On Adaptive Gauss-Hermite Quadrature for Estimation in GLMM’s

Kabaila, Paul; Ranathunga, Nishika

doi:10.1007/978-981-15-1960-4_9

Cited by 8 publications

(8 citation statements)

References 10 publications

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“…The binary logistic regression was tested using a generalized linear mixed-effects model (GLME) with Language, String type, and Position as fixed effects and Participants and Items as random effects. The computation of the log-likelihood function for generalized linear mixed models was based on adaptive Gauss-Hermite quadrature as recommended by many authors (e.g., Kabaila and Ranathunga, 2019).…”

Section: Generalized Linear Mixed-e Ects Modelingmentioning

confidence: 99%

Can the word superiority effect be modulated by serial position and prosodic structure?

et al. 2022

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In this study, we examined the word superiority effect in Arabic and English, two languages with significantly different morphological and writing systems. Thirty-two Arabic–English bilingual speakers performed a post-cued letter-in-string identification task in words, pseudo-words, and non-words. The results established the presence of the word superiority effect in Arabic and a robust effect of context in both languages. However, they revealed that, compared to the non-word context, word and pseudo-word contexts facilitated letter identification more in Arabic than in English. In addition, the difference between word and pseudo-word contexts was smaller in Arabic compared to English. Finally, there was a consistent first-letter advantage in English regardless of the context, while this was more consistent only in the word and pseudo-word contexts in Arabic. We discuss these results in light of previous findings and argue that the differences between the patterns reported for Arabic and English are due to the qualitative difference between word morphophonological representations in the two languages.

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Section: Generalized Linear Mixed-e Ects Modelingmentioning

confidence: 99%

Can the word superiority effect be modulated by serial position and prosodic structure?

et al. 2022

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“…More recently, adaptive Gauss-Hermite quadrature (AQ; Naylor and Smith, 1982) has become a standard method for approximating the marginal likelihood in a limited class of GLMMs (Pinheiro and Bates, 1995;Kabaila and Ranathunga, 2019). In contrast to GQ, AQ has been shown to have compelling statistical properties in theory and practice.…”

Section: Introductionmentioning

confidence: 99%

Fitting Generalized Linear Mixed Models using Adaptive Quadrature

Stringer¹,

Bilodeau²

2022

Preprint

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We describe how to approximate the intractable marginal likelihood that arises when fitting generalized linear mixed models. We prove that non-adaptive quadrature approximations yield high error asymptotically in every statistical model satisfying weak regularity conditions. We derive the rate of error incurred when using adaptive quadrature to approximate the marginal likelihood in a broad class of generalized linear mixed models, which includes non-exponential family response and non-Gaussian random effects distributions. We provide an explicit recommendation for how many quadrature points to use, and show that this recommendation recovers and explains many empirical results from published simulation studies and data analyses. Particular attention is paid to models for dependent binary and survival/time-to-event observations. Code to reproduce results in the manuscript is found at https://github.com/awstringer1/glmm-aq-paper-code.

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“…The relation of this simple change of measure with importance sampling is only mentioned in [23], although the methodology is not developed. The change of measure is also compared with the Laplace approximation [24] (see also [25] for a recent application). In a recent paper [26], the authors apply a change of measure in a more restricted setup (similarly to [22]), in order to approximate the marginal likelihood with quadrature rules in the context of Gaussian processes.…”

Section: Introductionmentioning

confidence: 99%

Importance Gaussian Quadrature

Elvira

Martino

Closas

2021

IEEE Trans. Signal Process.

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Importance sampling (IS) and numerical integration methods are usually employed for approximating moments of complicated target distributions. In its basic procedure, the IS methodology randomly draws samples from a proposal distribution and weights them accordingly, accounting for the mismatch between the target and proposal. In this work, we present a general framework of numerical integration techniques inspired by the IS methodology. The framework can also be seen as an incorporation of deterministic rules into IS methods, reducing the error of the estimators by several orders of magnitude in several problems of interest. The proposed approach extends the range of applicability of the Gaussian quadrature rules. For instance, the IS perspective allows us to use Gauss-Hermite rules in problems where the integrand is not involving a Gaussian distribution, and even more, when the integrand can only be evaluated up to a normalizing constant, as it is usually the case in Bayesian inference. The novel perspective makes use of recent advances on the multiple IS (MIS) and adaptive (AIS) literatures, and incorporates it to a wider numerical integration framework that combines several numerical integration rules that can be iteratively adapted. We analyze the convergence of the algorithms and provide some representative examples showing the superiority of the proposed approach in terms of performance.

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On Adaptive Gauss-Hermite Quadrature for Estimation in GLMM’s

Cited by 8 publications

References 10 publications

Can the word superiority effect be modulated by serial position and prosodic structure?

Can the word superiority effect be modulated by serial position and prosodic structure?

Fitting Generalized Linear Mixed Models using Adaptive Quadrature

Importance Gaussian Quadrature

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