| Attachment | Size |
|---|---|
 SingleFactor24.R | 15.98 KB |
| SingleFactorCohortManifestFixed24.R | 15.99 KB |
| SingleFactorNoCohort24.R | 14.57 KB |
| SingleFactorCohortManifest24.R | 15.97 KB |
 CohortACE.csv | 1.48 KB |
Hi all,
I've been playing around with various ways to include a cohort covariate in a single-factor model. I've tried four approaches, three of which have pretty consistent results and the fourth, which is fairly different. I've attached the four scripts here, as well as a table of selected output (ACE estimates with CIs, factor loadings, and expected means for observed variables).
For all models, the factor is identified by fixing the variance to 1 and there are four observed drug use variables (AlcFreq, AlcQuant, CPD_TOB, and MJ_FREQ). Models are fit separately by sex and by zygosity (MZ males, MZ females, DZ males, DZ females). I have three intake cohorts, indexed by two dummy variables OC and YC.
The first script, SingleFactorNoCohort24.R evaluates a factor model for which cohort is not regressed out at any point.
The second script, SingleFactor24.R, evaluates a factor model for which the mean of the factor is fixed to 0 and cohort is regressed onto the factor.
The third script, SingleFactorCohortManifest24.R, evaluates a factor model for which cohort is regressed onto the manifest variables and the effect of cohort is freely estimated for each of the four variables.
The fourth script, SingleFactorCohortManifestFixed24.R, evaluates a factor model for which cohort is regressed onto the manifest variables and the effect of cohort is fixed to be the same across drugs.
The part of the output that I am finding confusing is how different the ACE estimates are for the SingleFactor24.R script where cohort is regressed on the factor compared to the other 3. The C effect is large (.62 for males, .68 for females) in this version, whereas none of the other 3 show much of a C effect (0-.09) and I am generally surprised when I see a C effect of that magnitude at that developmental point (~24 years old). There also seem to be some differences in the factor loadings.
Does anyone have any insight as to why the ACE estimates would be so different when cohort is regressed on the factor rather than on the manifest variables or not at all?
Thanks!
-Stephanie
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In your script SingleFactor24.R, why are you using the unstandardized loadings in the algebras for the expected covariances, but using the standardized loadings in the algebras for the expected means? Or, am I missing something?
That is a good catch.
I used the unstandardized loadings in the expected covariances because I think I have to, as standardized loadings are a function of the standard deviations of the manifest variables and the unstandardized factor loadings.
For the algebras for the expected means though, I am not sure why I chose standardized vs. unstandardized in this instance. I reviewed other models of mine where regressed factor means on cohort, and I've used unstandardized up to this point. The other instances where I've used unstandardized loadings in the expected means algebra have been in latent growth models where factor loadings were fixed to participant age at assessment using definition variables, so standardized loadings didn't make sense in that case. I am not sure why I switched to standardized in SingleFactor24.R, I don't have a good annotation in my script at that point unfortunately, lesson learned!
I reran SingleFactor24.R with the unstandardized loadings rather than the standardized in the algebras for the expected means to see what impact that has; there are some differences in estimate and model fit. Both versions of output are attached here. I don't know that I understand if one (standardized or not) is more appropriate than the other in the factor model case.
Thanks!
You need to use the unstandardized loadings in lines 212 and 225 of SingleFactor24.R . It makes no sense to use the standardized loadings there.