Growth modeling with factor scores? PreviousNext
Mplus Discussion > Growth Modeling of Longitudinal Data >
 Jungmeen Kim posted on Monday, December 19, 2005 - 12:09 pm
I have used growth curve modeling based on raw scores. I wonder if I can somehow incorporate multiple scores by multiple reporters on the same construct. Using standardized scores at each measurement wouldn't make sense. What would be the best way, if any, that I can look at the growth curves of the scores that "combine" multiple reporters? May I use factor scores based on confirmatory factor analyses at each occasion? Thanks very much!

Jungmeen at Virginia Tech
 Linda K. Muthen posted on Monday, December 19, 2005 - 1:17 pm
See if Example 6.14 helps you.
 Researcher posted on Tuesday, December 20, 2005 - 7:32 am

My model is like the one in Example 6.14. Is it okay to let the residuals of the factor indicators to correlate (=three factor indicators, two indicators/
factor)? Otherwise the RMSEA estimate is too large.

Also, why the growth curve examples in the manual are described in terms of random effects of the factor indicators? I see many researchers using the program by defining intercept and trend factors with the usual "BY" command.

Thank you!
 bmuthen posted on Tuesday, December 20, 2005 - 8:18 am
Yes, if the residual correlations for the factor indicators make substantive sense.

The term random effects is used by statisticians for what behavioral scientists now tend to call growth factors - same thing. You can use the BY statement or the newer growth language using the bar ( | ) statement.
 Jungmeen Kim posted on Tuesday, December 20, 2005 - 3:38 pm
Dear Linda and Bengt,

It's awesome to know that I can use Mplus to test a "multiple indicator growth model" that looks like a second order factor analysis model. Thanks for your helpful answers and guidance. Merry Christmas!!
 Linda K. Muthen posted on Tuesday, December 20, 2005 - 5:04 pm
I'm glad you think it is awesome but it has been available since 1998 when Mplus first came out.

Merry Christmas to you too.
 Alexis Brieant posted on Friday, October 27, 2017 - 1:43 pm
I would like to use factor scores from CFA in a growth curve model (I do not have enough power for a multiple indicator growth curve model). Is there a way that I can use the mean and SD from the first measurement occasion for the repeated measures so that they represent changes in SD units across occasions?

 Bengt O. Muthen posted on Friday, October 27, 2017 - 4:41 pm
I think instead you want to impose measurement invariance over time in your CFA so that you get the scores in comparable metric. You may also want to seek the opinion of SEMNET.
 Madison Aitken posted on Tuesday, November 27, 2018 - 6:48 pm
Dear Drs. Muthen,

I would like to use saved factor scores from CFAs across several time points in a growth model. Are the saved factor scores standardized within the sample and, if so, would this affect my ability to detect change over time?

Thank you in advance for any input you can provide.
 Bengt O. Muthen posted on Wednesday, November 28, 2018 - 4:59 pm
They are not standardized. But if you don't have too many factor indicators, why not do the growth analysis on the factors in 1 step?
 Madison Aitken posted on Friday, November 30, 2018 - 7:13 am
Hi Dr. Muthen,

Thank you for your response. I have a few follow-up questions:

Perhaps standardized is not the correct term, but are the factor scores calculated in reference to others in the sample (i.e., indicate position within the sample, rather than a raw score)?

Re: doing the analysis in 1 step, I have 36 factor indicators. Would estimating all of the latent factors across time and using the resulting latent variables in the growth analysis in a single input file overcome issues caused by using saved factor scores in a growth model?

Thank you again for your help!
 Bengt O. Muthen posted on Friday, November 30, 2018 - 4:43 pm
Q1: No, they are raw.

