Amery Wu posted on Monday, February 05, 2007 - 10:47 pm
Dear Dr. Muthen,
I am working on “Multiple indicator linear growth model for continuous outcomes”. The problem I have with the four waves of data was that the intervals between the four waves of data are unequal. The first wave (W1) was observed at time 0, the second wave (W2) was observed at six months later, the third wave (W3) was observed 10 years after the first wave, and the last wave (W4) was six months after the third wave. That is, there were two 6-month intervals at the two ends and one 10-year long-term interval in-between.
I was wondering if the free-time score still works for such big difference in the intervals between waves of observations? i.e., i s| w1@0w2@1 w3 w4
Also, I was wondering how I should actually code the “s” to be meaningful when the change from W1 to W2 is actually negative, should I code “s” for W2 as –1 (fixing the slope parameter for W2 at –1, instead of the typical unit increment of 1)? i.e., i s| w1@0w2@-1 w3 w4
I think this should be fine. My concern would be that measurement invariance might not hold across such a long time period.
It is not necessary to use negative time scores. If the development is a decrease, this is reflected in the sign of the slope.
Amery Wu posted on Wednesday, February 07, 2007 - 11:26 pm
Thanks for your reply.
You wrote: "It is not necessary to use negative time scores. If the development is a decrease, this is reflected in the sign of the slope."
I found that if I use positive time score for the second wave (1), the model did not converge after 1000 iterations.
What is interesting was that if I use a negative time score (-1), the same model did converge and the model fit was pretty good (RMSEA=0.044-0.046; SRMR=0.036). Also, the parameters estimates for the free time score were consistent with the observed trend.
I don't think you should use a negative time score. You should instead find out why the model does not converge with a positive time score. If you want help with that, please send your input, data, output, and license number to email@example.com.
I am also working on a growth model for a continuous variable with very unequal time intervals and I wonder how I should include this in the syntax. The time intervals are 6 months between time 0 and time 1, 4 months between time 1 and time 2, and thirty months between time 3 and time 4.
I also am working on a growth model for a continuous variable collected at unequal time intervals: baseline, then 1 year, 4 years, 10 years, and 20 years after baseline. Means and graphs suggest the "growth" pattern for this variable is downward, especially between 10 and 20 years,i.e. quadratic. Model will not converge when I ask for: i s q|x1@0,x2@1, x3@4, x4@10, x5@20 . It WILL converge when I use i s q| x1@0x2@.1x3@.firstname.lastname@example.org@2.0. However, I am now having trouble interpreting the output. How does this transformation of time affect the output?
In terms of reporting the results (i.e., construction of tables to communicate the model characteristics)do you think it is better to rescale the affected parameters to read "as if" they resulted from treating time as "whole years" (i.e., 0, 1, 4, 10, 20)[It looks like this can be accomplished through dividing linear parameters in the output by 10 and quadratic parameters by 100] or to leave them "as is", the parameter values that resulted from the rescaling of time to 0,.1, .4, 1, 2, then to clarify the meaning through written example in the results? I would like to be able to communicate to reader the findings in terms of "per 1 year of time, y on average increased __ amount." Do you have advice about which approach might be best for interpretation of and clearest communication about the behavior of my growth model? Do you have or can you point me to others' publications that discuss this issue?
Thank you very much for your time and patience in answering my questions.
I now understand above, with regard to the linear part of my unconditional growth model. However, I still do not understand how use of time as 0, .1, .4, 1, 2 affects interpretation of the quadratic component of the model. My unconditional growth model, modeling time as 0, .1, .4, 1.0 , 2.0 yields an estimated mean quadratic growth factor of. -.42. Can I interpret this to mean that my outcome changed ("accelerated downward") by -.004 annually(-.42 * .01 [.1 squared because of quadratic term]) OR that it accelerated downward by -.042 (mean quadratic growth factor * .1, following your example above) annually? Or does it not make sense to talk about "annually", because I am now trying to interpret curvature of the growth, not linear rate of growth?
The scale of the timescores does not change the interpretation of the model. The linear and quadratic growth factors are not independent which makes interpretation difficult. You can say is that the trend is upward or downward and significant or not. You may find the following article which is available on the website useful:
Muthén, B. & Muthén, L. (2000). The development of heavy drinking and alcohol-related problems from ages 18 to 37 in a U.S. national sample. Journal of Studies on Alcohol, 61, 290-300.
What does "sx|EBtime4 = 0.44" (which was freely estimated) actually mean?
Shouldn't the estimate for sx|EBwave4 have been larger as there are much more weeks between time3 and time4 in comparison to, for example, time2 and time3? Or does this estimate mean that the growth in EB decelarates from time 3 to time 4 ?
You said the first three measurements were six weeks apart and the the fourth one year later. The first time score is 0 if the centering is at time one, the second is 6 which is six weeks later, the third is 12 which is six weeks later and the fourth is 64 which is 52 weeks (one year) later. I divided by ten to keep them on a better scale.
Thank you for your prompt answer; my problem is solved.
However, I have another (more theoretical) question:
If one sets "EBtime4" in the growth model free by using an asterix, what does the estimate "sx|EBtime4" mean?
If, for example in my case (using your suggestions for the time points), sx|EBtime4 is freely estimated to .22, how should I interpret this estimate? Does this mean that the growth between timepoint 3 and time4 decelerates, and that there is no linear growth?
There seems to be an issue using negative IV scores in m plus. Let me explain briefly why I'd like to do so and perhaps you can tell me how to move forward with that plan or a better alternative.
I'm interested in growth prior to and following discharge from treatment, especially the possibility that treatment gains might be lost following discharge, as well as whether additional predictors might be associated with attenuation of this "relapse" effect. Because of this, I'd like to center time at discharge, and scale pre- and post- time points accordingly (-1 as 1 time point pre-discharge, -2 as 2 time points, pre- etc.)