# Questions about biometric LGC

I'm performing biometric latent growth curve analysis with OpenMx and there a few open questions which I hope some of you might know the answer to. I have three cohorts of twins which are each surveyed three times and I am doing separate analysis of every cohort. Variation of age within cohort and wave (survey time point) is small, so I decided to feed waves into the model rather than ages (so the manifests are, phenotypes at t1, phenotype at t2 and phenotype at t3) which leads to my first question

1) I have two options: Controlling for time-invariant age at t1 and sex at t1 by using definition variables which point directly to intercept and slope. Or: including time-variant age (for t1, t2 and t3, i.e. age at measurement occasion instead of just t1). The second options does require the use of separate manifests (as covariates) which point directly to the measurement occasions (instead of pointing to intercept and slope) as definition variables do not allow for missing values (?) and later waves do have missing values due to attrition. Also: with the second options, would the wise choice still be to control for sex with the definition variable while time-variant age is controlled for a separate manifest? Or would it be wiser to integrate manifests for BOTH sex and age for each measurement occasion pointing to the manifests of the measurement ocassios and letting these manifests correlate freely?

2) I have read somewhere that fixing thresholds across time is the right way to go, is this true? I cant remember where I read it. I have four categories, therefore three threeholds, fixing the first ones to 0 and 1 and freely estimating the last one, but constraining it to be equal across time.

3) I have seen some papers who decompose the residual error variances and some who do not. I am not interested in the ACE estimates of the error variances, but I would still do it if there were some other upsides to it? Does the model get more power due to the additional covariances?

4) If I have two Slopes (linear and quadratic) in one model (and this actually is the best model), and decompose variances of both slopes, does this make sense? Because I have not found literature that actually did this. Is there any? Edit: it seems not to be possible with three waves, I.e. one random factor has to be fixed. I could, in theory do separate models, once estimating the random part of the linear factor and once the quadratic factor and decompose each variance separately. Does that make any sense?

Thank you very much in advance!

edit: by decompose variance, i mean decompose variance into A, C, E components