Pairwise Fitting of Mixed Models for the Joint Modeling of Multivariate Longitudinal Profiles

Fieuws, Steffen; Verbeke, Geert

doi:10.1111/j.1541-0420.2006.00507.x

Cited by 197 publications

(316 citation statements)

References 30 publications

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“…A pairwise likelihood estimation, where the likelihood function is defined as the product of the bivariate likelihoods, is proposed in Katsikatsou et al (2012) for SEM for ordinal variables and in Katsikatsou (2013) for continuous and ranking data. PML estimation has been developed for panel models of ordered-responses (Bhat et al, 2010), latent variable models for ordinal longitudinal responses (Vasdekis et al, 2012), autoregressive ordered probit models (Varin & Vidoni, 2006), longitudinal mixed Rasch models (Feddag & Bacci, 2009), mixed models for joint modelling of multivariate longitudinal profiles (Fieuws & Verbeke, 2006), analysis of variance models (Lele & Taper, 2002), generalized linear models with crossed random effects (Bellio & Varin, 2005), spatial models with binary data (Heagerty & Lele, 1998), and spatial generalized linear mixed models (see also the special issue of Statistica Sinica, Vol 21(1), 2011, for more areas of application).…”

Section: Introductionmentioning

confidence: 99%

Pairwise Likelihood Ratio Tests and Model Selection Criteria for Structural Equation Models with Ordinal Variables

Katsikatsou

Moustaki

2016

Psychometrika

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This document is the author's final accepted version of the journal article. There may be differences between this version and the published version. You are advised to consult the publisher's version if you wish to cite from it.Pairwise likelihood ratio tests and model selection criteria for structural equation models with ordinal variablesCorrelated multivariate ordinal data can be analysed with structural equation models. Parameter estimation has been tackled in the literature using limited-information methods including three-stage least squares and pseudo-likelihood estimation methods such as pairwise maximum likelihood estimation. In this paper, two likelihood ratio test statistics and their asymptotic distributions are derived for testing overall goodness-of-fit and nested models respectively under the estimation framework of pairwise maximum likelihood estimation. Simulation results show a satisfactory performance of type I error and power for the proposed test statistics and also suggest that the performance of the proposed test statistics is similar to that of the test statistics derived under the three-stage diagonally weighted and unweighted least squares. Furthermore, the corresponding, under the pairwise framework, model selection criteria, AIC and BIC, show satisfactory results in selecting the right model in our simulation examples. The derivation of the likelihood ratio test statistics and model selection criteria under the pairwise framework together with pairwise estimation provide a flexible framework for fitting and testing structural equation models for ordinal as well as for other types of data. The test statistics derived and the model selection criteria are used on data on 'trust in the police' selected from the 2010 European Social Survey. The proposed test statistics and the model selection criteria have been implemented in the R package lavaan 1 .

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Section: Introductionmentioning

confidence: 99%

Pairwise Likelihood Ratio Tests and Model Selection Criteria for Structural Equation Models with Ordinal Variables

Katsikatsou

Moustaki

2016

Psychometrika

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“…To obtain θ * , Fieuws and Verbeke (2006) take averages of all available estimates for that specific parameter, implying that θ * = A θ for an appropriate linear combination matrix A. Further, combining this step with general pseudo-likelihood inference, a sandwich estimator is used:…”

Section: Pseudo-likelihood For Split Samples D1 General Consideratmentioning

confidence: 99%

“…In some cases, such a sub-vector can be conditioned upon another sub-vector. Fieuws and Verbeke (2006) and Fieuws et al (2006) used pseudo-likelihood to fit mixed models to high-dimensional multivariate longitudinal data. They supplemented the standard method with an additional device.…”

Section: Pseudo-likelihood For Split Samples D1 General Consideratmentioning

confidence: 99%

Clusters with random size: maximum likelihood versus weighted estimation

Hermans¹,

Molenberghs²,

Kenward³

et al. 2018

STAT SINICA

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The analysis of hierarchical data that take the form of clusters with random size has received considerable attention. The focus here is on samples that are very large in terms of number of clusters and/or members per cluster, on the one hand, as well as on very small samples (e.g., when studying rare diseases), on the other. Whereas maximum likelihood inference is straightforward in medium to large samples, in samples of sizes considered here it may become prohibitive. We propose sample-splitting (Molenberghs et al., 2011) as a way to replace iterative optimization of a likelihood that does not admit an analytical solution, with closed-form calculations. We use pseudo-likelihood (Molenberghs et al., 2014), consisting of computing weighted averages over solutions obtained for each cluster size occurring. As a result, the statistical properties of this approach need to be investigated. This is especially important because the minimal sufficient statistics involved are incomplete. The operational characteristics are studied using a first set of simulations. Simulations are also done to compare the proposed method to existing techniques developed to circumvent difficulties with unequal cluster sizes, such as multiple imputation. It follows that the proposed non-iterative methods have a strong beneficial impact on computation time; at the same time, the method is the most precise among its competitors considered. The findings are illustrated using data from a developmental toxicity study, where clusters are formed of fetuses within litters.

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“…Tibshirani (1996) studied regression shrinkage and selection via the lasso; his paper is an excellent example of the need for and popularity of methods for high-dimensional data. Fieuws and Verbeke (2006) proposed several approaches to fit multivariate hierarchical models in settings where the responses are high-dimensional vectors of repeated observations. Xia et al (2002) categorized methods that deal with high dimensionality into data reduction and functional approaches [Li (1991), Johnson and Wichern (2007)].…”

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confidence: 99%

A permutational-splitting sample procedure to quantify expert opinion on clusters of chemical compounds using high-dimensional data

Milanzi¹,

Alonso²,

Buyck³

et al. 2014

Ann. Appl. Stat.

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Expert opinion plays an important role when selecting promising clusters of chemical compounds in the drug discovery process. We propose a method to quantify these qualitative assessments using hierarchical models. However, with the most commonly available computing resources, the high dimensionality of the vectors of fixed effects and correlated responses renders maximum likelihood unfeasible in this scenario. We devise a reliable procedure to tackle this problem and show, using theoretical arguments and simulations, that the new methodology compares favorably with maximum likelihood, when the latter option is available. The approach was motivated by a case study, which we present and analyze.

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Pairwise Fitting of Mixed Models for the Joint Modeling of Multivariate Longitudinal Profiles

Cited by 197 publications

References 30 publications

Pairwise Likelihood Ratio Tests and Model Selection Criteria for Structural Equation Models with Ordinal Variables

Pairwise Likelihood Ratio Tests and Model Selection Criteria for Structural Equation Models with Ordinal Variables

Clusters with random size: maximum likelihood versus weighted estimation

A permutational-splitting sample procedure to quantify expert opinion on clusters of chemical compounds using high-dimensional data

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