On the effect of the number of quadrature points in a logistic random effects model: an example

By Emmanuel Lesaffre, B. Spiessens. 2001

260 citations recorded by the source corpus.

Subfields: Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/efdf49e20e991710a12617a39047098c668862cd

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In Management Science and Operations Research

In Statistics and Probability

Citations in the corpus

Bayesian and likelihood-based methods in multilevel modeling 1 A comparison of Bayesian and likelihood-based methods for fitting multilevel models (2006, methodology): “In particular, methods such as Gaussian quadrature may produce poor results in RELR models if not used carefully (see Lesaffre and Spiessens 2001 for a striking example); we intend to report elsewhere on a thorough comparison of quadrature with the methods examined here.”
High-dimensional maximum marginal likelihood item factor analysis by adaptive quadrature (2005, background): “Similar considerations apply in other multilevel treatments of binary and polytomous data (see Hedeker and Gibbons, 1994), a fact confirmed by a number of recent papers on generalized linear mixed models ( Lesaffre and Spiessens, 2001; Rabe-Hesketh, Skrondal, and Pickles 2002, 2005b).”
Reliable Estimation of Generalized Linear Mixed Models using Adaptive Quadrature (2002, background): “Lesaffre and Spiessens (2001) show that the integrals required for the analytical derivatives are often more poorly approximated by quadrature and adaptive”
Apples and Oranges? The Problem of Equivalence in Comparative Research (2011, methodology): “13Since resultscan be sensitive to the number of integration points (Lesaffre and Spiessens 2001), one should carry out robustness checks using more points.”
On a signal detection approach to m-alternative forced choice with bias, with maximum likelihood and Bayesian approaches to estimation (2012, background): “Lesaffre and Spiessens (2001) cautioned against using too few quadrature points and noted that the use of adaptive quadrature, as in NLMIXED, solved the problem for an example they presented.”
An EM algorithm for the estimation of parametric and nonparametric hierarchical nonlinear models (2004, background): “Lesaffre and Spiessens (2001) and Rabe-Hesketh, Skrondal, and Pickles (2002) showed that the number of quadrature points needs to be very large in some situations.”
A pairwise likelihood approach to generalized linear models with crossed random effects (2005, methodology): “2) may be efficiently approximated by quadrature techniques (Evans and Swartz, 2000; Lesaffre and Spiessens, 2001).”
Modelling sparse generalized longitudinal observations with latent Gaussian processes (2008, methodology): “data are discussed by Lesaffre and Spiessens (2001) .”
Maximum likelihood estimation of limited and discrete dependent variable models with nested random effects (2005, background): “Albert and Follmann (2000) and Lesaffre and Spiessens (2001) illustrate this problem for Poisson and logit models,”
Use of the Probability Integral Transformation to Fit Nonlinear Mixed-Effects Models With Nonnormal Random Effects (2006, unknown): “…marginal density function in (2.3) by a weighted average of the integrand evaluated at a number, Q, of predetermined abscissas (quadrature points) dq (q = 1, . . . , Q) over the random effects ai (Pinheiro and Bates 1995; Davidian and Gallant 1993; Lesaffre and Spiessens 2001; Liu and Pierce 1994).”
Handbook of multilevel analysis (2008, methodology): “A regression spline [61] consists of piecewise polynomials that are joined at locations on the x-axis named knots.”
Correcting for covariate measurement error in logistic regression using nonparametric maximum likelihood estimation (2003, background): “This is likely to be due to the integrands having sharp peaks that can easily fall between adjacent quadrature locations (e.g., Lesaffre and Spiessens, 2001 ).”
Multilevel Models for Ordinal and Nominal Variables (2008, methodology): “Also, Lesaffre and Spiessens [61] present an example where the method only gives valid results for a high number of quadrature points.”
Generalized multilevel structural equation modeling (2004, background): “Since adaptive quadrature is derived by assuming approximate normality of the posterior density of the latent variables, it tends to work well for continuous responses, large counts, and large clusters, precisely where standard quadrature often works poorly (Lesaffre & Spiessens, 2001).”