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Biometrika 1984 71(1):35-42; doi:10.1093/biomet/71.1.35
© 1984 by Biometrika Trust
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Tied, grouped continuous and ordered categorical data: A comparison of two models

A. N. PETTITT

Department of Mathematics, University of Technology Loughborough, Leicestershire, U.K.

Likelihood ratio tests for no regression effect are considered when a linear model is used to explain the sample outcome where the observations are tied, grouped continuous or ordered categorical data. Two likelihoods are considered: one is an adaptation of a likelihood based on ranks modified for ties, and the second is a likelihood for grouped continuous data. The two likelihoods give asymptotically equivalent test statistics provided that the number of tied values or categories does not increase too quickly with N, the total number of observations. Approximate estimation procedures are proposed based on average rank scores and two examples are given.

Key Words: Average score • Likelihood ratio • Linear model • Ordered categories • Rank • Ties


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