26.00 (26)

19.00 (19)

108.01 (108)

153.01 (153)

Note. "Quasi-Independence Model I represents the quasi-independence model with exactly fitted cell frequencies on the main diagonal: 8j = 0.61; 82 = 3.06; 53 = 2.86.

''Quasi-Independence Model II represents the quasi-independence model with the fitted sum of cell frequencies on the main diagonal: 8 = 2.10.

Note. "Quasi-Independence Model I represents the quasi-independence model with exactly fitted cell frequencies on the main diagonal: 8j = 0.61; 82 = 3.06; 53 = 2.86.

''Quasi-Independence Model II represents the quasi-independence model with the fitted sum of cell frequencies on the main diagonal: 8 = 2.10.

If all parameters are equal to each other, all expected cell frequencies on the main diagonal differ from chance agreement to the same degree. Hence, a simpler model holds, which assumes to be constant:

The sum of the expected cell frequencies on the main diagonal is exactly equal to the sum of the observed frequencies, whereas single expected cell frequencies may differ from the observed (see Table 17.6b). This model also fits the data well (%2 = 5.96, d/=3,p = .ll). The expected cell frequencies on the main diagonal are exp(8;) = exp(2.10) = 8.17 times larger than would be expected by independent ratings. The difference between both models is that in the latter, the degree of agreement between both methods is the same for all categories, whereas in the first model, agreement may differ from category to category.

To decide which model fits better, the likelihood ratio difference test can be calculated (e.g., Hagenaars, 1990; Knoke & Burke, 1980). This test is only available for hierarchical models. Hierarchical (or nested) models are models from which the more restrictive model is obtained by imposing restrictions on parameters of the less-restricted model (such as equality constraints or the fixation on a special value). As the latter quasi-independence model constrains all parameters 8j to be equal, it is the more restrictive model compared to the first one. The conditional likelihood ratio test yields a value of =

This test indicates that the more restrictive model fits the data as well as the less restrictive and, thus, should be preferred as the more parsimonious representation.

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