Q2: With 36 indicators in a one-step analysis it would be time-consuming to analyze more than say 2 time points.
 J.D. Haltigan posted on Friday, November 30, 2018 - 5:32 pm

If CFA model is identified by fixing variance of factors to 1 and then you save factor scores, how are they not standardized? I ask as well given reports in the literature (e.g., Wade et al., JAMA PSY, 2018) where saved factor scores are used to model growth traj and in those processes the growth appears to be tracked by the variation around a mean of zero (within group) but it is less clear how one would compare means between groups if mean slope is zero to begin with.
 Bengt O. Muthen posted on Saturday, December 01, 2018 - 10:28 am
The factor scores are not standardized in the sense that after they are computed they are standardized; they are not. I agree with your implication that it is improper to do CFA at each of several occasions, then computing factor scores, and then using those factor scores to do growth modeling. You need measurement invariance over time for that, allowing the factor means and variances to vary across time as they are expected to do in a growth model.
 J.D. Haltigan posted on Sunday, December 09, 2018 - 6:04 pm
Bengt: a follow-up.

A) If one does growth modeling with factor scores (assuming MI for the moment), the growth would be at the interindividual level (between) and one could predict deviation from this if the i and s factor variances are significant. Here b/c wide, one could first test for MI and then model the growth.

On the other hand, with multilevel CFA, one could truly look at intraindivudal change (within) with the drawback being that MI is 'assumed' for all intents and purposes.

Would the above be an accurate take?

B)Would it make a difference to the growth part if (after establishing configural, metric, and scalar MI on indicators) one scales the factors by fixing variances to 1 as opposed to marker indicator approach?
 Bengt O. Muthen posted on Monday, December 10, 2018 - 5:03 pm
A) Yes. But also see the discussion on slides 42-46 of alternatives in my recent SMEP address on our home page at

This is useful with many time points, like T>10.

B) You want to study changes in factor variance across time, so I wouldn't choose to fix variances.
 J.D. Haltigan posted on Wednesday, December 12, 2018 - 3:06 am
Thanks so much Bengt. Are any of the submitted 2018 papers (referenced in the SMEP address slides) available as preprints? Judging from their titles they address precisely the issues I am wrapping my head around.
 Bengt O. Muthen posted on Wednesday, December 12, 2018 - 5:08 pm
The Asparouhov-Muthen 2018 paper is on our website at

Regarding the Hamaker-Muthen paper, you should email her:

Let me know if there were other submitted papers you are interested in.
 Alissa Mahler posted on Tuesday, March 26, 2019 - 8:58 am

I am running a series of growth/autoregressive models, and was originally planning on just using the observed, mean score for each scale (the complexity of the model prevents me from using latent factors for each measure).

Someone recommended that I use the factor scores instead of the mean score, to better account for the fact that items load onto the factor differently.

When conducting the CFAs, I set the factor score mean to zero and variance to 1 to set the scale. However, as noted in a comment above, I then realized this was problematic for the growth models (as now all of the means were identical).

Would simply using a different scaling method (e.g., using a marker variable) to estimate the means for each factor solve this issue? Thanks in advance for your help.
 Bengt O. Muthen posted on Tuesday, March 26, 2019 - 5:19 pm
I would not go there. To make sure you get the factor scores in a comparable metric, you would have to analyze all time points together imposing measurement invariance - and then you are basically doing as much work as the longitudinal model with factors.
 Alissa Mahler posted on Wednesday, March 27, 2019 - 7:26 am
Thank you for your response. One clarification, the problem is not so much that the items load differently across waves, but instead the reviewer noted that within each wave, the items load with varying strengths (i.e, item 1 = .55, item 2 = .89, etc). Her argument was that when you take a scale average, you are assuming each item contributes equally, which the CFA suggests is not the case.

Her solution was to export factor scores and use those, rather than mean scores. However, because the mean of the factor scores is zero, when I run the growth models the slope is not significant (which is not accurate based on the mean scale data). I'm not quite following how the measurement invariance would correct for this?

I really appreciate your assistance.
 Bengt O. Muthen posted on Wednesday, March 27, 2019 - 4:11 pm
I understand the reviewer concern about different loadings within time point. My answer concerns avoiding the problem you mention about factor score means being zero if you do them one time point at a time. To avoid that, you have to do what I mentioned using measurement invariance.
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