Parameter estimations in linear mixed models with heavy-tailed and skew distributions

Date

2023-12-21

Author

Kapucu, Tuğba

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Modern statistical modeling grapples with the complexities of continuous longitudinal data, where traditional linear mixed models (LMMs) may fall short in capturing the full spectrum of nuances. In this research, we present a novel approach that marries the intricacies of a multivariate skew Laplace distribution for random effects with the robustness of a multivariate Laplace distribution for error terms. This approach allows our model to capture both skewness and heavy tails in continuous longitudinal data. By expressing the skew Laplace distribution as a normal mean-variance mixture distribution and modeling the error term of the proposed framework as a scale mixture of normal distribution, we establish a hierarchical structure for our model. Importantly, the skew Laplace distribution involves fewer parameters compared to the skew 𝑡 distribution, which is also a robust alternative of normal distribution, simplifying the estimation process. Parameter estimations for our skew Laplace linear mixed model (SL-LMM) are achieved through the Expectation Conditional Maximization (ECM) algorithm, an extended EM-type algorithm. Within the ECM algorithm, a Bayesian approach is employed to infer unobserved latent variables, with a specific case of the Markov Chain Monte Carlo (MCMC) method, known as the Metropolis algorithm, utilized for parameter estimation. To validate our model, we apply it to schizophrenia data and conduct several simulation studies, comprehensively evaluating the model's performance under varying conditions. The results show that the proposed model accurately estimates the underlying parameters and presents a better fit when compared to the competitive models.

Subject Keywords

Linear mixed models, Skew Laplace distribution, ECM algorithm, Metropolis algorithm, Longitudinal data

URI

https://hdl.handle.net/11511/107829

Collections

Graduate School of Natural and Applied Sciences, Thesis