A small sample investigation of rank-based profile analyses

Four rank-based procedures for profile analysis of repeated measure responses are
discussed in detail. All four offer the user a complete analysis including estimation
of regression coefficients, tests of general linear hypotheses, and confidence
procedures. The fitting for each is based on minimizing a norm, hence, their
geometry is similar to that of the traditional LS analysis. Two of the analyses are
multivariate with theory not requiring assumptions on the covariance structure
of the repeated measures, while the other two are univariate analyses with theory
requiring compound symmetry covariance structure. All of the analyses are easily
computed with existing R software. An example is discussed in some detail, including
a sensitivity analysis. A Monte Carlo study investigates the validity and
power of the analyses over the normal and Cauchy distributions and a large family
of contaminated normal distributions and over two covariance structures. Generally
the rank-based procedures were valid. In the normally distributed situations,
the traditional LS analysis was more powerful, but by little; on the other hand,
all the rank-based analyses dominated LS over the other distributions. One of the
univariate analyses (ATR) performed better than the others over the compound
symmetric situations.