۱٫ Introduction

۲٫ Inverse Gaussian Mixed-Effects Model

۳٫ Estimating Model Parameters

۴٫ Framingham Cholesterol Data

۵٫ Conclusion

Acknowledgements

References

Following [7], we introduce the nested Inverse Gaussian Mixed-Effects model to analyze right-skewed and continuous longitudinal data. The nested random effects don’t follow a specific parameter distribution and rely only on the first two moments assumptions in our model. We apply the truly orthodox best linear unbiased predictor (BLUP) approach to estimate the nested random effects. We derive an optimal estimating equation for the regression parameters under the case of known BLUP of random effects. A real example for Framingham cholesterol data is presented to illustrate our proposed methodology.

Introduction

Skewed continuous longitudinal data frequently appear in many areas of research. Various skew normal models have been proposed to analyze skewed longitudinal data in recent years. For example, [5] for linear mixed models by substituting the skew-normal assumption of random effects for the normal assumption; [9] for Bayesian partial linear model; [1] for Skew-normal antedependence models; [8] for mixed effects model with the skew-normal and skew-t assumption of the distribution of responses and random effects. However, these approaches are generally computationally intensive. The inverse Gaussian regression model is a powerful method for analyzing right-skewed continuous data. Following [6] and [7], we consider a class of nested Inverse Gaussian Mixed-Effects Model for right-skewed and continuous longitudinal data. [7] introduced the nested Tweedie mixed model based on an orthodox BLUP approach. Similarly, this orthodox BLUP approach to our models is still computationally simple and efficient. In addition, our approach consolidates conditional and marginal modeling interpretations.