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 Julien Lemay posted on Friday, December 29, 2017 - 6:24 am

I have data in which each individual has 3 characteristics, and each of those characteristics is part of a distinct hierarchy of levels. Is it possible to have many multiple levels simultaneously? I.E. Level1a is nested within level2a within level3a; level1b is nested within level2b within level3b; level1c is nested within level2c within level3c, and each individual has a distict level1a level1b and level1c characteristic.

I am trying to figure out if I have to stack the different nesting hierarchies (i.e. nest c within b within a, which is no longer hierarchical, although it would remain logical) and lose some of the subgroup information (ex. level3a x level2b x level 1c information would not be accessible), or if this is something that stratification could partially address since the sample is stratified at the level1a domain.

Full disclosure, I do not yet have a license, but I would appreciate your help as I am currently trying to write up the justification for my employer to purchase licenses for our division so that we can address this specific type of modeling problem.
 Bengt O. Muthen posted on Friday, December 29, 2017 - 10:50 am
Not sure, but perhaps multiple membership modeling is helpful. We talk about that in short course Topic 19, part 3.

You may also want to post this on Multilevelnet.
 Julien Lemay posted on Saturday, December 30, 2017 - 3:50 pm
I can only find the short courses up to 13

I just signed up to multilevelnet and semnet. I will be seeking further advice there as well.

I had read the threads on multiple membership models, but it seemed like this was a set of cases where individuals could belong to multiple level 2 groups; but in my case each individual is part of single group of each of the hierarchies. I see how it is multiple groups, but these hierarchies are mutually exclusive, that is no unit will ever be in two groups within a level of a given hierarchy. The other question I have, is that my "multigroup" is tarting at level 1. Was I misinterpreting the examples in the thread in which the multiple group affiliation begins at level 2 as a general rule when it was not meant to be so?

Thank you, and happy new year! I can't get to get back into MPLUS!:-) (assuming my proposal is accepted)
 Bengt O. Muthen posted on Saturday, December 30, 2017 - 4:11 pm
I meant to type Topic 10.

Although I may be wrong, it sounds like you area saying that each individual is measured on 3 variables, the characteristics, and that each of those variables has "a distinct hierarchy of levels". I wonder what you mean by that last part.
 Julien Lemay posted on Saturday, December 30, 2017 - 4:32 pm
Sorry, what I meant by that is that each of the 3 variables have the nesting structure which follows: using an example, we could have

city nested within province or state, nested within country

They are nested in an inherently hierarchical fashion in that the cities of Ottawa and Toronto will always be part of the Province of Ontario, and all individuals within those cities MUST belong to the same higher level geography (province). However, they can belong in any of the groups of the other two variables, but once that affiliation is established, the same invariability in the nesting levels applies. This means that groups within hierarchies A, B, and C can be crossed between each other, but that groups within A can NOT be crossed within A through the levels, and likewise for B and C.

I hope this clarifies what I meant. I am looking forward to reading lesson 10, and thank you again!
 Bengt O. Muthen posted on Sunday, December 31, 2017 - 12:51 pm
The example of cities and province helps, but I would need your example to illustrate what you mean by "they can belong in any of the groups of the other two variables". Giving the whole example you consider is probably best here.
 Julien Lemay posted on Tuesday, January 02, 2018 - 7:49 am
Sorry for the delay, it took me a while to find a suitable example.

To narrow it down to a hypothetical example with two hierarchical variables, where the outcome variable is the average weight of the animals recovered by animal control

Var1-Level1 city : Ottawa Toronto Montreal New-York...
Var1-Level2 province : Ontario Ontario Quebec New-York...
Var1-Level3 country : Canada Canada Canada USA...

And for variable 2, it is the categorization of the animals

Var2-Level1 species: squirrel moose mouse moose ...
Var2-Level2 family : rodents/ odd-toed ungulates/ rodends/ odd-toed ungulates ...
Var2-Level3 class : mammal mammal mammal mammal ...

So this presents my question where it is impossible for the individuals to cross within a variable, but they can cross between, and the subsequent levels respect that nesting.

Down the road, this example also illustrates another issue I know I will be facing, and that is that Var1 and Var2 are not independent, since we can assume that the type of animal found varies by region.
 Bengt O. Muthen posted on Tuesday, January 02, 2018 - 2:15 pm
Seems like Var1 is a DV and Var2 an IV where for the latter perhaps only the level1 species classification is a sufficient predictor (or set of dummy variable predictors) of Var1. In this example it doesn't seem relevant to for instance decompose the variance contribution to Var2 at the 3 different levels as one does in a multilevel analysis for a DV.
 Julien Lemay posted on Tuesday, January 02, 2018 - 2:42 pm
I am having trouble creating an example, I can't provide you with the actual work. What I was trying to illustrate is the mutual exclusivity aspect of the groups within the different nested levels of the respective variables, because you asked for clarification on "they can belong in any of the groups of the other two variables"; just as the moose was in different geographies, and mammals were in all geographies.

Setting aside the ridiculous research question I tried to make up, the point was that there was no crossing of groups within variable 1, nor within variable 2, but there was crossing between variables 1 and 2.

The different levels are of interest, and dummy variables are a problem because there exists nearly 2 000 000 combinations possible between my 3 variables, most of which don't exist in the data. Analyzing at a higher level using vastly simplified models does yield interesting results, but not useful ones.

Thank you for your patience.
 Bengt O. Muthen posted on Wednesday, January 03, 2018 - 2:40 pm
Hmm; I am stumped here.
 Julien Lemay posted on Thursday, January 04, 2018 - 12:14 am
Thank you for your time. I am thinking of accepting a loss in detail and treating it as cross classified, but I do wonder, will it be an issue that the groups won't be part of a coherent whole? Just as in the hypothetical scenario above, level 2 would have geographies and animal families? Otherwise, I can't see how I can model the three multilevel variables in there, unless there is a way to make SEM models where sub sections are multilevel, independently of the rest.

Thanks again
 Tihomir Asparouhov posted on Friday, January 05, 2018 - 9:42 am
It sounds like type=crossclassified is the way to go in your situation.

I would also recommend running two and three level models to evaluate the need for each of these nesting levels (i.e. first run each nesting separately). If random effect variance comes out very small - discard the nesting level as it doesn't contribute anything.

Another recommendation would be for models that Mplus does not support such as say a cross classified three level model x two-level model x two-level model. You can use plausible values obtained from two or three level model separately. That way you can still parse out the contributions from each level.

Finally from the discussion above I think you are hinting towards interactions between random effects from different levels. In Mplus we have that capability in cross-classified models under the "random item" topic, see the user's manual.
 Julien Lemay posted on Monday, January 08, 2018 - 7:54 am
Thank you both. Your time and help is much appreciated.
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