Optimal cross-over designs for nonlinear mixed models using a first-order expansion

2009 ◽  
Vol 139 (2) ◽  
pp. 203-212
Author(s):  
Jixian Wang ◽  
Byron Jones
Keyword(s):  
Mixed Models ◽  
First Order ◽  
Nonlinear Mixed Models ◽  
Order Expansion

Comparison of different methods for fitting nonlinear mixed forest models and for making predictions

2011 ◽  
Vol 41 (8) ◽  
pp. 1671-1686 ◽  
Author(s):  
Yuqing Yang ◽  
Shongming Huang
Keyword(s):  
Maximum Likelihood ◽  
Conditional Expectation ◽  
Mixed Models ◽  
Mixed Forest ◽  
Restricted Maximum Likelihood ◽  
Order Method ◽  
First Order ◽  
Nonlinear Mixed Models ◽  
Model Predictions ◽  
First Order Method

Nonlinear mixed models have become popular in forestry applications, and various methods have been proposed for fitting such models. However, it is difficult or even confusing to choose which method to use, and there is not much relevant information available, especially in the forestry context. The main objective of this study was to compare three commonly used methods for fitting nonlinear mixed models: the first-order, the first-order conditional expectation, and the adaptive Gaussian quadrature methods. Both the maximum likelihood and restricted maximum likelihood parameter estimation techniques were evaluated. Three types of data common in forestry were used for model fitting and model application. It was found that the first-order conditional expectation method provided more accurate and precise predictions for two models developed from data with more observations per subject. For one model developed on data with fewer observations per subject, the first-order method provided better model predictions. All three models fitted by the first-order method produced some biologically unrealistic predictions, and the problem was more obvious on the data with fewer observations per subject. For all three models fitted by the first-order and first-order conditional expectation methods, the maximum likelihood and restricted maximum likelihood fits and the resulting model predictions were very close.

scholarly journals Light-cone distribution amplitudes of light mesons with QED effects

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Martin Beneke ◽  
Philipp Böer ◽  
Jan-Niklas Toelstede ◽  
K. Keri Vos
Keyword(s):  
Light Cone ◽  
Electromagnetic Coupling ◽  
First Order ◽  
Order Expansion ◽  
Group Evolution ◽  
Fixed Order ◽  
Light Mesons ◽  
Charged Mesons ◽  
Qed Effects ◽  
Exclusive Processes

Abstract We discuss the generalization of the leading-twist light-cone distribution amplitude for light mesons including QED effects. This generalization was introduced to describe virtual collinear photon exchanges at the strong-interaction scale ΛQCD in the factorization of QED effects in non-leptonic B-meson decays. In this paper we study the renormalization group evolution of this non-perturbative function. For charged mesons, in particular, this exhibits qualitative differences with respect to the well-known scale evolution in QCD only, especially regarding the endpoint-behaviour. We analytically solve the evolution equation to first order in the electromagnetic coupling αem, which resums large logarithms in QCD on top of a fixed-order expansion in αem. We further provide numerical estimates for QED corrections to Gegenbauer coefficients as well as inverse moments relevant to (QED-generalized) factorization theorems for hard exclusive processes.

scholarly journals Flexible estimation of serial correlation in nonlinear mixed models

2010 ◽  
Vol 37 (5) ◽  
pp. 833-846
Author(s):  
Jan Serroyen ◽  
Geert Molenberghs ◽  
Marc Aerts ◽  
Ellen Vloeberghs ◽  
Peter Paul De Deyn ◽  
...  
Keyword(s):  
Mixed Models ◽  
Serial Correlation ◽  
Nonlinear Mixed Models

Nonlinear Mixed Models

2014 ◽  
pp. 398-424 ◽  
Author(s):  
Katrien Antonio ◽  
Yanwei Zhang
Keyword(s):  
Mixed Models ◽  
Nonlinear Mixed Models

Evaluating remotely sensed rainfall estimates using nonlinear mixed models and geographically weighted regression

2008 ◽  
Vol 23 (12) ◽  
pp. 1438-1447 ◽  
Author(s):  
Y. Kamarianakis ◽  
H. Feidas ◽  
G. Kokolatos ◽  
N. Chrysoulakis ◽  
V. Karatzias
Keyword(s):  
Geographically Weighted Regression ◽  
Mixed Models ◽  
Remotely Sensed ◽  
Weighted Regression ◽  
Nonlinear Mixed Models ◽  
Rainfall Estimates
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