Adaptive quadrature

About: Adaptive quadrature is a research topic. Over the lifetime, 553 publications have been published within this topic receiving 12110 citations.

Differential Quadrature and Its Application in Engineering

Abstract: Application of Differential Quadrature to Engineering ProblemsApplication of Differential Quadrature to the Analysis of Structural ComponentsTsinghua Science and TechnologyApplication of Differential Quadrature Method to the Analysis of Delamination Buckling of Laminated CompositesDifferential Quadrature and Differential Quadrature Based Element MethodsApplication of the Differential Quadratire Method to Problems in Engineering MechanicsProceedings of the International Conference on Advances in Computational Mechanics 2017Advanced Differential Quadrature MethodsA Differential Quadrature Hierarchical Finite Element MethodLaminated Composite Doubly-Curved Shell StructuresRecent Advances in Mathematics for EngineeringComputer Modeling in Engineering & SciencesMeshfree Approximation Methods with MatlabApplication of Differential Quadrature to the Analysis of Static Aeroelastic PhenomenaApplication of the Differential Quadrature Method to the Plane Elasticity ProblemMathematical Methods in Interdisciplinary SciencesDiQuMaSPABWave Propagation in Materials for Modern ApplicationsDifferential Quadrature Methods and Its ApplicationsA Generalization and Application of the Differential Quadrature MethodApplication of the Differential Quadrature Method to the Buckling Analysis of Cylindrical Shells and TanksBoundary Elements and Other Mesh Reduction Methods XXXVDifferential Quadrature and Its Application in EngineeringDifferential Quadrature Method in Computational MechanicsUse of Differential Quadrature in a Recursive FilterApplication of Differential Quadrature to Nuclear Engineering ProblemsMathematical PhysicsStructural Dynamics of Earthquake EngineeringDeterministic Flexibility AnalysisHandbook of Research on Computational Science and Engineering: Theory and PracticeNonlinear DynamicsInternational Petroleum Conference & Exhibition of MexicoVibration Analysis of Non-uniform Beams Using the Differential Quadrature MethodApplication of Differential Quadrature Method to the Analysis of Delamination Buckling of Laminated CompositesMechanical Vibration: Where Do We Stand?Scientific and Technical Aerospace ReportsA New Differential Quadrature Method Based on Bernstein PolynomialsA Primer on Radial Basis Functions with Applications to the GeosciencesMechanics of laminated Composite doubly-curvel shell structuresProceedings of the Sixth International Colloguium on Differential Equations

Reliable estimation of generalized linear mixed models using adaptive quadrature.

Abstract: Generalized linear mixed models or multilevel regression models have become increasingly popular. Several methods have been proposed for estimating such models. However, to date there is no single method that can be assumed to work well in all circumstances in terms of both parameter recovery and com- putational efficiency. Stata's xt commands for two-level generalized linear mixed models (e.g., xtlogit) employ Gauss-Hermite quadrature to evaluate and maxi- mize the marginal log likelihood. The method generally works very well, and often better than common contenders such as MQL and PQL, but there are cases where quadrature performs poorly. Adaptive quadrature has been suggested to overcome these problems in the two-level case. We have recently implemented a multilevel version of this method ingllamm, a program that fits a large class of multilevel latent variable models including multilevel generalized linear mixed models. As far as we know, this is the first time that adaptive quadrature has been proposed for multilevel models. We show that adaptive quadrature works well in problems where ordinary quadrature fails. Furthermore, even when ordinary quadrature works, adaptive quadrature is often computationally more efficient since it requires fewer quadrature points to achieve the same precision.

Multilevel modelling of complex survey data

Abstract: Summary. Multilevel modelling is sometimes used for data from complex surveys involving multistage sampling, unequal sampling probabilities and stratification. We consider generalized linear mixed models and particularly the case of dichotomous responses. A pseudolikelihood approach for accommodating inverse probability weights in multilevel models with an arbitrary number of levels is implemented by using adaptive quadrature. A sandwich estimator is used to obtain standard errors that account for stratification and clustering. When level 1 weights are used that vary between elementary units in clusters, the scaling of the weights becomes important. We point out that not only variance components but also regression coefficients can be severely biased when the response is dichotomous. The pseudolikelihood methodology is applied to complex survey data on reading proficiency from the American sample of the ‘Program for international student assessment’ 2000 study, using the Stata program gllamm which can estimate a wide range of multilevel and latent variable models. Performance of pseudo-maximumlikelihood with different methods for handling level 1 weights is investigated in a Monte Carlo experiment. Pseudo-maximum-likelihood estimators of (conditional) regression coefficients perform well for large cluster sizes but are biased for small cluster sizes. In contrast, estimators of marginal effects perform well in both situations. We conclude that caution must be exercised in pseudo-maximum-likelihood estimation for small cluster sizes when level 1 weights are used.