A Model for Contingency Tables Having an Ordered Response Classification

Abstract

A common case of ordered categories in contingency tables is where objects are classified according to a rating procedure with respect to some dependent variable. A rating mechanism for such ordered categories, resulting in a log-linear response model in which successive categories are scored with successive integers, is proposed. Two sets of data which have been analysed with other models are reanalysed. In thefirst example, the original and new analyses give the same substantive interpretation, but whereas the former requires interpreting interactions, the latter requires interpreting main effiects only. Consequently, the latter analysis is considered simpler. In the second example, the relationship between the variables of interest is again found to be the same as in the original analysis, but in addition, a new insight into the operation of the rating mechanism is suggested. Specifically, it is suggested that one of the cut-offpoints on the rating continuum is not discriminating. Because the original classification was trichotomous, the implication is that the categories on either side of the non-discriminating cut-ofJ point may be pooled and that the same information can therefore be obtained from the collapsed dichotomous classification.