measures data and have received a lot of attention in the field. It is of common interest to test for the correlation within clusters and the heterogeneity across different clusters. In this paper, we address these problems by proposing a class of score tests for the null hypothesis that all components of within- and between-subject variance are zeros in a kind of nonlinear mixed-effects model, and the asymptotic properties of the proposed tests are studied. The finite sample performance of this test is examined through simulation studies, and an illustrative example is presented.

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21

Pinheiro, José C., Douglas M. Bates, and Jose C. Pinheiro. "Approximations to the Log-Likelihood Function in the Nonlinear Mixed-Effects Model." Journal of Computational and Graphical Statistics 4, no. 1 (March 1995): 12. http://dx.doi.org/10.2307/1390625.

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22

Chen, Huaihou, Donglin Zeng, and Yuanjia Wang. "Penalized nonlinear mixed effects model to identify biomarkers that predict disease progression." Biometrics 73, no. 4 (February 9, 2017): 1343–54. http://dx.doi.org/10.1111/biom.12663.

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23

Pinheiro, José C., and Douglas M. Bates. "Approximations to the Log-Likelihood Function in the Nonlinear Mixed-Effects Model." Journal of Computational and Graphical Statistics 4, no. 1 (March 1995): 12–35. http://dx.doi.org/10.1080/10618600.1995.10474663.

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24

Khraibani, Hussein, Tristan Lorino, Philippe Lepert, and Jean-Marie Marion. "Nonlinear Mixed-Effects Model for the Evaluation and Prediction of Pavement Deterioration." Journal of Transportation Engineering 138, no. 2 (February 2012): 149–56. http://dx.doi.org/10.1061/(asce)te.1943-5436.0000257.

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25

Rossenu, S., C. Gaynor, A. Vermeulen, A. Cleton, and A. Dunne. "A nonlinear mixed effects IVIVC model for multi-release drug delivery systems." Journal of Pharmacokinetics and Pharmacodynamics 35, no. 4 (August 2008): 423–41. http://dx.doi.org/10.1007/s10928-008-9095-3.

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26

Bender, Andreas, Andreas Groll, and Fabian Scheipl. "A generalized additive model approach to time-to-event analysis." Statistical Modelling 18, no. 3-4 (February 14, 2018): 299–321. http://dx.doi.org/10.1177/1471082x17748083.

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Abstract: This tutorial article demonstrates how time-to-event data can be modelled in a very flexible way by taking advantage of advanced inference methods that have recently been developed for generalized additive mixed models. In particular, we describe the necessary pre-processing steps for transforming such data into a suitable format and show how a variety of effects, including a smooth nonlinear baseline hazard, and potentially nonlinear and nonlinearly time-varying effects, can be estimated and interpreted. We also present useful graphical tools for model evaluation and interpretation of the estimated effects. Throughout, we demonstrate this approach using various application examples. The article is accompanied by a new R -package called pammtools implementing all of the tools described here.

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27

Ciceu, Albert, Juan Garcia-Duro, Ioan Seceleanu, and Ovidiu Badea. "A generalized nonlinear mixed-effects height–diameter model for Norway spruce in mixed-uneven aged stands." Forest Ecology and Management 477 (December 2020): 118507. http://dx.doi.org/10.1016/j.foreco.2020.118507.

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28

Zhang, Hongbin, and Lang Wu. "An approximate method for generalized linear and nonlinear mixed effects models with a mechanistic nonlinear covariate measurement error model." Metrika 82, no. 4 (October 17, 2018): 471–99. http://dx.doi.org/10.1007/s00184-018-0690-z.

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29

Yuan, Min, Xu Steven Xu, Yaning Yang, Jinfeng Xu, Xiaohui Huang, Fangbiao Tao, Liang Zhao, Liping Zhang, and Jose Pinheiro. "A quick and accurate method for the estimation of covariate effects based on empirical Bayes estimates in mixed-effects modeling: Correction of bias due to shrinkage." Statistical Methods in Medical Research 28, no. 12 (November 9, 2018): 3568–78. http://dx.doi.org/10.1177/0962280218812595.

