Inference for the Linear Model Using a Likelihood Based on Ranks
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 1982 · Volume 44 · Issue 2
DOI: 10.1111/j.2517-6161.1982.tb01204.x
Abstract
An approximation to the marginal likelihood of the ranks of a set of observations is used to analyse data. The observations, after some arbitrary monotone transformation, are assumed to be independently normally distributed with means related by a linear model. An approximate posterior distribution for the parameters of the linear model is given and used to find predictive distributions for the ordering of future observations. A numerical example is given. Appendices give mathematical details of the approximation.
Keywords
distribution-free tests, kruskal-wallis test, linear model, multiple comparisons, normal scores, predictive probability, rank marginal likelihood
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