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Title: Linear mixed effects models with flexible random effects and error distributions Authors:  Tom Chen - Harvard Pilgrim Health Care Institute (United States)
Rui Wang - Harvard Pilgrim Health Care (United States) [presenting]
Abstract: In many biomedical investigations, parameters of interest, such as the intraclass correlation coefficient (ICC), are functions of higher order moments reflecting finer distributional characteristics. One popular method to make inference for such parameters is through postulating a parametric random effects model. We relax the standard normality assumptions on both the random effects and errors through the use of the Fleishman distribution, a flexible four-parameter distribution which accounts for the third and fourth cumulants. We propose a Fleishman bootstrap method to construct confidence intervals for correlated data and develop a normality test for the random effects and errors distributions. Recognizing that the ICC operates on a linear scale and may not be appropriate for wildly skewed or heavy-tailed distributions, we propose a modified, scale-free ICC. We evaluate our methods in simulation studies and apply these methods to the Childhood Adenotonsillectomy Trial sleep electroencephalogram data in quantifying wave-frequency agreement among different channels.