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Nonlinear mixed-effects modeling is a popular approach to describe the temporal trajectory of repeated measurements of clinical endpoints collected over time in clinical trials, to distinguish the within-subject and the between-subject variabilities, and to investigate clinically important risk factors (covariates) that may partly explain the between-subject variability. Due to the complex computing algorithms involved in nonlinear mixed-effects modeling, estimation of covariate effects is often time-consuming and error-prone owing to local convergence. We develop a fast and accurate estimation method based on empirical Bayes estimates from the base mixed-effects model without covariates, and simple regressions outside of the nonlinear mixed-effect modeling framework. Application of the method is illustrated using a pharmacokinetic dataset from an anticoagulation drug for the prevention of major cardiovascular events in patients with acute coronary syndrome. Both the application and extensive simulations demonstrated that the performance of this high-throughput method is comparable to the commonly used maximum likelihood estimation in nonlinear mixed-effects modeling.

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30

Ribbing, Jakob, Joakim Nyberg, Ola Caster, and E. Niclas Jonsson. "The lasso—a novel method for predictive covariate model building in nonlinear mixed effects models." Journal of Pharmacokinetics and Pharmacodynamics 34, no. 4 (May 22, 2007): 485–517. http://dx.doi.org/10.1007/s10928-007-9057-1.

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31

Sharma, Ram, Zdeněk Vacek, and Stanislav Vacek. "Generalized Nonlinear Mixed-Effects Individual Tree Crown Ratio Models for Norway Spruce and European Beech." Forests 9, no. 9 (September 10, 2018): 555. http://dx.doi.org/10.3390/f9090555.

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Tree crowns are commonly measured to understand tree growth and stand dynamics. Crown ratio (CR—crown depth-to-total height ratio) is significantly affected by a number of tree- and stand-level characteristics and other factors as well. Generalized mixed-effects CR models were developed using a large dataset (measurements from 14,669 trees of Norway spruce (Picea abies (L.) Karst.) and European beech (Fagus sylvatica (L.)) acquired from permanent research plots in various parts of the Czech Republic. Among several tree- and stand-level variables evaluated, diameter at breast height, height to crown base, dominant height, basal area of trees larger in diameter than a focal tree, relative spacing index, and variables describing the effects of species mixture and canopy height differentiation significantly contributed to CR variation. We included sample-plot-level variations caused by randomness in the data and other stochastic factors into the CR models using the mixed-effects modeling approach. The logistic function, which predicts the values between 0 and 1, was chosen to develop the generalized CR mixed-effects model. A large proportion of the CR variation (R2adj ≈ 0.63 (Norway spruce); 0.72 (European beech)) was described by generalized mixed-effects model without significant residual trends. Testing the CR model against a part of the model fitting dataset confirmed its high prediction precision. Our CR model can be useful for growth simulation using inventory databases that lack crown measures. Other potential implications of our CR models in forest management are mentioned in the article.

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32

Yan, Fang-Rong, Ping Zhang, Jun-Lin Liu, Yu-Xi Tao, Xiao Lin, Tao Lu, and Jin-Guan Lin. "Parameter Estimation of Population Pharmacokinetic Models with Stochastic Differential Equations: Implementation of an Estimation Algorithm." Journal of Probability and Statistics 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/836518.

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Population pharmacokinetic (PPK) models play a pivotal role in quantitative pharmacology study, which are classically analyzed by nonlinear mixed-effects models based on ordinary differential equations. This paper describes the implementation of SDEs in population pharmacokinetic models, where parameters are estimated by a novel approximation of likelihood function. This approximation is constructed by combining the MCMC method used in nonlinear mixed-effects modeling with the extended Kalman filter used in SDE models. The analysis and simulation results show that the performance of the approximation of likelihood function for mixed-effects SDEs model and analysis of population pharmacokinetic data is reliable. The results suggest that the proposed method is feasible for the analysis of population pharmacokinetic data.

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33

Baba, Yuko, Hirofumi Nishimaru, and Hiroto Hyakutake. "Confidence regions of parameters in a nonlinear repeated measurement model with mixed effects." Hiroshima Mathematical Journal 37, no. 1 (March 2007): 111–17. http://dx.doi.org/10.32917/hmj/1176324098.

