Joint Research Conference
June 24-26, 2014
Partial Antecorrelation Models with Independent Asymmetric Laplace InnovationsAbstract:
It is known that in longitudinal studies, repeated measurements might behighly skewed and thus the violation of Gaussian assumption may be expected. Al-though positive skewness could be reduced by a variance stabilizing transformationsuch as the logarithmic transformation, difficulties may arise in the interpretationof parameters with respect to the original scale of the data. We propose partialantecorrelation models with independent asymmetric laplace (ALD) innovationsfor modeling skewed longitudinal data. We derive the distribution of a linearcombination of independent standard ALD variables by an induction method andgive the explicit forms for its probability density function, cumulative distributionfunction and moments. These give us a convenient way to investigate the proper-ties for the marginals of the model such as mean, variance, skewness and so on.Furthermore, we give an iterative algorithm for maximum likelihood estimation.Method of moments estimates are used as initial values for the algorithm. Thesimulation results and experiments with a real longitudinal data set are reportedto illustrate the model and evaluate the accuracy of the estimation method.Key Words: Antedependence; Partial Antecorrelation; Asymmetric Laplace Distribu-tion; Maximum Likelihood Estimation.
Shu-Ching Chang (Email: shuching91@gmail.com) is Doctoral Graduate, Department of Statisticsand Actuarial Science, University of Iowa, Iowa City, IA 52242.
Dale L. Zimmerman (Email: dale-zimmerman@uiowa.edu) is Robert V. Hogg Professor and Directorof Graduate Studies, Department of Statistics and Actuarial Science, 233 Schaeffer Hall, University ofIowa, Iowa City, IA 52242.