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 language | English |
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Number of pages | 20 |
Journal | Journal of applied mathematics and decision sciences |
Publication status | Published - 2004 |
Keywords
- contingency tables
- estimation theory
- linear models (statistics)
- mathematical statistics
- ordinal variables
- orthogonal polynomials