A non-iterative alternative to ordinal log-linear models

Eric J. Beh, Pamela J. Davy

    Research output: Contribution to journalArticle

    13 Citations (Scopus)

    Abstract

    Log-linear modeling is a popular statistical tool for analysing a contingency table. This presentation focuses on an alternative approach to modeling ordinal categorical data. The technique, based on orthogonal polynomials, provides a much simpler method of model fitting than the conventional approach of maximum likelihood estimation, as it does not require iterative calculations nor the fitting and re-fitting to search for the best model. Another advantage is that quadratic arid higher order effects can readily be included, in contrast to conventional tog-linear models which incorporate linear terms only. The focus of the discussion is the application of the new parameter estimation technique to multi-way contingency tables with at least one ordered variable. This will also be done by considering singly and doubly ordered two-way contingency tables. It will be shown by example that the resulting parameter estimates are numerically similar to corresponding maximum likelihood estimates for ordinal log-linear models.
    Original languageEnglish
    Number of pages20
    JournalJournal of applied mathematics and decision sciences
    Publication statusPublished - 2004

    Keywords

    • contingency tables
    • estimation theory
    • linear models (statistics)
    • mathematical statistics
    • ordinal variables
    • orthogonal polynomials

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