Pairwise Likelihood Methods Research Articles

The dimension-wise quadrature estimation of dynamic latent variable models for count data

When dynamic latent variable models are specified for discrete and/or mixed observations, problems related to the integration of the likelihood function arise since analytical solutions do not exist. A recently developed dimension-wise quadrature is applied to deal with these likelihoods with high-dimensional integrals. A comparison is performed with the pairwise likelihood method, one of the most often used remedies. Both a real data application and a simulation study show the superior performance of the dimension-wise quadrature with respect to the pairwise likelihood in estimating the parameters of the latent autoregressive process.

Marginal Logistic Regression for Spatially Clustered Binary Data

Summary Clustered data are often analysed under the assumption that observations from distinct clusters are independent. The assumption may not be correct when the clusters are associated with different locations within a study region, as, for example, in epidemiological studies involving subjects nested within larger units such as hospitals, districts or villages. In such cases, correct inferential conclusions critically depend on the amount of spatial dependence between locations. We develop a modification of the method of generalized estimating equations to detect and account for spatial dependence between clusters in logistic regression for binary data. The approach proposed is based on parametric modelling of the lorelogram as a function of the distance between clusters. Model parameters are estimated by the hybrid pairwise likelihood method that combines optimal estimating equations for the regression parameters and pairwise likelihood for the lorelogram parameters. The methodology is illustrated with an analysis of prevalence disease survey data.

Analysis of progressive multi-state models with misclassified states: likelihood and pairwise likelihood methods

ABSTRACTMulti-state models are commonly used in studies of disease progression. Methods developed under this framework, however, are often challenged by misclassification in states. In this article, we investigate issues concerning continuous-time progressive multi-state models with state misclassification. We develop inference methods using both the likelihood and pairwise likelihood methods that are based on joint modelling of the progressive and misclassification processes. We assess the performance of the proposed methods by simulation studies, and illustrate their use by the application to the data arising from a coronary allograft vasculopathy study.

Gaussian copula distributions for mixed data, with application in discrimination

The construction of a joint model for mixed discrete and continuous random variables that accounts for their associations is an important statistical problem in many practical applications. In this paper, we use copulas to construct a class of joint distributions of mixed discrete and continuous random variables. In particular, we employ the Gaussian copula to generate joint distributions for mixed variables. Examples include the robit-normal and probit-normal-exponential distributions, the first for modelling the distribution of mixed binary-continuous data and the second for a mixture of continuous, binary and trichotomous variables. The new class of joint distributions is general enough to include many mixed-data models currently available. We study properties of the distributions and outline likelihood estimation; a small simulation study is used to investigate the finite-sample properties of estimates obtained by full and pairwise likelihood methods. Finally, we present an application to discriminant analysis of multiple correlated binary and continuous data from a study involving advanced breast cancer patients.

Regression analysis of longitudinal data with irregular and informative observation times.

In longitudinal data analyses, the observation times are often assumed to be independent of the outcomes. In applications in which this assumption is violated, the standard inferential approach of using the generalized estimating equations may lead to biased inference. Current methods require the correct specification of either the observation time process or the repeated measure process with a correct covariance structure. In this article, we construct a novel pairwise likelihood method for longitudinal data that allows for dependence between observation times and outcomes. This method investigates the marginal covariate effects on the repeated measure process, while leaving the probability structure of the observation time process unspecified. The novelty of this method is that it yields consistent estimator of the marginal covariate effects without specification of the observation time process or the covariance structure of the repeated measures process. Large sample properties of the regression coefficient estimates and a pairwise likelihood ratio test procedure are established. Simulation studies demonstrate that the proposed method performs well in finite samples. An analysis of weight loss data from a web-based program is presented to illustrate the proposed method.

Incorporating spatial dependence in regional frequency analysis.

The efficiency of regional frequency analysis (RFA) is undermined by intersite dependence, which is usually ignored in parameter estimation. We propose a spatial index flood model where marginal generalized extreme value distributions are joined by an extreme-value copula characterized by a max-stable process for the spatial dependence. The parameters are estimated with a pairwise likelihood constructed from bivariate marginal generalized extreme value distributions. The estimators of model parameters and return levels can be more efficient than those from the traditional index flood model when the max-stable process fits the intersite dependence well. Through simulation, we compared the pairwise likelihood method with an L-moment method and an independence likelihood method under various spatial dependence models and dependence levels. The pairwise likelihood method was found to be the most efficient in mean squared error if the dependence model was correctly specified. When the dependence model was misspecified within the max-stable models, the pairwise likelihood method was still competitive relative to the other two methods. When the dependence model was not a max-stable model, the pairwise likelihood method led to serious bias in estimating the shape parameter and return levels, especially when the dependence was strong. In an illustration with annual maximum precipitation data from Switzerland, the pairwise likelihood method yielded remarkable reduction in the standard errors of return level estimates in comparison to the L-moment method.

