This is kyle. I am currently working on a longitudinal study consisting of three waves. The outcome is a continuous variable (Depression).
I tried to use growth curve model to explain the social factors of depression in later life. I added several time-varying covariates in the model. But I have difficulty in understanding the means of time-varying covariates.
My understandings is that stvc means the random slopes of time-varying covariates. Therefore, if the means of stvc are significant, the corresponding time-varying covariates have significant effects on the outcome variables over time.
May I ask did I interpret it correctly?
I also have difficulty in interpreting the following status: for example, stvc has significant means, but its relationships with intercept growth factor and slope growth factor are both insignificant. What does it mean? My understanding is that this stvc does not affect the growth trajectory of the outcome, but it has significant affects on the outcome variable in all 3 time points. May I ask your opinion?
Further, I add 6 time-varying covariates in the growth curve model. The means of some time-varying covariates became insignificant after I entered additional time-varying covariates. Does it mean that their effects on the outcome variable become insignificant after all other time-varying covariates are controlled for?
In the output, I got the intercept of stvc. I guess it is because that stvc is regressed on three time-invarying covariates (age, gender and education). Gender and education are binary variables. Age is centered at its grandmean. May I ask whether the intercept of stvc is its mean in this case?
Further, in your previous reply, you suggested that stvc can be significantly associated with the outcome variables but insignificantly relate to the intercept and slope growth factors. And it is because the relationship between the growth factors and the random slope mean is not significant. I have difficulty in interpreting random slope mean.
My understanding is that stvc includes individual differences in the association between time-varying covariates and outcome variables. Therefore, it is a random slope. The effects of the time-varying covariates are different across people. Even the same score of a time-varying covariates means differently for different people. Random slope mean is the average effects of the time-varying covariates on the outcome variables.
If the mean of stvc is significant and stvc is not significantly related to intercept and slope growth factors, it means only higher level or lower level of random slope can affect the initial status or growth trajectory of the outcome. May I ask whether I interpret it correctly?
No, a mean is not estimated in a conditional model. An intercept is estimated.
Your third paragraph is correct. Your fourth paragraph is not.
Yes, time-varying covariates can be binary.
Please limit your posts to one window.
Joe posted on Tuesday, February 03, 2015 - 1:57 pm
What is the equation for the estimated outcome mean at timepoint t with random slope for the time-varying covariates?
Would I add the estimated latent mean of the STVC to the formulas on slides 97-98 of Topic 3?
My model is below: i l q | MA_Rit08@0MA_Rit09@1MA_Rit10@2MA_Rit11@3MA_Rit12@4MA_Rit13@5; stCD | MA_Rit08 ON CD_08; stCD | MA_Rit09 ON CD_09; stCD | MA_Rit10 ON CD_10; stCD | MA_Rit11 ON CD_11; stCD | MA_Rit12 ON CD_12; stCD | MA_Rit13 ON CD_13; stED | MA_Rit08 ON ED_08; stED | MA_Rit09 ON ED_09; stED | MA_Rit10 ON ED_10; stED | MA_Rit11 ON ED_11; stED | MA_Rit12 ON ED_12; stED | MA_Rit13 ON ED_13; stOHI | MA_Rit08 ON OHI_08; stOHI | MA_Rit09 ON OHI_09; stOHI | MA_Rit10 ON OHI_10; stOHI | MA_Rit11 ON OHI_11; stOHI | MA_Rit12 ON OHI_12; stOHI | MA_Rit13 ON OHI_13;
You add the estimated mean of the random slope times the value of the tvc that you consider - either a specific value or its mean.
C. Lechner posted on Friday, April 01, 2016 - 10:57 am
Suppose I have a three-wave panel model with a random effect for a binary time-varying covariate x. Effects of x vary by a time-invariant covariate z, which is also binary (coded 0-1):
stvc | y1 ON x1; stvc | y2 ON x2; stvc | y3 ON x3; stvc ON z;
To compute the conditional effects of x on y for the two levels of z, I add:
[stvc] (z0); stvc on z (z1)
Model constraint: new (ref treat); ref = z0; treat = z0+z1;
Do the new parameters "ref" and "treat"... a) give the correct point estimates for the effect of x on y for z=0 ("ref") and z=1 ("treat")? b) provide correct significance tests for the conditional effects of x on y for z=0 and z=1, respectively? c) To what extent are these estimates likely to differ from "classical" interaction terms x1z, x2z, x3z created in the DEFINE command?
c) Similar results but the stvc approach allows for a residual in the regression on z and this means
- standard approach may get too large SEs
- the stvc approach allows for heteroscedastic residual variances in the regression on x1 -x3.
C. Lechner posted on Wednesday, April 06, 2016 - 5:43 am
Thank you, Bengt, very helpful. Two specific and a more general follow-up question:
a) So the stvc approach has higher power to detect potential interactions than the standard approach (using manifest product terms or the LMS approach via XWITH)?
b) When predicting stvc (x-->y) from several predictors (z1, z2, z3), one may run into convergence problems if a binary x has a lot of empty cells for a combination of the predictors z1, z2, z3. Correct?
c) On a more general note, in which cases would you advocate using the standard or LMS approach to testing interactions vs. random slopes. Are there any rules of thumb?
Can you give a citation for using the random slope time-varying covariate (stvc in your examples)?
Also, I have been looking carefully for such a reference on your list of references and I found an error. The following paper has the wrong page numbers listed (which gets you to the wrong issue). This is the correct citation:
McArdle, J. J., Hamagami, F., Chang, J. Y., & Hishinuma, E. S. (2014). Longitudinal dynamic analyses of depression and academic achievement in the Hawaiian High Schools Health Survey using contemporary latent variable change models. Structural Equation Modeling: A Multidisciplinary Journal, 21(4), 608-629. doi:10.1080/10705511.2014.919824