Cross-lagged effects inconsistent with cross-sectional covariances in ALT model

[Sara]

Hello,

I am estimating an Autoregressive Latent Trajectory (ALT) model in lavaan with three constructs (drug use, health, depression), measured across six time points (2000–2010). Drug use and health are ordinal (theta parameterization).

The results show a consistent pattern at the cross-sectional level:

• drug use ↔ positively correlated with depression,

• drug use ↔ negatively correlated with health,

• health ↔ negatively correlated with depression.

So far, so good.

In addition, the growth factors (intercepts and slopes) show significant covariances that confirm the same structure:

• intercept of drug use positively correlated with intercept of depression,

• intercept of drug use negatively correlated with intercept of health,

• intercept of health negatively correlated with intercept of depression,

• slopes of health and depression negatively correlated.

This suggests a clear and consistent underlying pattern among the constructs.

However, when I look at the cross-lagged regressions, the picture changes:

• Health sometimes predicts higher drug use at the next wave (e.g., health2002 → drug2004 = +0.152, p < .001).

• Depression almost never predicts drug use longitudinally, despite strong positive contemporaneous covariances.

• In one wave, better health even predicts higher depression two years later (health2002 → depression2004 = +0.015, p = .002)

I am wondering how this is possible and whether there is a methodological/statistical reason.

Also, since drug use is dichotomous, I had to remove the slope factor for drug because it led to identification problems (zero variance). Was this the correct decision in this context?

I attach below the main output from the model for reference.

Thank you very much for any insights!

[Jeremy Miles]

• Health sometimes predicts higher drug use at the next wave (e.g., health2002 → drug2004 = +0.152, p < .001).
  

That's not completely surprising to me but it seems like a theoretical problem, not a statistical one.  Health is predicting drug use, controlling for prior drug use - so you're not predicting drug use, you're predicting change in drug use. People who are in poorer health might reduce their drug use in a subsequent wave (or be forced to - perhaps they're unable to work and can't afford drugs any more, if these are recreational). 

• Depression almost never predicts drug use longitudinally, despite strong positive contemporaneous covariances
  

Again, not necessarily surprising, because you're predicting change. My depression right now might be associated with my drug use, which might mean next week or month, but depending on the stability of depression, it might not have any effect in two years.

• In one wave, better health even predicts higher depression two years later (health2002 → depression2004 = +0.015, p = .002)

Could this be some sort of suppressor effect? They are correlated negatively within wave. 

 * I had to remove the slope factor for drug because it led to identification problems (zero variance). Was this the correct decision in this context?

Yes. If there's no variance in the slope, it's OK to remove, usually. (In a multilevel model, having no variance is often the default and you might add it. In a SEM, you tend to start with free variance, and constrain it if necessary).

Jeremy  

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