【文章內(nèi)容簡介】 101euuyeuuy??????????Where classification 2 is neighbourhood and classification 3 is school. Classification 1 always corresponds to the classification at which the response measurements are made, in this case patients. For pupils 1 and 11 equation (1) bees: Classification diagrams School Pupil Neighbourhood School Pupil Neighbourhood Nested structure where schools are contained within neighbourhoods Crossclassified structure where pupils from a school e from many neighbourhoods and pupils from a neighbourhood attend several schools. In the single subscript notation we lose information about the relationship(crossed or nested) between classifications. A useful way of conveying this information is with the classification diagram. Which has one node per classification and nodes linked by arrows have a nested relationship and unlinked nodes have a crossed relationship. Example : Artificial insemination by donor W o m e n w1 w2 w3 C y c le s c 1 c 2 c 3 c 4… c 1 c 2 c 3 c 4… c 1 c 2 c 3 c 4… Do n a t i o n s d1 d2 d1 d2 d3 d1 d2 Do n o r s m 1 m 2 m 3 1901 women 279 donors 1328 donations 12100 ovulatory cycles response is whether conception occurs in a given cycle In terms of a unit diagram: Donor Woman Cycle Donation Or a classification diagram: Model for artificial insemination data ),0(~),0(~),0(~)()l o g i t (),1(~2)4()4()(2)3()3()(2)2()2()()4()()3()()2()(iuid o n o ruid o n a t i o nuiw o m a nid o n o rid o n a t i o niw o m a niiiNuNuNuuuuXB i n o m i a ly??????????We can write the model as 2 )4(u??0?1?2?3?4?5?6?72 )2(u?2)3(u?Parameter Description Estimate(se) intercept () azoospermia * () semen quality () womens age35 () sperm count () sperm motility () insemination to early () insemination to late () women variance () donation variance () donor variance () Results: Note crossclassified models can be fitted in IGLS but are far easier to fit using MCMC estimation. Extension 2: Multiple membership models When level 1 units are members of more than one higher level unit we describe a model for such data as a multiple membership model. For example, ? Pupils change schools/classes and each school/class has an effect on pupil outes. ? Patients are seen by more than one nurse during the course of their treatment. Notation ),0(~)2(),0(~)(22)2()2()()2()2(,eiujin u r s ejijjiiiNeNueuwXBy???????Note that nurse(i) now indexes the set of nurses that treat patient i and w(2)i,j is a weighting factor relating patient i to nurse j. For example, with four patients and three nurses, we may have the following weights: n1(j=1) n2(j=2) n3(j=3) p1(i=1) 0 p2(i=2) 1 0 0 p3(i=3) 0 p4(i=4) 0 4)2(2)2(1443)2(3)2(2332)2(1221)2(3)2(111)()(1)()(euuXByeuuXByeuXByeuuXBy???????????????Here patient 1 was seen by nurse 1 and 3 but not nurse 2 and so on. If we substitute the values of w(2)i,j , i and j. from the table into (2) we get the series of equations : Classification diagrams for multiple membership relationships Double arrows indicate a multiple membership relationship between classifications. patient nurse We can mix multiple membership, crossed and hierarchical structures in a single model. patient nurse hospital GP practice Here patients are multiple members of nurses, nurses are nested within hospitals and GP practice is crossed with both nurse and hospital. Example involving nesting, crossing and multiple membership – Danish chickens Production hierarchy 10,127 child flocks 725 houses 304 farms Breeding hierarchy 10,127 child flocks 200 parent flocks fa rm f1 f 2… Hous