Hybrid Pairwise Likelihood Analysis of Animal Behavior Experiments

The study of the determinants of fights between animals is an important issue in understanding animal behavior. For this purpose, tournament experiments among a set of animals are often used by zoologists. The results of these tournament experiments are naturally analyzed by paired comparison models. Proper statistical analysis of these models is complicated by the presence of dependence between the outcomes of fights because the same animal is involved in different contests. This paper discusses two different model specifications to account for between-fights dependence. Models are fitted through the hybrid pairwise likelihood method that iterates between optimal estimating equations for the regression parameters and pairwise likelihood inference for the association parameters. This approach requires the specification of means and covariances only. For this reason, the method can be applied also when the computation of the joint distribution is difficult or inconvenient. The proposed methodology is investigated by simulation studies and applied to real data about adult male Cape Dwarf Chameleons.

A pairwise likelihood approach for longitudinal data with missing observations in both response and covariates

Missing observations occur commonly in longitudinal studies, and it has been documented that biased results could arise if such a feature is not properly accounted for in the analysis. A large body of methods handle missingness arising either from response components or covariate variables, but relatively little attention has been directed to addressing missingness in both response and covariate variables simultaneously. The sparsity of the research on this topic is partially attributed to substantially increased complexity of modeling and computational difficulty. In particular, the likelihood method may become infeasible in handling high dimensional data. This paper explores pairwise likelihood methods to handle longitudinal data with missing observations in both response and covariate variables. A unified framework based on bivariate normal distributions is invoked to accommodate various types of missing data patterns, including non-ignorable and non-monotone missingness. The performance of the proposed methods is assessed under a variety of circumstances. In particular, issues on efficiency and robustness are investigated. Longitudinal survey data from the Waterloo Smoking Prevention Project are analyzed with the proposed methods.

On weighting of bivariate margins in pairwise likelihood

Composite and pairwise likelihood methods have recently been increasingly used. For clustered data with varying cluster sizes, we study asymptotic relative efficiencies for various weighted pairwise likelihoods, with weight being a function of cluster size. For longitudinal data, we also study weighted pairwise likelihoods with weights that can depend on lag. Good choice of weights are needed to avoid the undesirable behavior of estimators with low efficiency. Some analytic results are obtained using the multivariate normal distribution. For clustered data, a practically good choice of weight is obtained after study of relative efficiencies for an exchangeable multivariate normal model; they are different from weights that had previously been suggested. For longitudinal data, there are advantages to only include bivariate margins of adjacent or nearly adjacent pairs in the weighted pairwise likelihood.

A Hybrid Pairwise Likelihood Method

A modification to the pairwise likelihood method is proposed, which aims to improve the estimation of the marginal distribution parameters. This is achieved by replacing the pairwise likelihood score equations, for estimating such parameters, by the optimal linear combinations of the marginal score functions. A further advantage of the proposed estimator of marginal parameters, over pairwise likelihood, is that it is robust to misspecification of the bivariate distributions as long as the univariate marginal distributions are correctly specified. While alternating logistic regression can be seen as a special case of the proposed method, it is shown that an existing generalization of alternating logistic regression applicable to ordinal data is not the same as and is inferior to the proposed method because it replaces certain conditional densities by pseudodensities that assume working independence. The fitting of the multivariate negative binomial distribution is another scenario involving intractable likelihood that calls for the use of pairwise likelihood methods, and the superiority of the modified method is demonstrated in a simulation study. Two examples, based on the analyses of salamander mating and patient-controlled analgesia data, demonstrate the usefulness of the proposed method. The possibility of combining optimally the pairwise, rather than marginal, scores is also considered and its difficulty and potential are discussed.

Pairwise likelihood methods for inference in image models

SUMMARY We consider parameter estimation for certain random set models for image data. For the spatial models considered here, a full likelihood-based approach to this problem is often difficult, since the likelihood generally cannot be computed for images of typical size. This has motivated the consideration of various less computationally demanding parameter estimation techniques. We discuss one method based on likelihoods for small subsets of the data. Consideration of the basic technique within the framework of the theory of estimating functions leads to a weighted version of the basic approach. Results of a simulation study are reported for some variants of the Boolean model and excursion sets of random fields. The methods are illustrated for some data on the spatial incidence of heather.