Collapsibility and response variables in contingency tables

摘要: SUMMARY Various definitions of the collapsibility a hierarchical log linear model for multidimensional contingency table are considered and shown to be equivalent. Necessary sufficient conditions found in terms generating class. It is that models appropriate tables with response explanatory variables if only they collapsible onto variables. Some key word8: Collapsibility; Contingency table; Graphical model; Interaction graph; Log Response variable; S-sufficiency. closely related. have property relations between set classifying factors may studied by examination marginal totals formed summing over remaining factors. Such said given Collapsibility has important consequences hypothesis testing selection, can useful data reduction. We consider various show their equivalence. Furthermore, necessary collapsi- bility Many analysed practice involve Simple examples, one which ? 3, suffice importance distinguishing variables: first, inappropriate avoided, second natural relevant not considered. This paper characterizes some alternative approaches analysis such briefly N based on F. For subset F we interested Na, say cell counts summed aC, complement identify L, probabilities p E its class, whose elements, generators, square brackets: thus example (AB) (BCD) 4-way corresponds