Growth factor intercepts vs means PreviousNext
Mplus Discussion > Growth Modeling of Longitudinal Data >
 Cameron McPhee posted on Tuesday, October 24, 2006 - 8:16 am

I have run a growth model where the growth factors have been regressed on a set of covariates. I know that when this is done the parameters that are estimated for the growth factors are intercepts, residuals, etc. This, I know, is different from the means and covariances given in TECH4. My questions, however, are the following:
1. If I want to present and estimated mean intercept and slope should I use what is given in TECH4 or in the model output?
2. Can you clarify for me what the "intercept" number is?
3. I am pretty sure that what is being plotted when I look at the estimated means plot is the TECH4 information. Is this still adjusted for covariates?

 Linda K. Muthen posted on Tuesday, October 24, 2006 - 11:39 am
1. If you want to report the mean of the intercept and slope growth factors, you would need to get that from TECH4 because means are not estimated when the growth factors are regressed on covariates.
2. The intercept is the same as in regression. Think of y = a + bx. The intercept is a.
3. The plots are based on residual output not TECH4.
 Cameron McPhee posted on Tuesday, October 24, 2006 - 12:02 pm
Thanks, I think for my question 2. I was not totally clear. I guess I meant that I was wondering how I interpret the estimated growth factors that show up under "Intercepts" in the output?
 kristin denton flanagan posted on Wednesday, October 25, 2006 - 6:19 am
What is a little confusing is that we have presented information in our table that seems to contradict what is being graphed.

Literally, we tabled the coefficients from the M-Plus output that appear right under the model fit information right below "MODEL RESULTS". However, the Beta value "B"(I think this is the right word) associated with the intercept is 29.484. We visualized this to be basically, where achievement point 1 crosses the x-axis.

However, the information on "ESTIMATED SAMPLE STATISTICS" lists... (these are all, what we perceive to be mean scale scores, on the same scale that we administered across 5 different time points)

Achievement, time 1, 23.628
Achievement, time 2, 34.429
Achievement, time 3, 60.139
Achievement, time 4, 95.014
Achievement, time 5, 115.825

Are we thinking about this incorrectly?
That is, should the Beta associated with the intercept correspond to the Achievement, time 1 estimate (29.484 does not equal 23.638).

Sorry, if this is silly. I am newer to M-Plus than Cameron.
 Linda K. Muthen posted on Wednesday, October 25, 2006 - 7:51 am
I'm unclear about what you are descibing in the results section. What is being graphed is the information you will find if you ask for RESIDUAL in the OUTPUT command. Do that and see if it matches. If you have further questions, you should send your input, data, output, and license number to Include the table you have made.
 kristin denton flanagan posted on Wednesday, October 25, 2006 - 9:05 am
Thanks so much.

In terms of presenting a graphic of children's growth curves, it would seem that M-plus plots the unadjusted mean achievement score for any time point. That is, the points on the plot we produced match the mean achievement score for any point in time, unadjusted for the covariates in the growth model.

The growth factors in our growth model (i.e., children's achievement at 5 time points) are regressed on a set of covariates (e.g., sex, race/ethnicity, household income). If we wanted to present a picture of the average growth curve, will M-plus produce this using the adjusted means?

Would this be appropriate?

Or is the curve with the means (unadjusted for the covariates in the model) the appropriate picture/graph of the curve to present?

Again, thank you for your time.
 Linda K. Muthen posted on Wednesday, October 25, 2006 - 10:41 am
If you look under the plot menu, you will find sample and estimated means. These are unadjusted. You will also find adjusted means.
 Sylvana Robbers posted on Monday, June 02, 2008 - 7:46 am

I have 2 categorical time-invariant covariates in my growth model (SES scored as 1-2-3 and gender scored as 1-2). I am doing two-group analysis (twins versus singletons) and I would like to report that my observed group differences in i and s are not due to any of the covariates. My questions are:

1. When I make a plot with 'estimated means', are the graphs then corrected for the influence of the covariates?

2. I read that the values of i and s under the heading Intercepts correspond with the predicted value when the covariates are both zero (please correct me if I'm wrong). But my covariates do not have values of zero, so how do I interpret these intercepts?

3. I would like to report mean intercepts and slopes that are adjusted for the influence of the covariates. Where can I find these values?

4. When I do chi-square difference testing of the growth factors between the two groups, is this difference then also corrected for the influence of covariates?

Thanks in advance for your time.

 Sylvana Robbers posted on Tuesday, June 03, 2008 - 3:44 am
A following question to the second post of this threat:
The value of my first y-variable in the residual output is the same as the estimated mean intercept in TECH4. So what is the difference between residual output and tech4? If I understand all preceding posts correctly, these values are uncorrected for covariates.
If I use adjusted means in the plot menu, should I then use the sample means as values for the covariates?

 Linda K. Muthen posted on Tuesday, June 03, 2008 - 10:42 am
You should recode your binary covariate to have values of zero and one. You can also center the continuous covariate. Then the intercept of the intercept growth factor in the growth model is the mean of the growth factors for observations with gender equal to zero.

1. No.
2. Recode and center you covariates.
3. Under intercepts.
4. If the covariates are in the model, then they are controlled for.

The mean of y1 is equal to the intercept of the intercept growth factor when the time score is equal to zero.
 Rachel Ellis posted on Tuesday, September 17, 2013 - 6:37 pm
Hi, I have a related question -

I've graphed the estimated means of depression scores for a growth mixture model with four classes. The graph seems to reflect the means in the RESIDUAL output.

Out of interest, I duplicated the depression scores and treated them as auxiliary variables using DCON, to test for mean differences between the groups at each timepoint.

The means given in the DCON test output are different to those in the RESIDUAL output. For example, the mean score of group 1 at time 1 in the residual output was 38.982, but in the DCON output it was 33.841. There was no missing data at time 1.

Is this because DCON takes the uncertainty in class membership into account? Does the graph not do that?

 Bengt O. Muthen posted on Wednesday, September 18, 2013 - 11:22 am
The DCON approach assumes that the auxiliary variable is independent of the latent class indicators conditional on the latent class variable. So no direct relationships. In your case there are clearly direct relationships since your auxiliary is the same as one of the indicators.
 Rachel Ellis posted on Saturday, September 21, 2013 - 7:28 pm
Thanks for your reply Bengt. Does the same apply to the DU3STEP approach? i.e., does the DU3STEP approach also assume that the auxiliary variable is independent of the latent class indicators?
 Linda K. Muthen posted on Monday, September 23, 2013 - 2:18 pm
Yes. See Web Note 15.
 Hsien-Yuan Hsu posted on Sunday, May 03, 2015 - 10:07 am
Hi, Dr. Muthen,

Similar to your ex9.12. I specify a TWO-LEVEL GROWTH MODEL FOR A CONTINUOUS OUTCOME without covariate X and W. I can get the estimated means of intercept and slope in the between-model but "cannot" get the estimated means of intercept and slope in the within-model unless I put Tech4 in the model output. Can you provide more information why Mplus does not directly report means of intercept and slope in the within-model? Thanks.
 Bengt O. Muthen posted on Sunday, May 03, 2015 - 12:37 pm
There is only one set of means for the growth factors - you can't identify them on both levels. See the "gamma" coefficients of "three-level growth modeling" in our Topic 8 short course handout, slide 58.
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