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Hi y'all,
Wondered if anyone out there could help clarify something about notation in MLwin:
Having read a few books about longitudinal data use and MlwiN, as I understand it, "occasions" are clustered within "individuals" - ie level 1 ("i" in mlwin notation) is the occasion (1,2,3...n) and level 2 is the individual ("j" in MLwin notation)
All clear so far.... but where I get confused is when some authors talk about individual "i" on occasion "j"...is this statistical notation with no regard to MLWin and "multilevel" analysis or are there times when it is necessary to have the individual at level 1 and the occasion at level 2? If so, could someone clarify when this would occur (ie is it something to do with time dependent variables).
Regards
Nick
There are two possibilities here. First, I believe there may be some software packages/ groups of multilevel modellers who use i to index level 2 and j to index level 1- this could be the case for the example you've seen. Secondly, yes there are some situations where you would want to put individual at level 1 and occasion at level 2, for example:
1) Suppose you have students nested in teachers nested in schools. In 2005 we give exams to the 16 year olds from each school. In 2006 we again give exams to the 16 year olds from each school, but these are now different students, one year younger than the ones who sat the exam in 2005. We repeat every year till 2009. We now have five occasions, and on each occasion the students are nested within teachers, who are nested within schools. But the occasions are not nested within students, because each student is only measured once. Instead we have students nested within occasions: at each occasion we measure many students. Occasions are nested within teachers, who are nested within schools. We can think of this as being repeated measures on teachers, rather than repeated measures on students. Level 1: student; Level 2: occasion; Level 3: teacher; Level 4: school
2) Imagine we have the same situation, but we are in Japan, where each teacher changes schools every 3 years, and we are only measuring every 3 years (1997, 2000, 2003, 2006, 2009). So at each measurement occasion we have different teachers. (In reality, the teachers would probably move to another school in our dataset, giving us a cross-classified model, but let's ignore this for simplicity and pretend we have a completely different set of teachers at each time point!). Now at each individual occasion we still have students nested within teachers nested within schools. Taking all the occasions together, as in the first example occasions are not nested in students, because still each student is only measured once. This time, occasions are not nested in teachers either, because each teacher also only appears at one occasion. Instead we have students nested in teachers nested in occasions, and we can think of this as repeated measures on schools (which are the only units that are present at all occasions). Level 1: student; Level 2: teacher; Level 3: occasion; Level 4: school
3) Similar structure to example 1 but different data: imagine we have a survey where we administer the same questionnaire in 5 different waves, but instead of taking the same participants for each wave, we instead keep the same primary sampling units (areas) and for each wave pick a new sample of individuals. (An example which does this would be the European Social Survey). Now once again we have only one measurement occasion for each individual, so we have individuals nested in occasions nested in areas (or countries) not occasions nested in individuals nested in areas/countries. Level 1: individual; Level 2: occasion; Level 3: area.
Basically, the short answer is that we might have individuals at level 1 and occasions at a higher level whenever we have completely different individuals measured at each occasion. (If we have some individuals who appear on more than one occasion and only a few who only appear on one occasion, we can do occasions nested in individuals and it will be ok that many (or even all) individuals do not have all occasions, so long as the proportion of individuals with only one occasion is small). The occasion level will go just below the lowest level which contains units appearing at more than one measurement occasion.
