Trouble fitting CFA at both levels in multilevel data

[rjrich...@gmail.com]

I'm trying to fit a CFA in a multilevel data situation where the construct of interest at both the within and between levels. However, I'm having convergence issues when I assess the latent construct at both the within and between levels. 

When assessing the construct at the between level (and adding a x1 and x2 association at the within level to avoid an error message), I have no issues:

m1 <- '

level: 1

x1 ~ x2

level: 2

fb  =~ item1 + item2 + item3 + item4

'

fit1 <-cfa(m1, data=data1,cluster = "group")

summary(fit1, fit.measures=TRUE)

Similarly, there is no trouble when assessing the construct at the within level:

m2 <- '

level: 1

fw  =~ item1 + item2 + item3 + item4

level: 2

x1 ~ x2

'

fit2 <- cfa(m2, data=data1,cluster = "group")

summary(fit2, fit.measures=TRUE)

However, I cannot get convergence when assessing the construct at both levels:

m3 <- '

level: 1

fw  =~ item1 + item2 + item3 + item4

level: 2

fb  =~ item1 + item2 + item3 + item4

'

fit3 <- cfa(m3, data=data1,cluster = "group")

summary(fit3, fit.measures=TRUE)

Does anyone have any ideas for why I might be encountering this issue? I've attached the data in case it's helpful for addressing my query. 

[Richard]

So after doing some additional analyses, it seems like part of the problem might be that the variation between clusters is extremely small (e.g., ICC = .01). Going off the info on the lavaan multilevel SEM page, this seems like a likely candidate for why I'm not getting convergence. So while I'm eventually interested in testing predictors measured at the cluster level, does anyone know if it's acceptable to ignore clustering since the ICCs are so low? In other words, not do multilevel SEM and just treat all variables like they are measured at level 1?

Thanks for any advice.

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[Edward Rigdon]

     That is exactly what is indicated--ignoring the clustering. With ICC as small as .05, custering may have notable impact on results, but with ICC much lower than .05, multilevel analysis fails. Still, you don't want to forget the clustering--when you conduct diagnostics at the end, remember to examine the behavior of clusters, just in case there are nonlinear effects that ICC does not pick up. But this is really a question for the multilevel list:

http://www.bristol.ac.uk/cmm/learning/support/jisc.html