مدل هاي رگرسيون چندكي اثرات آميخته توسط توزيع هاي نامتقارن

In recent years, quantile regression models have gained significant popularity for analyzing empirical data across various scientific fields. By examining distribution percentiles, these models provide more comprehensive insights, facilitating more informed decision-making processes. In likelihood-based quantile regression, the asymmetric Laplace distribution is often employed due to its convenience. However, its flexibility can be constrained, as the degree of skewness is inherently tied to the location parameter, resulting in a fixed skewness that cannot be adjusted independently. This limitation poses challenges in practical applications where datasets exhibit complex structures an‎d deman‎d more adaptable distributions to capture additional distributional features while preserving skewness. As a result, traditional quantile modeling with the asymmetric Laplace distribution may fall short in such scenarios. Addressing these limitations requires adopting more flexible models with additional parameters capable of accounting for diverse characteristics within the data. Consequently, this paper proposes a quantile regression model using the multivariate asymmetric power-exponential distribution. This model introduces four additional free parameters alongside the quantile parameter, enabling it to capture asymmetry in the tails as well as the behavior of both right an‎d left tails with greater accuracy. This study develops the proposed quantile regression model within both Bayesian an‎d frequentist frameworks an‎d conducts a comparative analysis against existing approaches. Furthermore, it presents a novel multivariate quantile-based regression model designed specifically for the analysis of longitudinal data with complex structures. By employing a well-defined concept of multivariate quantiles, this model enables the fitting of both marginal an‎d separate mixed-effects models. It also incorporates a combination of the Gram-Schmidt orthogonalization process an‎d a flexible family of multivariate asymmetric distributions for error terms, providing an effective tool for analyzing complex longitudinal datasets.

4

149659