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34

Li, Yaoxiang, Lichun Jiang, and Mingyu liu. "A Nonlinear Mixed-Effects Model to Predict Stem Cumulative Biomass of Standing Trees." Procedia Environmental Sciences 10 (2011): 215–21. http://dx.doi.org/10.1016/j.proenv.2011.09.037.

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35

Rakêt, Lars Lau, Stefan Sommer, and Bo Markussen. "A nonlinear mixed-effects model for simultaneous smoothing and registration of functional data." Pattern Recognition Letters 38 (March 2014): 1–7. http://dx.doi.org/10.1016/j.patrec.2013.10.018.

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36

Yuan, X. X., and M. D. Pandey. "A nonlinear mixed-effects model for degradation data obtained from in-service inspections." Reliability Engineering & System Safety 94, no. 2 (February 2009): 509–19. http://dx.doi.org/10.1016/j.ress.2008.06.013.

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37

Nigh, Gordon. "Calculating empirical best linear unbiased predictors (EBLUPs) for nonlinear mixed effects models in Excel/Solver." Forestry Chronicle 88, no. 03 (June 2012): 340–44. http://dx.doi.org/10.5558/tfc2012-061.

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Nonlinear mixed-effects models have become common in the forestry literature. Calibration of these models for a new subject (one not used in the fitting of the model) involves estimating the values of the of random-effects parameters. Estimators can be obtained by taking a Taylor-series expansion of the nonlinear model around the expected value or the conditional expectation of the random-effects parameters. The conditional expectation method requires an iterative technique to find the estimates, which can be a complicated programming exercise. This note describes a relatively easy way to do the calculations necessary for both the zero expansion and conditional expectation methods in Excel and demonstrates the procedure on a small example.

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38

Xia, Tian, Jiancheng Jiang, and Xuejun Jiang. "Local Influence Analysis for Quasi-Likelihood Nonlinear Models with Random Effects." Journal of Probability and Statistics 2018 (August 8, 2018): 1–9. http://dx.doi.org/10.1155/2018/4878925.

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We propose a quasi-likelihood nonlinear model with random effects, which is a hybrid extension of quasi-likelihood nonlinear models and generalized linear mixed models. It includes a wide class of existing models as examples. A novel penalized quasi-likelihood estimation method is introduced. Based on the Laplace approximation and a penalized quasi-likelihood displacement, local influence of minor perturbations on the data set is investigated for the proposed model. Four concrete perturbation schemes are considered in the local influence analysis. The effectiveness of the proposed methodology is illustrated by some numerical examinations on a pharmacokinetics dataset.

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39

Li, Yao Xiang, and Li Chun Jiang. "Modeling Radial Variation in Microfibril Angle of Scots Pine." Advanced Materials Research 284-286 (July 2011): 1997–2001. http://dx.doi.org/10.4028/www.scientific.net/amr.284-286.1997.

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Microfibril angle (MFA) was determined at each growth ring from disks at breast height (1.3 m) from four scots pine (Pinus sylvestris) trees grown in northeastern China. Significant variation in microfibril angle was observed among growth rings. MFA at breast height showed a decreasing trend from pith to bark for each tree. The modified logistic model with nonlinear mixed-effects was used for modeling earlywood MFA. The NLME procedure in S-Plus is used to fit the mixed-effects models for the MFA data. The results showed that logistic model with two random parameters and could significantly improve the model performance. The CS, AR(1), MA(1), and ARMA(1,1) correlation structures were incorporated into mixed-effects models. The mixed model with the AR(1), MA(1), and ARMA(1,1) correlation structures improved model performance (P<0.0001).

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40

CARVALHO, Lídia Raquel, Martha Maria MISCHAN, José Raimundo de Souza PASSOS, and Sheila Zambello de PINHO. "THE USE OF CONTRASTS IN MULTIVARIATE NONLINEAR MIXED MODELS TO COMPARE TREATMENTS IN LONGITUDINAL FACTORIAL EXPERIMENTS." REVISTA BRASILEIRA DE BIOMETRIA 36, no. 4 (December 27, 2018): 880. http://dx.doi.org/10.28951/rbb.v36i4.314.

