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Mplus Discussion > Multilevel Data/Complex Sample >
 Lucy Barnard posted on Sunday, October 07, 2007 - 6:28 am
In doing some multilevel modeling, my ICC appears to be quite low (barely .01). My thought is that it would be foolish to run a multilevel model with such a low ICC. To still acccount for this very slight effect of clusters, I was thinking I should run the analysis in TYPE=Complex as conceptually and by design there are in fact clusters. Please tell me if that's logical enough. :-)
 Linda K. Muthen posted on Sunday, October 07, 2007 - 8:45 am
It is not the size of the intraclass correlation alone that determines whether non-indpendence of observations needs to be accounted for. It is the design effect which is a function of the size of the intraclass correlation and average cluster size. TYPE=TWOLEVEL and TYPE=COMPLEX are two different ways to take non-independence of observations into account. With TWOLEVEL, non-independence of observations is modeled. With COMPLEX, it is taken into account. The choice depends on whether you want to know something about the cluster-level parameters or just control for non-independence of observations.
 Lucy Barnard posted on Sunday, October 07, 2007 - 4:03 pm
Thanks Linda!
 Matthew Cole posted on Monday, October 08, 2007 - 7:10 am
Hi Lucy,

I would also calculate the Design Effect which is based on the ICC and the average cluster size, where DEFF = 1 + (Average cluster size - 1)*ICC. If you find that DEFF >= 2, then you should address the clustering.
 Linda K. Muthen posted on Monday, October 08, 2007 - 6:00 pm
Note that this formula holds for means with equal cluster sizes. It is probably a decent approximation in other cases though.
 Lucy Morgan posted on Tuesday, February 03, 2015 - 3:44 am

I hope this hasn't been answered elsewhere (I did have a good search first!). My study was designed to be multilevel, measuring care assistant variables (Level 1) within nursing homes (manager variables - level 2). The ICCs for dependent variables are very low (.062 and .086), both DEFF values are < 2 and all manager (L2) variables are non-significant predictors so I have decided that multilevel analysis is not suitable. I have then run the analyses with TYPE = COMPLEX to account for the clustered data but this in fact makes the overall model fit worse. My questions are 1) am i correct to get rid of multilevel modelling given the low ICC AND low DEFF? And would it be better NOT using the TYPE = COMPLEX analysis since it makes model fit worse? (In another post you state that TYPE = COMPLEX is the right analysis to use with clustered data but in that instance the person posting found that model fit improved using TYPE = COMPLEX)

Many thanks for your help
 Bengt O. Muthen posted on Tuesday, February 03, 2015 - 8:22 am
I think you should use Type=Complex if you have at least 20 clusters.
 Lucy Morgan posted on Wednesday, February 04, 2015 - 1:27 am
Hi, thanks so much. I have 38 clusters so will go ahead with Type = complex analyses. And thanks so much for this forum and your speedy and helpful responses, this is an invaluable resource!
 Katarzyna Zebrak posted on Sunday, July 22, 2018 - 10:05 am
Hi, is there a citation for the need to address clustering when DEFF >=2 but ICCs are low? What about the reverse: high ICCs and low DEFF? Also, does non-independence mean that there is sufficient between group variation to say that the measure distinguishes among clusters?
 Bengt O. Muthen posted on Sunday, July 22, 2018 - 2:27 pm
Q1: Not that I know of.

Q2: With DEFF = V_C/V_SRS = 1+(s-1)*rho,
a high ICC (rho) and a low DEFF can happen for a low cluster size, say s = 2.

Q3: A high ICC says that the measure has a relatively large variation across clusters, so yes, that can perhaps be seen as distinguishing between clusters.

I think the important aspect is how different the SEs are when assuming independent clusters (Type=General) versus when allowing for cluster variation using Type=Twolevel or Type=Complex.
 Katarzyna Zebrak posted on Tuesday, July 24, 2018 - 6:27 am
Thanks so much, Dr. Muthen!
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