You are here

UCF Digital Collections ยป ETD Collection

A COMPARISON OF ORDINARY LEAST SQUARES, WEIGHTED LEAST SQUARES, AND OTHER PROCEDURES WHEN TESTING FOR THE EQUALITY OF REGRESSION SLOPES WITH HETEROSCEDASTICITY ACROSS GROUPS: A MONTE CARLO STUDY

Download pdf | Full Screen View

Date Issued:
2006
Abstract/Description:
When testing for the equality of regression slopes based on ordinary least squares (OLS) estimation, extant research has shown that the standard F performs poorly when the critical assumption of homoscedasticity is violated, resulting in increased Type I error rates and reduced statistical power (Box, 1954; DeShon & Alexander, 1996; Wilcox, 1997). Overton (2001) recommended weighted least squares estimation, demonstrating that it outperformed OLS and performed comparably to various statistical approximations. However, Overton's method was limited to two groups. In this study, a generalization of Overton's method is described. Then, using a Monte Carlo simulation, its performance was compared to three alternative weight estimators and three other methods. The results suggest that the generalization provides power levels comparable to the other methods without sacrificing control of Type I error rates. Moreover, in contrast to the statistical approximations, the generalization (a) is computationally simple, (b) can be conducted in commonly available statistical software, and (c) permits post hoc analyses. Various unique findings are discussed. In addition, implications for theory and practice in psychology and future research directions are discussed.
Title: A COMPARISON OF ORDINARY LEAST SQUARES, WEIGHTED LEAST SQUARES, AND OTHER PROCEDURES WHEN TESTING FOR THE EQUALITY OF REGRESSION SLOPES WITH HETEROSCEDASTICITY ACROSS GROUPS: A MONTE CARLO STUDY.
45 views
22 downloads
Name(s): Rosopa, Patrick, Author
Stone-Romero, Eugene, Committee Chair
University of Central Florida, Degree Grantor
Type of Resource: text
Date Issued: 2006
Publisher: University of Central Florida
Language(s): English
Abstract/Description: When testing for the equality of regression slopes based on ordinary least squares (OLS) estimation, extant research has shown that the standard F performs poorly when the critical assumption of homoscedasticity is violated, resulting in increased Type I error rates and reduced statistical power (Box, 1954; DeShon & Alexander, 1996; Wilcox, 1997). Overton (2001) recommended weighted least squares estimation, demonstrating that it outperformed OLS and performed comparably to various statistical approximations. However, Overton's method was limited to two groups. In this study, a generalization of Overton's method is described. Then, using a Monte Carlo simulation, its performance was compared to three alternative weight estimators and three other methods. The results suggest that the generalization provides power levels comparable to the other methods without sacrificing control of Type I error rates. Moreover, in contrast to the statistical approximations, the generalization (a) is computationally simple, (b) can be conducted in commonly available statistical software, and (c) permits post hoc analyses. Various unique findings are discussed. In addition, implications for theory and practice in psychology and future research directions are discussed.
Identifier: CFE0001332 (IID), ucf:47013 (fedora)
Note(s): 2006-08-01
Ph.D.
Sciences, Department of Psychology
Doctorate
This record was generated from author submitted information.
Subject(s): regression slopes
heteroscedasticity
nonconstant variance
heterogeneity of variance
Persistent Link to This Record: http://purl.flvc.org/ucf/fd/CFE0001332
Restrictions on Access: campus 2007-01-31
Host Institution: UCF

In Collections