Anonymous posted on Friday, September 20, 2002 - 10:56 am
The time scores (loadings) associated with a slole growth factor in LGM can be set as 0, 1, a3, ... aT (Muthen, et al., 2000), where the time score a1 is fixed at 0, defining the intercept growth factor as baseline initial status at t1; and the time scores for t3 and later time points are set to vary freely. However, the time score a2 is fixed at 1 for t2. I guess, this has something to do with parameter idenfication (if a2 were set free as are the loadings for t3, t4, ..., the model won't run). Can you explain the statistical rationale on this issue? In addition, if we set a3=0, while free a1 and other loadings, which loading should be set to 1? Thanks a lot for your help.
For identification purposes, one time score in addition to the zero time score for the intercept growth factor must be fixed to a non-zero value. This defines the metric of the slope factor as the change between the two fixed timepoints.
If you fix the time score for the third time point to 0, the time score you fix to a non-zero value can be any of the other time scores.
Wim Beyers posted on Monday, May 05, 2003 - 7:50 am
Suppose a classic latent growth function summarizing 3 repeated measures (with equally spaced time points) of an attribute, with a linear shape, and centered at the first measurement, so the interpretation of the intercept is the true (without measurement error)initial level of the attribute (at Time 1), and the slope refers to the linear change of the attribute across time. Now, I want to recenter my growth function at the second measurement (by changing the fixed loadings of the slope to -1, 0, 1). The meaning of the slope stays the same, but the meaning of the intercept now becomes the true score at Time 2. So far, so good. However, is it true that the more substantive interpretation of the intercept now is the true mean level of the attribute across time, or let's say, the overall or basic level? Of course, given the above mentioned restrictions of linear change and equally spaced time points? And, if yes, do you agree that recentering therefore is a good thing when you have three repeated measures in a time-structured format as mentioned?
Thanks for all comments and for your previous replies to my questions,
Sounds right given the time scores of -1, 0, 1. But it would seem to depend on the research question if this recentering is the most desirable. For instance, sometimes you want to predict the variation in the starting point, sometimes in the ending point.
Li Lin posted on Thursday, September 02, 2010 - 1:04 pm
Hi,I am trying to mimic the example 12.9 using Monte Carlo simulation for a two-part growth model. My purpose of doing this is to decide an adequate sample size for a longitudinal study. Data will be collected at baseline, 1 month, 6 months, and 12 months. The PIs anticipate a growth curve like down-up-accelerated up, for example: proportion of 1 in u = 1, .3, .5, .8; y equals to population mean at baseline, declines to mean-2sd at 1 month, then up to mean-1sd at 6 months, and then recover to mean at 12 months. I am thinking of using fixed time scores to specify the curve. My questions are: 1)what values I should give to the time scores for the above hypothesized change pattern? 2)do the time score sets need to be the same for u and y? Thanks!
Dear Prof.Muthen, I apply parallel process LGM for mediation analysis. I have 4 time points (baseline, 8 months (post treatment), 12 months (1st follow up, and 20 months (last follow-up)). I am trying to model the earlier change in the mediator (from baseline to post treatment) and its effect on the later change in the outcome (from post treatment to the end of the 2nd follow-up). I am not sure if i do correct time coding in my models. Is the coding showed below correct coding for it? MODEL: i1 s1| ssb0lt@0ssb1lt@1ssb2lt@0ssb3lt@0; i2 s2| bmi0@-1bmi1@firstname.lastname@example.org@1.5;
p.s.The models work fine with this coding and fit well.
For the outcome, actually I do not use only 2 time points as you mentioned in your message. I only change the intercept to the post treatment and reflect the change after post treatment; i2 s2| bmi0@-1bmi1@email@example.com@2.5;
When I apply my parallel process LGM (with 1000 bootstrapping), the model fits good and gives the slope variances (in my case residual variances since I have covariates in the model too). MODEL: i1 s1| ssb0lt@0ssb1lt@1ssb2lt@1ssb3lt@1; i2 s2| bmi0@-1bmi1@firstname.lastname@example.org@2.5; i1 s1 ON group gender ethnic; i2 s2 ON group gender ethnic; s2 ON i1 s1; s2 ON i2; s1 ON i2 i1; i1 WITH i2; group WITH gender ethnic; MODEL INDIRECT: s2 IND s1 group;
Is this method and coding right for PPLGM for mediation analysis? Thank you.
Thanks for the reply, was helpful indeed. According to the growth shape (acceleration, deceleration) of the variable that has a quadratic growth, i use transformation of time and model it. It is explained as an alternative way to deal with non-linear growth in the Applied Longitudinal Data Analyses book from Singer and Willett. An example of this coding was published by Ruehlman et al in Pain, 2012 Feb.