combination of ratings "hyperactive" and "normal" by both raters differ by the same amount from their observed frequencies (e13 - nu = 6.81 - 6 = 0.81, and e31 - n31 = 7.19 - 8 = -0.81). The quasi-symmetry model fits the data very well (%2 = 1.37, d/=l,p=.24).
If the one-variable effects do not differ between variables the more restrictive assumptions of the symmetry model hold. Formally, the symmetry model appears to be quite similar to the quasi-sym-metry model:
with lAB = XAB for all i and /; XA = V. for i = j ij jl J ' l J J
In contrast to the quasi-symmetry model, the one-variable effects are set to equal each other. Thus, the marginal distributions of both variables have to be equal, meaning that neither rating is biased (see Table 17.7b). Hence, the symmetry model is a special case of the quasi-symmetry model. In this model, even the expected cell frequency of contrary combinations of categories is the same. For example, the combination of "hyperactive" and "normal" yields the same expected frequencies for both combinations (e13 = e31 = 7.00). The expected cell frequencies are mirrored around the main diagonal. The symmetry model also fits the data very well (%2 = 1.49, df= 3, p = .69). The likelihood ratio difference test between the quasi-symmetry and the symmetry model yields a value of 0.11 (df = 2, p = .95); the symmetry model represents the empirical data as well as the quasi-symmetry model. One may now conclude that both raters use the categories with the same frequencies (implied by the equality constraints on the one-variable effects) and that neither rating is biased compared to the other because all expected cell frequencies are the same for contrary combinations of categories. Therefore, both raters are interchangeable (Agresti, 1992).
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