Modeling approaches in the social sciences are always implemented to give an appropriate but parsimonious representation of social phenomena or— more precisely—of the empirical data representing these phenomena. Saturated loglinear models exactly reproduce these data and do not put restrictions on the data. They always fit the data perfectly. In contrast, nonsaturated loglinear models impose a priori restrictions on the data and, thus, contain testable consequences. These consequences can be tested by the Pearson %2 goodness of fit index or the log-likelihood ratio y} statistic L2 (see, e.g., Bishop et al., 1975; Hagenaars, 1990; Knoke & Burke, 1980). The number of degrees of freedom equals the number of independent a priori restrictions. Parameters of nonsaturated loglinear models cannot be easily computed. Among others, Hagenaars (1990), Knoke and Burke (1980), as well as Vermunt (1997a) represent the relevant formulas for their maximum likelihood estimates.
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