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Multiple treatment comparisons in analysis of covariance with interaction

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  • Frank Schaarschmidt

    (Leibniz Universitaet Hannover)

Abstract

When multiple treatments are analyzed together with a covariate, a treatment-covariate interaction complicates the interpretation of the treatment effects. The construction of simultaneous confidence bands for differences of the treatment specific regression lines is one option to proceed. The application of these methods is difficult because they are described as a collection of special cases and the implementation requires additional programming or relies on non-standard or proprietary software. If inferential interest can be restricted to a pre-specified set of covariate values, a flexible alternative is to compute simultaneous confidence intervals for multiple contrasts of the treatment effects over this grid. This approach is available in the R software: next to treatment differences in the linear model, approximate simultaneous confidence intervals for ratios of expected values and asymptotic extensions to generalized linear models are straightforward. The paper summarizes the available methodology and presents three case studies to illustrate the application to different models, differences and ratios, as well as different types of between treatment comparisons. Simulation studies in the general linear model, for different parameters and different types of comparisons are provided. The R code to reproduce the case studies and a hint to a related R package is provided.

Suggested Citation

  • Frank Schaarschmidt, 2017. "Multiple treatment comparisons in analysis of covariance with interaction," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(4), pages 609-628, November.
    • Handle: RePEc:spr:stmapp:v:26:y:2017:i:4:d:10.1007_s10260-017-0383-1
    DOI: 10.1007/s10260-017-0383-1
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    References listed on IDEAS

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    1. Lenth, Russell V., 2016. "Least-Squares Means: The R Package lsmeans," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 69(i01).
    2. Jamshidian, Mortaza & Liu, Wei & Zhang, Ying & Jamishidian, Farid, 2005. "Simreg: a Software Including Some New Developments in Multiple Comparison and Simultaneous Confidence Bands for Linear Regression Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 12(i02).
    3. Liu W. & Jamshidian M. & Zhang Y., 2004. "Multiple Comparison of Several Linear Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 395-403, January.
    4. Jamshidian, Mortaza & Liu, Wei & Bretz, Frank, 2010. "Simultaneous confidence bands for all contrasts of three or more simple linear regression models over an interval," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1475-1483, June.
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