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oai:www.ideals.illinois.edu:2142/42126 2023-07-11 col_2142_5131 col_2142_17362 com_2142_5130 com_2142_17361 com_2142_8903

Portnoy, Stephen L. Portnoy, Stephen L. Simpson, Douglas G. Douglas, Jeffrey A. He, Xuming Bawawana, Bavwidinsi 2013-02-03T19:16:33Z 2013-02-03T19:16:33Z 2015-02-03T11:00:25Z 2012-12 2012-12 2012-12 Traditional linear mixed effect models assume the distributions of the random effects and errors follow normal distribution with mean zero and homoscedastic variance sigma square. This thesis presents a new nonparametric testing approach for normality for the random effects distribution based on the piecewise linear interpolate of the log characteristic function along the grid when the number of replications is low. The ideas behind this approach were presented first by Meintanis and Portnoy (2011). The best initial grid and grid length were found, and empirical powers from the presented approach were compared with the empirical powers from Kolmogorov-Smirnov test under two venues, the first one assuming the variance of the random errors is less than the variance of the random effects distribution and the second one assuming the contrary. The method was proved to be square root n consistent. Real data set from the Modification of Diet in Renal Disease Trial (MDRD) Study A --a longitudinal study-- was used to test for normality of the random effects and errors distributions, and further, from the empirical characteristic function of the random effects and errors, the empirical density functions were estimated through the deconvolution of the empirical characteristic functions. Item withdrawn by Alexis Thompson (athmpsn1@illinois.edu) on 2012-07-13T13:43:28Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Bawawana_Bavwidinsi.pdf: 2613581 bytes, checksum: 0cfb74dc0d614cb22d00ff99672f447a (MD5) Made available in DSpace on 2013-02-03T19:16:33Z (GMT). No. of bitstreams: 2 Bavwidinsi_Bawawana.pdf: 2654322 bytes, checksum: a7f5a0ffd2874d5518e10aa62c5bf2b5 (MD5) license.txt: 4069 bytes, checksum: ba1311ca17bd7d7ca134a275fe507783 (MD5) Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Seth Robbins (srobbins@illinois.edu) on 2013-02-03T19:18:55Z Item is restricted until 2015-02-03T19:18:53Z Restriction data tranferred 2014-07-01T11:11:50-05:00 Original Data Group with Access UIUC Users [automated] Release Date: 2015-02-03 13:18:53 UTC Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system U of I Only Restriction Lifted for Item 42073 on 2015-02-03T11:00:25Z. http://hdl.handle.net/2142/42126 en Copyright 2012 Bavwidinsi Bawawana Linear Mixed Effect Model (LMEM) Characteristic function Normal distribution Nonparametric testing Power Deconvolution Density function Nonparametric testing for random effects in mixed effects models based on the piecewise linear interpolate of the log characteristic function text Statistics 1583 Statistics 0329 University of Illinois at Urbana-Champaign Dissertation Ph.D. PHD:Statistics -UIUC 10KS0329PHD