A pairwise likelihood approach to estimation in multilevel probit models

Renard, Didier; Molenberghs, Geert; Geys, Helena

doi:10.1016/s0167-9473(02)00263-3

Cited by 80 publications

(80 citation statements)

References 18 publications

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“…A composite likelihood is constructed by low-dimensional likelihood objects defined over small subsets of data. This dimension reduction methodology on the likelihood function has been successfully applied in many areas, including for example, generalized linear mixed models (Renard et al, 2004), genetics (Fearnhead & Donnelly, 2002), spatial statistics (Hjort & Omre, 1994;Heagerty & Lele, 1998;Varin & Vidoni, 2005) and multivariate survival analysis (Parner, 2001 andLin, 2006). It has demonstrated to possess desirable theoretical properties, such as estimation consistency and asymptotic normality, and can be utilized to establish hypothesis testing procedures in a similar fashion to the classical likelihood ratio test; see a recent review paper by Varin (2008) and more references therein.…”

Section: Introductionmentioning

confidence: 99%

Composite Likelihood Bayesian Information Criteria for Model Selection in High-Dimensional Data

Gao

Song

2010

Journal of the American Statistical Association

109

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For high-dimensional data set with complicated dependency structures, the full likelihood approach often renders to intractable computational complexity. This imposes di±culty on model selection as most of the traditionally used information criteria require the evaluation of the full likelihood. We propose a composite likelihood version of the Bayesian information criterion (BIC) and establish its consistency property for the selection of the true underlying model. Under some mild regularity conditions, the proposed BIC is shown to be selection consistent, where the number of potential model parameters is allowed to increase to in¯nity at a certain rate of the sample size. Simulation studies demonstrate the empirical performance of this new BIC criterion, especially for the scenario that the number of parameters increases with the sample size.

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Section: Introductionmentioning

confidence: 99%

Composite Likelihood Bayesian Information Criteria for Model Selection in High-Dimensional Data

Gao

Song

2010

Journal of the American Statistical Association

109

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“…Pairwise likelihood inference is much simpler than using the full likelihood since it involves only bivariate normal integrals. For instance (see also Renard et al, 2004), we have pr…”

Section: Binary Datamentioning

confidence: 98%

A note on empirical likelihoods derived from pairwise score functions

Lunardon

Pauli

Ventura

2013

Journal of Statistical Computation and Simulation

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Pairwise likelihood functions are convenient surrogates for the ordinary likelihood, useful when the latter is too difficult or even impractical to compute. One drawback of pairwise likelihood inference is that, for a multidimensional parameter of interest, the pairwise likelihood analogue of the likelihood ratio statistic does not have the standard chi-square asymptotic distribution. Invoking the theory of unbiased estimating functions, this paper proposes and discusses a computationally and theoretically attractive approach based on the derivation of empirical likelihood functions from the pairwise scores. This approach produces alternatives to the pairwise likelihood ratio statistic, which allow reference to the usual asymptotic chi-square distribution useful when the elements of the Godambe information are troublesome to evaluate or in the presence of large datasets with relative small sample sizes. Monte Carlo studies are performed in order to assess the finite-sample performance of the proposed empirical pairwise likelihoods.

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“…To our knowledge, no earlier study in the literature has considered the CML method in the context of unorderedresponse models (rather, all earlier studies have used the CML approach for multivariate models such as the multivariate binary probit or the multivariate ordered probit (see, for example, Renard et al, 2004, Zhao and Joe, 2005, Varin and Vidoni, 2006, Feddag and Bacci, 2009, Bhat and Sener, 2009, Varin and Czado, 2010, Bhat et al, 2010a. This is because the CML method by itself is not well suited to unordered-response models and does not provide substantial computational benefits in unordered-response models; rather, it is our specific proposal in this paper to combine the CML method with the normal orthant probability approximation method of the previous section that is the key to computational benefits.…”

Section: The Composite Marginal Likelihood (Cml) Estimatormentioning

confidence: 99%

The maximum approximate composite marginal likelihood (MACML) estimation of multinomial probit-based unordered response choice models

Bhat

2011

Transportation Research Part B: Methodological

155

151

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The likelihood functions of multinomial probit (MNP)-based choice models entail the evaluation of analytically-intractable integrals. As a result, such models are usually estimated using maximum simulated likelihood (MSL) techniques. Unfortunately, for many practical situations, the computational cost to ensure good asymptotic MSL estimator properties can be prohibitive and practically infeasible as the number of dimensions of integration rises. In this paper, we introduce a maximum approximate composite marginal likelihood (MACML) estimation approach for MNP models that can be applied using simple optimization software for likelihood estimation. It also represents a conceptually and pedagogically simpler procedure relative to simulation techniques, and has the advantage of substantial computational time efficiency relative to the MSL approach. The paper provides a "blueprint" for the MACML estimation for a wide variety of MNP models.

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A pairwise likelihood approach to estimation in multilevel probit models

Cited by 80 publications

References 18 publications

Composite Likelihood Bayesian Information Criteria for Model Selection in High-Dimensional Data

Composite Likelihood Bayesian Information Criteria for Model Selection in High-Dimensional Data

A note on empirical likelihoods derived from pairwise score functions

The maximum approximate composite marginal likelihood (MACML) estimation of multinomial probit-based unordered response choice models

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