A new estimation procedure for a partially nonlinear model via a mixed-effects approach

2007 ◽  
Vol 35 (3) ◽  
pp. 399-411 ◽  
Author(s):  
Runze Li ◽  
Lei Nie
Keyword(s):  
Nonlinear Model ◽  
Estimation Procedure ◽  
Mixed Effects ◽  
Partially Nonlinear Model

Nonlinear Model Based Estimation of Rigid-Body Motion Via an Indirect Measurement of an Elastic Appendage

2010 ◽  
Vol 132 (1) ◽  
Author(s):  
M. Senesh ◽  
A. Wolf ◽  
O. Gottlieb
Keyword(s):  
Nonlinear System ◽  
Rigid Body ◽  
Nonlinear Model ◽  
Estimation Procedure ◽  
Indirect Measurement ◽  
Body Motion ◽  
System Parameters ◽  
Model Based ◽  
Proposed Model ◽  
Linear And Nonlinear

In this paper, we develop and implement a nonlinear model based procedure for the estimation of rigid-body motion via an indirect measurement of an elastic appendage. We demonstrate the procedure by motion analysis of a compound planar pendulum from indirect optoelectronic measurements of markers attached to an elastic appendage that is constrained to slide along the rigid-body axis. We implement a Lagrangian approach to derive a theoretical nonlinear model that consistently incorporates several generalized forces acting on the system. Identification of the governing linear and nonlinear system parameters is obtained by analysis of frequency and damping backbone curves from controlled experiments of the decoupled system elements. The accuracy of the proposed model based procedures is evaluated and its results are compared with those of a previously reported point cluster estimation procedure. Two cases are investigated to yield 1.7% and 3.4% errors between measured motion and its model based estimation for experimental configurations, with a slider mass to pendulum frequency ratios of 12.8 and 2.5, respectively. Motion analysis of system dynamics with the point cluster method reveals a noisy signal with a maximal error of 3.9%. Thus, the proposed model based estimation procedure enables accurate evaluation of linear and nonlinear system parameters that are not directly measured.

scholarly journals Computationally Stable Estimation Procedure for the Multivariate Linear Mixed-Effect Model and Application to Malaria Public Health Problem

2019 ◽  
Vol 15 (2) ◽  
Author(s):  
Eric Houngla Adjakossa ◽  
Norbert Mahouton Hounkonnou ◽  
Grégory Nuel
Keyword(s):  
Em Algorithm ◽  
Covariance Matrix ◽  
Random Effects ◽  
Estimation Procedure ◽  
Mixed Effects ◽  
Mixed Effects Models ◽  
Consistent Estimate ◽  
Linear Mixed Effects Models ◽  
Linear Mixed Effects ◽  
The Em Algorithm

Abstract In this paper, we provide the ML (Maximum Likelihood) and the REML (REstricted ML) criteria for consistently estimating multivariate linear mixed-effects models with arbitrary correlation structure between the random effects across dimensions, but independent (and possibly heteroscedastic) residuals. By factorizing the random effects covariance matrix, we provide an explicit expression of the profiled deviance through a reparameterization of the model. This strategy can be viewed as the generalization of the estimation procedure used by Douglas Bates and his co-authors in the context of the fitting of one-dimensional linear mixed-effects models. Beside its robustness regarding the starting points, the approach enables a numerically consistent estimate of the random effects covariance matrix while classical alternatives such as the EM algorithm are usually non-consistent. In a simulation study, we compare the estimates obtained from the present method with the EM algorithm-based estimates. We finally apply the method to a study of an immune response to Malaria in Benin.

scholarly journals Empirical likelihood for varying coefficient partially nonlinear model with missing responses

2021 ◽  
Vol 6 (7) ◽  
pp. 7125-7152
Author(s):  
Liqi Xia ◽  
◽  
Xiuli Wang ◽  
Peixin Zhao ◽  
Yunquan Song ◽  
...  
Keyword(s):  
Empirical Likelihood ◽  
Nonlinear Model ◽  
Varying Coefficient ◽  
Missing Responses ◽  
Partially Nonlinear Model
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