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 Jan Fax posted on Saturday, December 27, 2008 - 2:58 am
Another question:

I encountered that the ICC's for some single indicators are quite low (.02).
However, when I summarize these single indicators to an index variable, the ICC for this index is substantively larger (.06).
A. Is this an artefact?

B. Or could this simply reflect the fact that the summative measures is less prone to measurement error?
 Linda K. Muthen posted on Sunday, December 28, 2008 - 4:51 pm
A. No.

B. Yes. Measurement error is in the denominator of the ICC. It is larger for a single item that the sum of a set of items. This results in a larger denominator for a single item resulting in a smaller ICC.
 Student 09 posted on Monday, December 29, 2008 - 1:35 am
Dear Linda

many thanks. May I ask a follow-up question:

When computing within- and between-group correlation coefficients of the single indicators (type = twolevel basic), I find that the size of the between-group correlations coefficients is modest (.3 to .5), but the coefficients never reach conventional levels of significance.

Question 1: Could (literally; I fear there is no definite answer to this question)the lack of significance also be due to measurement error of the single indicators?

Question 2: Does anybody in the Mplus forum know any published work on the impact of measurement error on ICC and perhaps between-group correlations?

 Bengt O. Muthen posted on Monday, December 29, 2008 - 10:31 am
Q1. No, measurement error usually adds to the within-level variance, not the between-level variance.

Q2. See

Muthén (1991). Multilevel factor analysis of class and student achievement components. Journal of Educational Measurement, 28,
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