Dear Forum,

I am trying to fit a longitudinal Cholesky model (two variables in two time-points) with the umxACE and umxModify commands from the umx package.

Looking at the raw correlations and univariate models, it seems like a DE model is the one that fits most of my variables. However, I saw in this discussion: https://openmx.ssri.psu.edu/thread/4201 and in this discussion: https://openmx.ssri.psu.edu/thread/4047 that it is wrong to do a DE model without considering the A of the variables, and that in relatively small sample sizes (as in my case) lack of A may simply mean lack of power to detect A.

My question is- how should I approach the fitting process (i.e., the process of dropping paths to check their significance)? If I drop only one path at a time- none of the paths are significant, and I think it is because each time the model has another path to which it can allocate the variance. But If I drop all, I have a model that doesn't have A in it.

Is there a systematic way to drop paths? Also, should I drop several paths at once, or drop them one by one? As mentioned, the latter option results in a model with no A (a practice that is not advised), and that doesn't fit the raw correlations in terms of heritability estimates.

I attach the raw correlations in case that it will help.

```
rMZ rDZ
```

var1_time1 0.29 (0.09) 0.04 (0.05)

var2_time1 0.39 (0.08) 0.17 (0.05)

var1_time2 0.37 (0.1) -0.01 (0.06)

var2_time2 0.38 (0.1) 0.01 (0.06)

Thank you very much,

Lior

umx tip: For a univariate ACE model, umxReduce() will give you a nice table of various models of your data and rate the likelihood of each among the choices.

In general, dropping big blocks of paths (like the lower triangle of C) can mask 1 factor being significant factor. My systematic pre-registered approach is drop all but 1 factor, then drop that.

You've only got a couple of paths to drop, if I read you right (2 vars at 2 times?)

If A and D fit as well, drop D. A can cope, and unless your model has one underlying major gene (say, eye color), it's unlikely to have zero A.

If you can drop either A or D (or C) but not both, then report this, and note that future studies should have more twins.

Build your preferred model. The best approach by far IMHO, is to have a pre-determined expected model: Do you expect that all the variance across time is carried by A: build that model and compare it to the base model. So maybe "these traits share no genes, and the same genes operate at both times, and neither C nor E explains any of the correlation between the two times"

Does that help?

Thank you for the fast and helpful answer!

Yes, it indeed clarified some important points, and I would like to ask two follow-up questions:

1) "My systematic pre-registered approach is drop all but 1 factor, then drop that."

Q: Could you explain what do you mean by that? Do you mean, for example, to drop all D, and then to examine the paths of A one by one? or, do you mean to drop all the paths that relate to one variable except for one (e.g., the three unique A paths that relate to var1 at time 2 but not the first A that is common to all vars), and then drop that one?

2) "If you can drop either A or D (or C) but not both, then report this, and note that future studies should have more twins."

Q: This is indeed my case. But, if I drop all As or all Ds, then I don't check the possibility that some vars have only A and some vars have both A and D (I admit I didn't have a strong theory to begin with regarding that possibility, but I am starting to think that this is the case). Should I check such possibilities? and, considering that there are many combinations (even with only four vars) should I check only the "pre-determined expected" possibilities (as you suggested in the last paragraph)?

Thanks again,

Lior