Very unequal time intervals
Message/Author
 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@0 w2@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@0 w2@-1 w3 w4

Amery
 Linda K. Muthen posted on Wednesday, February 07, 2007 - 7:55 am
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
Dr. Muthen,

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.

Amery
 Linda K. Muthen posted on Thursday, February 08, 2007 - 7:44 am
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 support@statmodel.com.
 Sofia Diamantopoulou posted on Monday, May 18, 2009 - 6:26 am
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.

Is the following correct?

i s | w0@0 w1@1 w2@1.6 w3@6;

 Linda K. Muthen posted on Monday, May 18, 2009 - 9:16 am
I think your last time score should be 6.4. The way I would specify it is

0 .6 1 4

taken from

0 6 10 40

which represent the months.
 Penny Brennan posted on Saturday, April 03, 2010 - 1:53 pm
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@0 x2@.1 x3@.4 x4@1.0 x5@2.0. However, I am now having trouble interpreting the output. How does this transformation of time affect the output?
 Linda K. Muthen posted on Sunday, April 04, 2010 - 8:33 am
The overall results will be the same. The scale of some parameters will be different.
 Penny Brennan posted on Sunday, April 04, 2010 - 11:07 am
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?
 Linda K. Muthen posted on Monday, April 05, 2010 - 8:31 am
The change in the slope growth factor for one year is the mean of the slope growth factor times the time score. See below for the time scores .1 and 1:

.1 * 5 = .5
1 * .5 = .5

where 5 and .5 are the means of the slope growth factor.

So the change is the same. It does not depend on the scale of the time score.
 Penny Brennan posted on Wednesday, April 21, 2010 - 1:55 pm
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?

Thanks again for your time & patience.
 Linda K. Muthen posted on Thursday, April 22, 2010 - 8:59 am
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.
 Penny Brennan posted on Thursday, April 22, 2010 - 10:02 am
Thank you!
 Caroline Vancraeyveldt posted on Wednesday, November 07, 2012 - 9:15 am
Dear Dr. Muthen,

I have a similar question as Penny. I am estimating a latent growth model in order to compare the growth in externalizing behavior (EB) in an intervention and a control condition.

The first three time moments are 6 weeks apart, the fourth time moment (= a follow-up measurement) is approximately one year later than the third time moment

I used the following syntax to describe the effect of the intervention on the latent growth of externalizing behavior (ix = intercept, sx = slope)

ix sx / EBtime1@0 EBtime2@1 EBtime3@2 EBtime4* ;
ix ON intervention;
sx on intervention;

First of all: is this syntax correct? (especially EBtime4*?)

When I looked at the output, I saw the following extimates

sx|EBtime1 = 0
sx|EBtime2 = 1
sx|EBtime3 = 2
sx|EBtime4 = 0.44

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 ?

Thank you very much in advance
 Linda K. Muthen posted on Wednesday, November 07, 2012 - 12:10 pm
I think you have a problem in your growth model statement. You have a slash (/) instead of a bar (|). I think this is causing the MODEL command to be misread.

If you want to specify a linear model, the time scores would be:

0 .6 1.2 6.4
 Caroline Vancraeyveldt posted on Thursday, November 08, 2012 - 12:53 am
Dear Dr. Muthen,

I mistyped, but I have indeed used a "slash". It is not quite clear why the time scores should be 0 .6 1.2 6.4 ?

And how should I interpret sx|EBtime = .44 in the case I freely estimate the last time moment?

 Linda K. Muthen posted on Thursday, November 08, 2012 - 6:15 am
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.

 Caroline Vancraeyveldt posted on Thursday, November 08, 2012 - 8:06 am
Dear Dr. Muthén,

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?

Thank you!
 Linda K. Muthen posted on Thursday, November 08, 2012 - 2:13 pm
This corresponds to a downturn between times 3 and 4 in the outcome mean.
 Mason G Haber posted on Monday, October 21, 2013 - 9:43 am
Dear Dr. Muthen

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.)

What would you suggest?
 Linda K. Muthen posted on Monday, October 21, 2013 - 3:04 pm
There is no issue that I know of with using negative time scores in Mplus. What is the issue? You can center at any time point.