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The purpose of this study was to establish contrasts in multivariate nonlinear mixed models to verify the effects of treatments in experiments with longitudinal data and multiple responses. The evaluated nonlinear functions were the three parameters curves logistic, Gompertz and von Bertalanffy. The random variables were added to the fixed parameters, asymptote α , abscissa of the inflection point β, and parameter γ. The best fitted model was expanded with covariates, which establish orthogonal contrasts, in order to verify main effects and interactions in factorial experiments. The methodology was applied to analyse data of an experiment with citrus, in which case the logistic bivariate mixed effects model was the best fit. The chosen model allowed comparisons between treatments in a global context of more than one dependent variable and throughout the measurement period.

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41

Wu, Lang, and Hongbin Zhang. "Mixed Effects Models with Censored Covariates, with Applications in HIV/AIDS Studies." Journal of Probability and Statistics 2018 (June 3, 2018): 1–7. http://dx.doi.org/10.1155/2018/1581979.

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Mixed effects models are widely used for modelling clustered data when there are large variations between clusters, since mixed effects models allow for cluster-specific inference. In some longitudinal studies such as HIV/AIDS studies, it is common that some time-varying covariates may be left or right censored due to detection limits, may be missing at times of interest, or may be measured with errors. To address these “incomplete data“ problems, a common approach is to model the time-varying covariates based on observed covariate data and then use the fitted model to “predict” the censored or missing or mismeasured covariates. In this article, we provide a review of the common approaches for censored covariates in longitudinal and survival response models and advocate nonlinear mechanistic covariate models if such models are available.

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42

Huang, Jian, Kathleen O’Sullivan, John Levis, Elizabeth Kenny-Walsh, Orla Crosbie, and Liam Fanning. "Retrospective analysis of chronic hepatitis C in untreated patients with nonlinear mixed effects model." Journal of Biomedical Science and Engineering 01, no. 02 (2008): 85–90. http://dx.doi.org/10.4236/jbise.2008.12014.

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43

Koue, Toshiko, Masanori Kubo, Tomoo Funaki, Tsuyoshi Fukuda, Junichi Azuma, Mari Takaai, Yuichiro Kayano, and Yukiya Hashimoto. "Nonlinear Mixed Effects Model Analysis of the Pharmacokinetics of Aripiprazole in Healthy Japanese Males." Biological & Pharmaceutical Bulletin 30, no. 11 (2007): 2154–58. http://dx.doi.org/10.1248/bpb.30.2154.

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44

Bilgel, Murat, Jerry L. Prince, Dean F. Wong, Susan M. Resnick, and Bruno M. Jedynak. "A multivariate nonlinear mixed effects model for longitudinal image analysis: Application to amyloid imaging." NeuroImage 134 (July 2016): 658–70. http://dx.doi.org/10.1016/j.neuroimage.2016.04.001.

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45

Li, Runze, and Lei Nie. "A new estimation procedure for a partially nonlinear model via a mixed-effects approach." Canadian Journal of Statistics 35, no. 3 (September 2007): 399–411. http://dx.doi.org/10.1002/cjs.5550350305.

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46

Wang, Rui, Ante Bing, Cathy Wang, Yuchen Hu, Ronald J. Bosch, and Victor DeGruttola. "A flexible nonlinear mixed effects model for HIV viral load rebound after treatment interruption." Statistics in Medicine 39, no. 15 (April 15, 2020): 2051–66. http://dx.doi.org/10.1002/sim.8529.

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47

McRoberts, R. E., R. T. Brooks, and L. L. Rogers. "Using nonlinear mixed effects models to estimate size-age relationships for black bears." Canadian Journal of Zoology 76, no. 6 (June 1, 1998): 1098–106. http://dx.doi.org/10.1139/z98-049.

