Short Course on Rank-Based Analyses of Linear Models

Joseph W. McKean
Professor of Statistics
Western Michigan University
joe@stat.wmich.edu

Abstract:

Outliers and aberrant data plague experiments in the medical and pharmaceutical fields. This is a short course which addresses methodology for such data. This course will focus on the use of nonparametric and robust techniques in analyzing problem data. Application of these techniques to real world problems, many drawn from pharmaceutical studies, will be emphasized. The course begins with application of these procedures to one and two sample problems and proceeds to linear models and ANOVA and ANCOVA type designs. A web interface to RGLM (Robust General Linear Models) will be discussed. This allows the computation of these procedures for anyone having web access.

These rank-based methods generalize traditional nonparametric (Wilcoxon) methods for simple location problems. They offer a complete analysis of linear models, including estimation of effects, diagnostics procedures to check quality of fit, confidence and multiple comparison methods, and tests of general linear hypotheses. They are highly efficient procedures which can also be extended to high breakdown procedures for observational studies.

References

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Chang, W. H., McKean, J. W., Naranjo, J. D. and Sheather, S. J. (1999), High Breakdown Rank Regression, The Journal of the American Statistical Association, 94, 205-219.

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Hettmansperger, T. P. and McKean, J. W. (1998), Robust Nonparametric Statistical Methods, London: Arnold.

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Hettmansperger, T. P., McKean, J. W. and Sheather, S. J. (2000), Robust nonparametric methods, The Journal of the American Statistical Association, 95, 1308-1311.

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Hollander, M. and Wolfe, D., A. (1999), Nonparametric Statistical Methods, 2nd Edition, New York: Wiley.

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Kapenga, J. A., McKean, J. W. and Vidmar, T. J. (1988), RGLM: Users Manual, Amer. Statist. Assoc. Short Course on Robust Statistical Procedures for the Analysis of Linear and Nonlinear Models, New Orleans.

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McKean, J. W. and Vidmar, T. J. (1994), A comparison of two rank-based methods for the analysis of linear models, The American Statistician, 48, 220-229.

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Vidmar, T. J., McKean, J. W. and Hettmansperger (1992), Robust procedures for drug combination problems with quantal responses, Applied Statistics, 41, 299-315.

Outline of Short Course on Rank-Based Analyses of Linear Models

1.

Location Models.

(a)

Traditional Wilcoxon tests for one and two sample location problems.

(b)

Introduce rank-based methods for estimates of treatment effects.

i.

Estimates of standard errors.

ii.

Symmetric type confidence intervals for treatment effects.

(c)

Discuss close analogy to traditional LS methods.

(d)

Introduction to web-based RGLM to compute these methods. This is an R interface with RGLM. All the user needs is access to the web. Site: www.stat.wmich.edu/slab/RGLM

2.

Simple linear regression models.

(a)

Wilcoxon rank tests for regression effects.

(b)

Rank-based estimates of regression parameters. Both highly efficient estimates and high breakdown estimates.

i.

Estimates of standard errors.

ii.

Symmetric type confidence intervals for regression effects.

(c)

Discuss close analogy to traditional LS methods.

(d)

Using web-based RGLM to compute these methods.

3.

Multiple linear regression models.

(a)

Rank-based fits of linear models.

i.

A brief discussion of their geometry emphasizing the close analogy between rank-based estimates and least squares (LS) fits.

ii.

Using web-based RGLM to obtain the fits.

(b)

Discussion of rank-based tests for general linear hypotheses.

(c)

Diagnostic procedures for checking quality of fit.

(d)

Discussion of a complete rank-based analysis for linear models.

(e)

High breakdown robust estimates.

(f)

Using web-based RGLM to obtain this complete analysis.

4.

ANOVA and ANCOVA type designs.

(a)

Discussion of rank-based analysis for ANOVA designs, including standard designs such as one way, crossed designs, nested designs.

i.

Rank-based estimates and tests of general contrasts.

ii.

Multiple comparison procedures.

iii.

Using web-based RGLM to obtain these complete analyses.

(b)

Discussion of rank-based analysis for ANCOVA type designs.

i.

Using web-based RGLM to obtain these complete analyses.

5.

Depending on the course length, other topics that could be covered include:

(a)

Survival type analyses.

(b)

Nonlinear and generalized linear models.

(c)

Regression to the mean effects.

(d)

Robust approaches to sliced-inverse-regression.