On the robustness of maximum composite likelihood estimate

Xu, Ximing; Reid, N.

doi:10.1016/j.jspi.2011.03.026

Cited by 75 publications

(56 citation statements)

References 8 publications

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“…The properties of the CML estimator may be derived using the theory of estimating equations (see Cox andReid, 2004, Yi et al, 2011). Specifically, under usual regularity assumptions (Molenberghs andVerbeke, 2005, page 191, Xu and, the CML estimator is consistent and asymptotically normal distributed (this is because of the unbiasedness of the CML score function, which is a linear combination of proper score functions associated with the marginal event probabilities forming the composite likelihood; for a formal proof, see Yi et al, 2011 andXu and. Further, the CML approach is robust against mis-specification of the full joint distribution of the endogenous variables in the multi-dimensional system, while the traditional maximum likelihood approach is not (Xu and Reid, 2011).…”

Section: The Macml Estimation Approachmentioning

confidence: 99%

“…Specifically, under usual regularity assumptions (Molenberghs andVerbeke, 2005, page 191, Xu and, the CML estimator is consistent and asymptotically normal distributed (this is because of the unbiasedness of the CML score function, which is a linear combination of proper score functions associated with the marginal event probabilities forming the composite likelihood; for a formal proof, see Yi et al, 2011 andXu and. Further, the CML approach is robust against mis-specification of the full joint distribution of the endogenous variables in the multi-dimensional system, while the traditional maximum likelihood approach is not (Xu and Reid, 2011). In particular, the consistency of the estimates in the CML approach is predicated only on the correct specification of the lower dimensional marginal densities appearing in the CML function, without any need for explicit distributional assumptions for the full dimensional density of the multi-dimensional system.…”

Section: The Macml Estimation Approachmentioning

confidence: 99%

See 1 more Smart Citation

A joint count-continuous model of travel behavior with selection based on a multinomial probit residential density choice model

Bhat

Astroza

Sidharthan

et al. 2014

Transportation Research Part B: Methodological

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This paper formulates a multidimensional choice model system that is capable of handling multiple nominal variables, multiple count dependent variables, and multiple continuous dependent variables.The system takes the form of a treatment-outcome selection system with multiple treatments and multiple outcome variables. The Maximum Approximate Composite Marginal Likelihood (MACML) approach is proposed in estimation, and a simulation experiment is undertaken to evaluate the ability of the MACML method to recover the model parameters in such integrated systems. These experiments show that our estimation approach recovers the underlying parameters very well and is efficient from an econometric perspective. The parametric model system proposed in the paper is applied to an analysis of household-level decisions on residential location, motorized vehicle ownership, the number of daily motorized tours, the number of daily non-motorized tours, and the average distance for the motorized tours. The empirical analysis uses the NHTS 2009 data from the San Francisco Bay area. Model estimation results show that the choice dimensions considered in this paper are inter-related, both through direct observed structural relationships and through correlations across unobserved factors (error terms) affecting multiple choice dimensions.The significant presence of self-selection effects (endogeneity) suggests that modeling the various choice processes in an independent sequence of models is not reflective of the true relationships that exist across these choice dimensions, as also reinforced through the computation of treatment effects in the paper.

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Section: The Macml Estimation Approachmentioning

confidence: 99%

Section: The Macml Estimation Approachmentioning

confidence: 99%

A joint count-continuous model of travel behavior with selection based on a multinomial probit residential density choice model

Bhat

Astroza

Sidharthan

et al. 2014

Transportation Research Part B: Methodological

View full text Add to dashboard Cite

show abstract

“…The maximum likelihood estimator need not be consistent in such a setting, since the likelihood relies on the full, misspecified, distribution of Y . Xu and Reid (2011) discuss this type of robustness in some detail, and provide a formal proof of the consistency of the composite likelihood estimator in this setting.…”

Section: Introductionmentioning

confidence: 99%

A caveat on the robustness of composite likelihood estimators: the case of mis-specified random effect distribution

Ogden¹

2016

STAT SINICA

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Abstract:Composite likelihoods are a class of alternatives to the full likelihood which may be used for inference in many situations where the likelihood itself is intractable. A composite likelihood estimator will be robust to certain types of model misspecification, since it may be computed without the need to specify the full distribution of the response. This potential for increased robustness has been widely discussed in recent years, and is considered a secondary motivation for the use of composite likelihood. The purpose of this paper is to show that there are some situations in which a composite likelihood estimator may actually suffer a loss of robustness compared to the maximum likelihood estimator. We demonstrate this in the case of a generalized linear mixed model under misspecification of the randomeffect distribution. As the amount of information available on each random effect increases, we show that the maximum likelihood estimator remains consistent under such misspecification, but various marginal composite likelihood estimators are inconsistent. We conclude that composite likelihood estimators cannot in general be claimed to be more robust than the maximum likelihood estimator.

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“…Further, being based on different functions of the data when T > 2, they will generally converge to different points in the parameter space. In fact, as pointed out by Varin et al (2011) and Xu and Reid (2012),β 2 is more robust to violations of the assumption of time-invariant unobserved heterogeneity thanβ 1 , as it only requires this assumption to be satisfied for the two-dimensional conditional likelihood quantities.…”

Section: The Statistical Frameworkmentioning

confidence: 94%

“…This is clearly the case when T = 2. When T > 2, the two estimators are based on different functions of the data, soδ will generally have a nonzero probability limit under the alternative (Xu and Reid, 2012), which means that our test will have power against a broad class of alternatives resulting in time-varying individual effects, such as omitted time-varying regressors, failure of functional form assumptions and general misspecification of the systematic part of the model.…”

Section: The Proposed Testmentioning

confidence: 99%

Testing for time-invariant unobserved heterogeneity in generalized linear models for panel data

Bartolucci

Belotti

Peracchi

2015

Journal of Econometrics

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Recent literature on panel data has emphasized the importance of accounting for time-varying unobserved heterogeneity, which may stem either from time-varying omitted variables or macro-level shocks that affect each individual unit differently. In this paper, we propose a computationally convenient test for the null hypothesis of time-invariant individual effects. The proposed test is an application of Hausman (1978) specification test procedure and can be applied to generalized linear models for panel data, a wide class of models that includes the Gaussian linear model and a variety of nonlinear models typically employed for discrete or categorical outcomes. The basic idea is to compare fixed effects estimators defined as the maximand of full and pairwise conditional likelihood functions. Thus, the proposed approach requires no assumptions on the distribution of the individual effects and, most importantly, it does not require them to be independent of the covariates in the model. We investigate the finite sample properties of the test through a set of Monte Carlo experiments. Our results show that the test performs quite well, with small size distortions and good power properties. A health economics example based on data from the Health and Retirement Study is used to illustrate the proposed test.

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On the robustness of maximum composite likelihood estimate

Cited by 75 publications

References 8 publications

A joint count-continuous model of travel behavior with selection based on a multinomial probit residential density choice model

A joint count-continuous model of travel behavior with selection based on a multinomial probit residential density choice model

A caveat on the robustness of composite likelihood estimators: the case of mis-specified random effect distribution

Testing for time-invariant unobserved heterogeneity in generalized linear models for panel data

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