Higher Order Effects in Log‐Linear and Log‐Non‐Linear Models for Contingency Tables with Ordered Categories

Jeffrey S. Simonoff and Chih‐Ling Tsai

Journal of the Royal Statistical Society Series C, 1991, vol. 40, issue 3, 449-458

Abstract: Contingency tables with ordered categories arise often in practice. The analysis of such tables is made easier through the use of models designed to take account of the ordering, such as association or correlation models. The ordinary (first‐order) properties of these models are well understood and are based on a quadratic approximation to the likelihood. In this paper higher order properties are examined. It is shown that first‐order inference can be misleading owing to sparseness of the table and/or curvature of the model. By ‘misleading’ it is meant that goodness‐of‐f it tests can give inappropriate conclusions, and the usual (approximate) inference regions can be far from the true likelihood regions. Diagnostics are derived that can gauge how misleading the quadratic approximation is for given data set. Several examples are given to illustrate these effects.

Date: 1991
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