difference between saturated model without constraints and with constraints (equality of mean and variance)

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pinki999's picture
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Joined: 01/17/2013

Hi,

I am trying to carry out heritability analysis with gene expression data.

After going through several tutorials and studies, I understood that a saturated model must be fitted for the data as a first step. The data must be tested for equal mean and variances by twin order and also by zygosity in subsequent steps. And all the three models must be compared to check if any differences exist between these models. The examples which I came across did not have significant differences between these models. So, my question is: What would be the appropriate way to proceed if there exists a significant difference between these models ?

Any response would be highly appreciated.

Thank you

neale's picture
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Joined: 07/31/2009
Try to understand why there is a difference

Obviously with many tests, the type I error rate may be high so one should probably not worry too much about the occasional p<.05. However, sometimes these tests fail badly and there are several possible reasons.

1. The data are non-normal. In my experience this is the most common reason for serious failure of the equal variances of twin 1 & twin 2.

2. MZ and DZ variances differ. This can indicate that twins have a mutual influence on each other, or in the case of ratings by their parents, the observers contrast the twins - possibly differently for MZ and DZ twins - and this creates differences in MZ and DZ variances. Sometimes mean differences can arise from these processes. There are papers on sibling contrast effects, which can be modeled.

3. You got unlucky. Outliers can cause pretty big differences when sample sizes are not large. Plot your data and see whether some outliers might be affecting the means and/or variances.

Good luck, and do let us know how you get on.