when it is 'necessary' to use multilevel models?

[sabahatbagci]

Hi,
I have a data collected from 9 schools (37 classrooms) and look at cross and same-ethnic friendships across different ethnic groups (5 group) and ethnic diversity (3 groups as low, moderate and high). I have seen in previous studies that I can use both multivariate ANOVA and multilevel modelling. I ran multilevel modelling in SPSS for an unconditional model and it gave me a significant classroom effect, but only explained around 4% of the variance in friendships. Would you still suggest using it, or go with multivariate anovas?

[noetsi]

I don't think it is neccessary to use almost any statistic if by that you mean mandatory If data is nested inside some factor regression (and I assume ANOVA which is a specialized form of regression) will generate incorrect results because two of the assumptions, homogenity of variance and independence of observations, won't be correct. For example, individuals inside a given schools will be systematically different than those outside it. For that the weighted least squares employed by multi-level methods is required (this assumes there is nesting which may or may not be true). From a practical perspective, explaining the variation by school or other parameter is highly useful as well. That is the random effects.

I am not sure what you mean by multivariate ANOVA (most ANOVA is multivariate if by that you mean two or more IV) but as far as I know all ANOVA requires equality of variance and indepenence of observation (well the later is not true in within subject ANOVA, but it does not seem like you are describing that).

[EliteResearch]

I would definitely use MLM with that kind of data setup. The variance accounted for is probably your intraclass correlation coefficient (ICC).

[Note: “An intraclass correlation tells you about the correlation of the observations (cases) within a cluster" [like classroom or school] (http://www.ats.ucla.edu/stat/Stata/Library/cpsu.htm)
"If the interclass correlation (IC) approaches 0 then the grouping by [a Level 2 variable is] of no use (you may as well run a
simple regression). If the IC approaches 1 then there is no variance to explain at the individual level, everybody is the same." [so your differences are between Level 2 variables] (http://dss.princeton.edu/training/Multilevel101.pdf) ]

True, 4% is kind of low, but you need to test it for significance before ruling out MLM.

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