Multiple membership multiple classification (MMMC) or Cross classification (CC) model ?

[zhaohaiyan]

Dear all,
we reported a multilevel modelling study based on a large scale education exam dataset (about 60k students) and were asked to revise our modelling by reviewers. Basically about the study: 60K student English writing were extracted from a national exam database. Each student’s writing was scored by two independent raters, only a small portion of student writing were scored by three independent raters. Therefore each student had at least 2 scores for same writing. The influence of rater’s characteristics on Student writing score was explored by Multilevel modelling. Due to the non-independence presented in the data, we conducted a multiple membership multiple classification (MMMC) modelling as we thought our data structure is the same as the household dataset mentioned in MLwiN MCMC manual and detailed in Brown et al (2001) paper titled “Multiple membership multiple classication_MMMC_ models” which could be accessed at http://www.bris.ac.uk/media-library/sit ... mmrev2.pdf. Our logic was that Each score was crossclassified with student and rater (hence cross classified). As each student have two(or three) scores and rated by two(or three) raters (hence MM), we used a modified weight tricks to reflex the Multi-membership . Here is an example of data structure and weighting scheme for one student having two scores.



One reviewer pointed out our model was not correct, especially the 0/1 weight is not correct as weight should be decimal number. after rethinking our model, we are thinking our data structure should be a general cross classification model, i.e. score cross classified between student and rater, there is no need to perform MMMC model indeed. However, if we treated the score as repeated measure for same student, our data structure looks same as household dataset so MMMC is not wrong, . Am I right? any help/advice please?
Many thanks in advance.
Zhaohy.

[billb]

Hi Zhaohaiyan,
Yes given you have a different response nested within a rater and a student it seems to me that XC is more appropriate. MMMC is generally for 1 response shared between the set of raters.
Hope that helps,
Bill.