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I'm running a multivariate growth model with two variables measured across 3 waves using lavaan/growth function.

Here's the model specification I'm using, with non-uniform time differences. Two variables here are "cyn" and "cms".

model.cms.cynic <- " icyn =~ 1*T1_Cynic + 1*T2_Cynic + 1*T3_Cynic
                     scyn=~ 0*T1_Cynic + 1*T2_Cynic + 5.8*T3_Cynic

                     icms =~ 1*T1_CMS + 1*T2_CMS + 1*T3_CMS
                     scms =~ 0*T1_CMS + 1*T2_CMS + 5.8*T3_CMS

                     scyn ~ icms
                     scms ~ icyn"

I was interested in looking at 1) associations between the two intercepts, 2) associations between the two slopes, and 3) whether an intercept for one variable predicts the slope of another variable.

My first question is whether the last two lines of my code adequately test my third research question.

My second question pertains to the results I got for the third question in tandem with the associations I found for the first two questions.

The results showed that the intercept of cms ("icms") negatively predicted the slope of cyn ("scyn"). That said, because I also observed that icms and icyn were positively associated, I'm not sure whether predicting scyn from the icyn needs to also control for the intercept of cms (icms), since

  1. higher icms predicted higher icyn,
  2. higher icyn would restrict the growth of cyn (=scyn) due to ceiling effect, which would
  3. contribute to the observed negative coefficient of icms predicting scyn (which could be considered as an artifact).

That is, I'm not sure whether I SHOULD specify the last two lines as follows:

                     scyn ~ icms + icyn
                     scms ~ icyn + icms

Is this reasoning correct, or unfounded? Does the growth curve model (based on my specification) take that ceiling effect into account already?

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Two points, which are sort of tangential.

  • Why are you using 5.8? Do you have a strong reason for that value, or could you let the slope be non-linear by freeing that estimate?

  • Regressing slope on intercept (or intercept on intercept, or slope on slope) is a bit weird. Intercept is indicated by three time points - including the final one. Slope is indicated by three time points, including the first one. When you regress slope on intercept you are saying that time 3 (intercept) has a predictive effect on time 1 (slope), but time 3 happened after time 1, so this requires an effect which goes backwards in time. For this reason, it is much more common to correlate slopes and intercepts.

If you use the second approach,

scyn ~ icms + icyn
scms ~ icyn + icms

Your structural model is saturated anyway.

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  • $\begingroup$ Thank you for your comments. I'm using 5.8 instead of a more conventional value of 2 because the time differences for time1/time2 and time2/time3 are significantly different. $\endgroup$
    – Simonet
    Commented Mar 23, 2023 at 17:06
  • $\begingroup$ About your comments about regressing slopes to intercepts; then if I'd like to know whether a slope for one variable can be predicted by an intercept of another variable, it would conceptually be more sound to just let the two covary (e.g., scyn ~~ icms)? Also thank you for the heads up about saturation. $\endgroup$
    – Simonet
    Commented Mar 23, 2023 at 17:08
  • $\begingroup$ You can free 5.8 and let it be estimated, that fits a non-linear effect. Unless you have a strong a priori reason to pick 5.8. Yes, covarying works. $\endgroup$
    – Jeremy Miles
    Commented Mar 24, 2023 at 1:38

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