Test of equality for sibling correlations across groups mixed

[Daniel Graeber]

Dear all,

I am estimating sibling correlation using Stata's mixed command via REML for different groups. We are interested in whether differences between groups are significant or not. How do I perform such a test. Maybe a joint test and a pairwise test. Please also keep in mind that we also have singletons in our estimation samples This might be of interest, because in general, a sibling correlation is the ratio of two chi^2 distributed variables. If we would divide them with the degrees of freedom in the nominator and denominator, we would end up with a F-distributed random variable. However, the degree of freedom are different for the variance of the sibling component and the individual component, aren't they? So, it is not so straightforward to me.

Below, you find a MWE. Thank you very much for your help.

use auto, clear

xtile group = rep78, nq(3)



mixed length if group == 1 ||foreign:, reml
estat icc
mixed length if group == 2 ||foreign:, reml
estat icc
mixed length if group == 3 ||foreign:, reml
estat icc

e.g. test icc1 = icc2 = icc3

Best

Daniel

EDIT: Maybe it is more general if we write: sibling correlations are basically interclass correlations in the example above. Maybe someone may also change the title?

[Phil Bromiley]

Look at suest. Also, remember you can do such estimates in one estimation by using appropriate dummies and interactions. Then the tests are easy.

[Daniel Graeber]

Hi Phil,

I tried suest in Stata14 and 15 and it returned that mixed is not supported by suest. In general, I should also add that in my problem at hand, I perform the test across disjoint groups.

use auto, clear

xtile group = rep78, nq(3)



mixed length if group == 1 ||foreign:, reml
estat icc
estimates store icc1
mixed length if group == 2 ||foreign:, reml
estat icc
estimates store icc2
mixed length if group == 3 ||foreign:, reml
estimates store icc3


suest icc1 icc2 icc3

Thank you very much. Any help is highly appreciated.

[Leonardo Guizzetti]

Since these are independent groups, the testing procedure is a little easier, but you will need to construct the test manually. The -corrtesti- command would suffice to compare up to two independent correlations, but not more than that. This is discussed in another Statalist thread.

Having not done this myself, I found an excerpt from the teaching notes of Alan Pickering (doc link).

There is also a simple formula for this given by Kullback (1958, pp. 321). The information statistic in favour of the hypothesis (H₁) that the correlations (between variables 1 and 2) differ across m samples of subjects, relative to the hypothesis (H₂) that the correlations are equal in all the samples is given by the formula:

2I(H₁:H₂) = S_{i=1 to m} N_i log_e [(1 – {r₁₂}²)/( 1 – {r_i12}²)]

where r_i12 = the correlation between variables 1 and 2 in sample i
N_i = the number of subjects in sample i
r₁₂ = {S _{i=1 to m} (N_i * r_i12)}/N
N = S _{i=1 to m} N_i

2I(H₁:H₂) is distributed as c² with (m – 1) degrees of freedom.