Nonparametric testing for random effects in mixed effects models based on the piecewise linear interpolate of the log characteristic function

Bawawana, Bavwidinsi

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https://hdl.handle.net/2142/42126 Copy

Description

Title

Nonparametric testing for random effects in mixed effects models based on the piecewise linear interpolate of the log characteristic function

Author(s)

Bawawana, Bavwidinsi

Issue Date

2012-12

Director of Research (if dissertation) or Advisor (if thesis)

Portnoy, Stephen L.

Doctoral Committee Chair(s)

Portnoy, Stephen L.

Committee Member(s)

• Simpson, Douglas G.
• Douglas, Jeffrey A.
• He, Xuming

Department of Study

Statistics

Discipline

Statistics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• Linear Mixed Effect Model (LMEM)
• Characteristic function
• Normal distribution
• Nonparametric testing
• Power
• Deconvolution
• Density function

Abstract

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.

Graduation Semester

2012-12

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http://hdl.handle.net/2142/42126

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Copyright 2012 Bavwidinsi Bawawana

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