A useful extension of the independence model is the quasi-independence model. In this model a new parameter is introduced that is only implemented for cells on the main diagonal, which represent agreement between methods:
This model fits the data in Table 17.3 (%2 = 1.38, df = 1, p = .24) very well. In contrast to the independence model, this model allows higher cell frequencies for cells on the main diagonal, but no overrepresentation in any other cell. For cells indicating disagreement, the independence model holds (see Table 17.6a). As a result of the newly introduced parameter 8p the estimated cell frequencies on the main diagonal indicating agreement are exactly equal to the empirical cell frequencies. The newly introduced parameter 8f can be used to compare the probability of receiving a particular response by one method, given the rating of the other method (see Agresti, 1992). The probability of receiving an answer in the first cell on the main diagonal is exp(8j) = exp(0.61) = 1.84 times larger than expected by chance. Similarly, the probabilities of falling into the second and third cell on the main diagonal are 21.25 and 17.54 times greater than expected by chance. This indicates that the agreement between both raters is much higher for the categories "dyslexic" and "normal" than for "hyperactive."
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