arXiv subjects

Subhajit Chattopadhyay

Publications and source records attributed to Subhajit Chattopadhyay.

4 recordsLinked to original sources

arXiv2025

Skew-elliptical copula based mixed models for non-Gaussian longitudinal data with application to an HIV-AIDS study

This study was sparked by an extensive longitudinal dataset focusing on HIV CD4 T$^+$ cell counts from Livingstone district, Zambia. Analysis of the corresponding histogram plots reveals an absence of symmetry in the marginal distributions, while pairwise scatter plots uncover non-elliptical dependence patterns. Traditional linear mixed models designed for longitudinal data fail to capture these complexities adequately. Therefore, it appears prudent to explore a broader framework for modeling such data. In this article, we delve into generalized linear mixed models (GLMM) for the marginals (e.g., the Gamma mixed model), and we address the temporal dependency of repeated measurements by utilizing copulas associated with skew-elliptical distributions (such as the skew-normal/skew-$t$). Our proposed class of copula-based mixed models simultaneously accommodates asymmetry, between-subject variability, and non-standard temporal dependence, thus offering extensions to the standard linear mixed model based on multivariate normality. We estimate the model parameters using the IFM (inference function of margins) method and outline the process of obtaining standard errors for parameter estimates. Through extensive simulation studies covering skewed and symmetric marginal distributions and various copula choices, we assess the finite sample performance of our approach. Finally, we apply these models to the HIV dataset and present our findings.

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arXiv2025

Factor copula models for non-Gaussian longitudinal data

This article presents factor copula approaches to model temporal dependency of non-Gaussian (continuous/discrete) longitudinal data. Factor copula models are canonical vine copulas which explain the underlying dependence structure of a multivariate data through latent variables, and therefore can be easily interpreted and implemented to unbalanced longitudinal data. We develop regression models for continuous, binary and ordinal longitudinal data including covariates, by using factor copula constructions with subject-specific latent variables. Considering homogeneous within-subject dependence, our proposed models allow for feasible parametric inference in moderate to high dimensional situations, using two-stage (IFM) estimation method. We assess the finite sample performance of the proposed models with extensive simulation studies. In the empirical analysis, the proposed models are applied for analysing different longitudinal responses of two real world data sets. Moreover, we compare the performances of these models with some widely used random effect models using standard model selection techniques and find substantial improvements. Our studies suggest that factor copula models can be good alternatives to random effect models and can provide better insights to temporal dependency of longitudinal data of arbitrary nature.

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arXiv2025

Modeling temporal dependency of longitudinal data: use of multivariate geometric skew-normal copula

Use of copula for the purpose of modeling dependence has been receiving considerable attention in recent times. On the other hand, search for multivariate copulas with desirable dependence properties also is an important area of research. When fitting regression models to non-Gaussian longitudinal data, multivariate Gaussian copula is commonly used to account for temporal dependence of the repeated measurements. But using symmetric multivariate Gaussian copula is not preferable in every situation, since it can not capture non-exchangeable dependence or tail dependence, if present in the data. Hence to ensure reliable inference, it is important to look beyond the Gaussian dependence assumption. In this paper, we construct geometric skew-normal copula from multivariate geometric skew-normal (MGSN) distribution proposed by Kundu (2014) and Kundu (2017) in order to model temporal dependency of non-Gaussian longitudinal data. First we investigate the theoretical properties of the proposed multivariate copula, and then develop regression models for both continuous and discrete longitudinal data. The quantile function of this copula is independent of the correlation matrix of its respective multivariate distribution, which provides computational advantage in terms of likelihood inference compared to the class of copulas derived from skew-elliptical distributions by Azzalini & Valle (1996). Moreover, composite likelihood inference is possible for this multivariate copula, which facilitates to estimate parameters from ordered probit model with same dependence structure as geometric skew-normal distribution. We conduct extensive simulation studies to validate our proposed models and therefore apply them to analyze the longitudinal dependence of two real world data sets. Finally, we report our findings in terms of improvements over multivariate Gaussian copula based regression models.

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arXiv2025

Finite mixture copulas for modeling dependence in longitudinal count data

Dependence modeling of multivariate count data has garnered significant attention in recent years. Multivariate elliptical copulas are typically preferred in statistical literature to analyze dependence between repeated measurements of longitudinal data since they allow for different choices of the correlation structure. But these copulas lack in flexibility to model dependence and inference is only feasible under parametric restrictions. In this article, we propose employing finite mixtures of elliptical copulas to better capture the intricate and hidden temporal dependencies present in discrete longitudinal data. Our approach allows for the utilization of different correlation matrices within each component of the mixture copula. We theoretically explore the dependence properties of finite mixtures of copulas before employing them to construct regression models for count longitudinal data. Inference for this proposed class of models is based on a composite likelihood approach, and we evaluate the finite sample performance of parameter estimates through extensive simulation studies. To validate our models, we extend traditional techniques and introduce the t-plot method to accommodate finite mixtures of elliptical copulas. Finally, we apply our models to analyze the temporal dependence within two real-world longitudinal datasets and demonstrate their superiority over standard elliptical copulas.

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