G. David Garson in his book Hierarchical Linear Modeling (2003) p. 64. asserts,
"The fact that the intercept component is significant means that the intraclass correlation coefficient, ICC, is also significant..."
I'm actually interested in the converse -- I have a non-significant intercept component in a null model and want to conclude that the ICC is not statistically significant -- but a referee has questioned that reasoning. Garson gives no justification or citation to support the assertion.
Dear Professor,
I think it's easy when we see the ICC estimators by using the ANOVA decomposition, (so your intercept here represente the mean of your observation), so the ICC estimator is the ratio between the unobserved random effect variance and the sum of the unobserved random effect variance and the unobserved noise variance.
This represents significant between-level variation.
Hope this helps
Matt
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