Two identical genetic path coefficients but one is significant and the other isn't.

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Jane's picture
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Joined: 07/13/2014

Hi everyone,
I just ran a multiple group ACE multivariate analysis and I found that a certain standardized genetic path coefficient is identical in both groups, but one is significant (i.e. confidence interval does not include 0) and the other is not significant. In regular multiple regression, the significance of a path coefficient is determined by: path estimate being divided by the standard deviation of that estimate so I am guessing that the reason that one estimate is significant here has something to do with the different variance associated with each group? Am I close? If it has something to do with the variance, how do I test for it?
Thank you in advance for your insights on this,
Jane

mhunter's picture
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Joined: 07/31/2009
I'm definitely suspicious

I'm definitely suspicious that the parameters are identical. Do you mean 1.434 vs 1.433 (same for three digits)? Or 1.434987615678901 vs 1.434987615678902 (same for 15 digits)? My first bet is there's a typo that forces these parameters to be identical.

As to your actual question, it can happen that the confidence interval for one group might not span zero, but will in another group. Sample size alone could drive this. If one group has 200 people (e.g. identical twins) and the other has 10,000 (e.g. DZ twins) then I imagine your situation might be common. Regardless of sample size, one group might just be noisy than the other.

A nice strategy for testing is create several variations on a model: one where variances are equal, another where variances are free, a third where an additional hypothesis can be tested, etc. Then use mxCompare to do likelihood ratio tests that compare the models.

Jane's picture
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Joined: 07/13/2014
Hi Mike, You are absolutely

Hi Mike,
You are absolutely right that the parameters are NOT identical. Sorry, I meant to say when I rounded both the estimates to the second decimal place, they were identical.
I should have added that the sample sizes are very similar across the two groups: they differ by a total of 2 twin pairs.

I have one follow up question for you but before I ask, here's some additional information that may be useful:
I ran a genetic Cholesky with two latent variables: the genetic factor A1 goes to Latent Variable 1 and Latent Variable 2 while genetic factor A2 path goes to Latent Variable 2 only (after controlling for shared variance with A1). It's the standardized path between A2 and the Latent Variable 2 that is similar in magnitude across the two groups, yet one is significant (for males) and the other is not (for females).

I noticed that the total genetic variance for both of these two latent traits across the two groups differ such that there is overall less variance for these traits in the male group than in the female group. Could you please explain why a similar estimate would be significant in a group with less variance? Sorry, I am very new to this and I just want to have a more thorough understanding of my data and what these estimates really mean.
Thank you in advance for you help.
Jane

mhunter's picture
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Joined: 07/31/2009
Thanks for describing your

Thanks for describing your situation in more detail!

It sounds like you have a second-order Cholesky model: that is, you have several indicators that are produced by two factors. You then have the Cholesky model on the two factors. The two factors also exist in two groups, one for males and one for females.

I'm not immediately sure why one estimate is noticeably different from zero whereas the other is not. With that said, I have a possible "squint and it looks okay" explanation. Think of this in a regression context with A1 predicting L1 and L2, and A2 predicting L2. The regression coefficient of A2 predicting L2 depends on the variance of L2. Suppose the raw regression coefficients of L2 on A2 in group1 and group2 are about equal. If L2 has more variance in group1, then the "standardized" effect of L2 regressed on A2 is smaller in group1 (assuming the variance of A2 is constant across groups).

That's how it makes sense to me. Hopefully this helps you, too!