In this model, only the one-variable effects are implemented, which means that the marginal distributions of both variables are reproduced. If these one-variable effects are similar to each other, both variables' marginal distributions are homogeneous. Homogeneous marginal distributions imply that both raters choose each category with almost the same frequency; accordingly, no rater prefers any category to a greater extent than the other, which means that no rating is biased (Agresti, 1992).
This type of model will only rarely fit empirical data because, in general, different measures of a construct are related to a certain degree, and this relatedness represents the convergent validity. Useful information provided by the independence model stems from the analysis of its adjusted cell residuals. Adjusted cell residuals compare observed with expected cell frequencies (see Agresti, 1992):
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