| Abstract: | The most common association models are the U-, R-, C- and RC-models, achieved when only one dimension on the association is considered as significant (M = 1). Whenever more than one dimensions are significant (M > 1), the only kind of association assumed for each dimension is of the RC-type with the exception of Goodman's R + C + RC, R + RC, C + RC, U + RC and R + C models. Extending the idea of U-, R-, and C-models to association models with M > 1, relaxing the equidistance principle for successive categories for the known scores and using orthogonal polynomials, some new models are developed. Two classical sets of data are used to illustrate the advantages of the newly introduced models. Comparisons in terms of chi-square goodness of fit indicate that some of the newly introduced models perform better than the models fitted so far on these data sets. © 1998 John Wiley & Sons, Ltd. |
