ABSTRACT
In this chapter we introduce a general framework for multiple hypotheses testing in parametric and semi-parametric models. This chapter provides the theoretical basis for the applications analyzed in Chapter 4. In Section 3.1 we review briefly the standard linear model theory and show how to perform multiple comparisons in this framework, including analysis-of-variance (ANOVA), analysis-of-covariance (ANCOVA) and regression models as special cases. We extend the basic approaches from Chapter 2 by using inherent distributional assumptions, particularly by accounting for the structural correlation between the test statistics, thus achieving larger power. In addition, we revisit the linear regression example from Chapter 1 to illustrate the resulting methods. In Section 3.2 we extend the previous linear model framework and introduce multiple comparison procedures for general parametric models relying on standard asymptotic normality results. The methods apply, for example, to generalized linear models, linear and non-linear mixed-effects models as well as survival data. Again, the use of the inherent stochastic dependencies leads to powerful methods. The multcomp package in R provides a convenient interface to perform multiple comparisons for the parametric models considered in Sections 3.1 and 3.2. An in-depth introduction to the multcomp package is given in Section 3.3. Detailed examples to illustrate and extend the results from this chapter are left for Chapter 4.
