Robust and Traditional Inference Procedures for Analysis of Covariance Under Heterogeneous Slopes

• Activity Number: 353
• Type: Contributed
• Date/Time: Tuesday, July 31, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Kuanwong Watcharotone*+ and Joseph W McKean and Bradley E Huitema
• Companies: University of Michigan and Western Michigan University and Western Michigan University
• Keywords: Rank-based procedures ; Pick-a-point ; Covariate ; Monte Carlo analysis ;

Abstract

One of the important assumptions for the analysis of covariance (ANCOVA) is that the regression slopes are homogeneous. When heterogeneous slopes occur, the pick-a-point methods can be used for inference. These procedures obtain the confidence interval for treatment differences at selected covariate points. This study discusses robust procedures for the ANCOVA models focusing on pick-a-point procedures. These methods are based on rank-based (R) fitting procedures, which are analogous to the traditional ANCOVA methods based on least squares (LS) fits. The results show that the validity of R procedures is similar to the LS procedures. There is a small loss in efficiency to LS methods when the random errors have a normal distribution but the R procedures are much more powerful for the heavy-tailed error distributions. Monte Carlo analysis is conducted to compare empirically the differences of the traditional and R methods. The results indicate that the R procedures have more power than the traditional LS for longer-tailed distributions for the situations investigated. We have developed R functions which obtain the rank-based ANCOVA, including the rank-based pick-a-point procedures.