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Sizeage relationships for three physical characteristics, body length, zygomatic width, and pad width, weremodeled for black bears (Ursus americanus) captured in northeastern Minnesota, U.S.A. Because the curves representingsizeage relationships were nonlinear, and because some of the data consist of repeated, longitudinal observations for multiplebears, nonlinear mixed effects model analyses were required. The results are presented as parameter estimates with standarderrors and estimated population curves with 95% confidence intervals. Variance estimates obtained using mixed-effects modelsare compared with erroneous estimates obtained using ordinary least-squares techniques. Comparisons are made between maleand female Minnesota bears with respect to parameter estimates and estimated population curves. In addition, the results forMinnesota bears are compared with results from similar studies on bears in other regions.

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Roland, Marius, and Martin Schmidt. "Mixed-integer nonlinear optimization for district heating network expansion." at - Automatisierungstechnik 68, no. 12 (November 18, 2020): 985–1000. http://dx.doi.org/10.1515/auto-2020-0063.

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AbstractWe present a mixed-integer nonlinear optimization model for computing the optimal expansion of an existing tree-shaped district heating network given a number of potential new consumers. To this end, we state a stationary and nonlinear model of all hydraulic and thermal effects in the pipeline network as well as nonlinear models for consumers and the network’s depot. For the former, we consider the Euler momentum and the thermal energy equation. The thermal aspects are especially challenging. Here, we develop a novel polynomial approximation that we use in the optimization model. The expansion decisions are modeled by binary variables for which we derive additional valid inequalities that greatly help to solve the highly challenging problem. Finally, we present a case study in which we identify three major aspects that strongly influence investment decisions: the estimated average power demand of potentially new consumers, the distance between the existing network and the new consumers, and thermal losses in the network.

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Calama, Rafael, and Gregorio Montero. "Interregional nonlinear heightdiameter model with random coefficients for stone pine in Spain." Canadian Journal of Forest Research 34, no. 1 (January 1, 2004): 150–63. http://dx.doi.org/10.1139/x03-199.

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An individual-tree heightdiameter model was developed for stone pine (Pinus pinea L.) in Spain. Five biparametric nonlinear equations were fitted and evaluated based on a data set consisting of 8614 trees from 455 plots located in the four most important regions where the species occurs in Spain. Because of the problem of high correlation among observations taken from the same sampling unit, a mixed-model approach, including random coefficients, is proposed. Several stand variables, such as density, dominant height, or diametric distribution percentiles, were included in the model as covariates to explain among plot variability. To determine interregional variability among the regions studied, regional effects were included in the model using fixed dummy variables. Two models, one for inland regions and one for coastal regions, were found to be sufficient to explain regional variability in the heightdiameter relationship for the species in Spain. Mixed models allow predictive role in two ways: a typical response, including only fixed effects, and a calibrated response, where random effects are predicted and included in the model from the prior measurement of the height in a subsample of trees. Different alternatives were tested to determine optimum subsample size. Measurement of the height of the 20% largest trees in the plot has been shown to be a useful approach.

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Capuano, Ana W., Robert S. Wilson, Sue E. Leurgans, Jeffrey D. Dawson, David A. Bennett, and Donald Hedeker. "Sigmoidal mixed models for longitudinal data." Statistical Methods in Medical Research 27, no. 3 (April 28, 2016): 863–75. http://dx.doi.org/10.1177/0962280216645632.

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Linear mixed models are widely used to analyze longitudinal cognitive data. Often, however, the trajectory of cognitive function is nonlinear. For example, some participants may experience cognitive decline that accelerates as death approaches. Polynomial regression and piecewise linear models are common approaches used to characterize nonlinear trajectories, although both have assumptions that may not correspond with the actual trajectories. An alternative is to use a flexible sigmoidal mixed model based on the logistic family of curves. We describe a general class of such a model, which has up to five parameters, representing (1) final level, (2) rate of decline, (3) midpoint of decline, (4) initial level before decline, and (5) asymmetry. Focusing on a four-parameter symmetric sub-class of the model, with random effects on two of the parameters, we demonstrate that a likelihood approach to fitting this model produces accurate estimates of mean levels across time, even in the case of model misspecification. We also illustrate the method on deceased participants who had completed at least 5 years of annual cognitive testing and annual assessment of body mass. We show that departures from a stable body can modify the trajectory curves and anticipate cognitive decline.

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