Anonymous posted on Thursday, July 07, 2005 - 3:09 pm
Hi, I have been to one of Dr. Muthen's short classes--growth modeling with latent variables using Mplus this March in Baltimore. On slide 189 to 194, there is an introducation about "Growth of latent variable construct measured by multiple indicators". Now I have a chance to use this model to model my data. Could you please give me some references or examples, so I can learn more about this modeling skills? Thank you very much for your kind assistance.
bmuthen posted on Thursday, July 07, 2005 - 3:29 pm
Unfortunately, there are no papers yet with examples as far as I know - other Mplus Discussion readers might know. We have some more details on the steps we recommend in our Day 2 handout from the annual Alexandria course and you can order that handout from Mplus (see web site).
Kersi Antia posted on Saturday, July 16, 2005 - 1:08 pm
Dear Bengt: Thanks for the quick (and helpful!) responses to my earlier queries about growth modeling using MPLUS...I have found this discussion list an invaluable resource as I learn the intricacies of growth modeling.
I attempted to set up a 2-indicator linear growth model for a continuous outcome (using monthly web pages viewed and monthly time spent on the website as the indicators of web use) pretty much along the lines of Example 6.14 on p.91 of the MPLUS manual. Although I was able to get output, I did get a warning as follows:
WARNING: THE RESIDUAL COVARIANCE MATRIX (THETA) IS NOT POSITIVE DEFINITE.
Sure enough, examination of the Theta matrix revealed the variances of each of the default-constrained indicators (in my case, the monthly web pages viewed) to be negative.
I will make sure to order Day 2's slide deck as you suggested in your response to the Anonymous poster's query of July 7, but is there a "fix" you could recommend in the meanwhile?
Thanks for your help, and for the Baltimore session last March...it was quite an eye-opener to the possibilities of MPLUS modeling!
One question is if you get negative residual variances also when running the growth model for problematic indicator separately. If yes, then this may be an indication of a very non-normal outcome which might call for other types of modeling. If the negative residual variance only happens when using the 2 indicators together, then that suggests that the factor model for these indicators is not quite right. As the handout suggests, a CFA should preceed the growth modeling.
Pettit, Laird, Bates, Dodge, & I are fitting a growth model with latent variable constructs of parental monitoring measured by multiple indicators at 4 different time points.
As is the case with a data set such as the CDP (a 20 year project) the monitoring construct was not quite measured at each time point with the same observed variables. So, we have some measures that are the same at two time points, some that are the same at three time points, some only measured once. Looks a bit like this:
age 5 Monitor 1 age 6 Monitor 1, Monitor 2, Monitor 3 age 8 Monitor 2, Monitor 3, Monitor 4 age 11 Monitor 2
Actually, the model looks a lot like the one on page 128 of the short course handout about "Growth Modeling with Multiple Indicators."
I wasn't in this course, so I'm not sure what the text was for that figure, but I assume that as long as we test invariance for the factor loadings, and intercepts across time, we're in pretty good shape to fit the model. Correct?
This procedure seems ideal for managing the developmental differences in measures that often occur in longitudinal data sets across multiple time points. Have there been some published articles using a CFA model that includes different measures at differnt time points and measurement equivalency to which you could refer us?
I did see in a previous posting that as of now you didn't know of any growth modeling studies that were already published that included latent factors with multiple indicators. Just wanted to let you know about Garber, J., Keiley, M. K., & Martin, N. (2002). Developmental trajectories of adolescents’ depressive symptoms: Predictors of change. Journal of Consulting and Clinical Psychology, 70, 79-95. In that article we do fit a growth model with Growth Modeling with Multiple Indicators.
BMuthen posted on Monday, October 17, 2005 - 8:08 am
That looks like it will work fine given that you have the same measure for at least two consecutive time points. Thanks for the reference.
Do you know of any papers in which the authors have fit a growth model in which the "observed" measures at each time point are SEM latent constructs of a second order factor which is then the actual "latent construct" for a growth model of these 1st order latent constructs over time?
I know it's confusing, but I have a powerpoint picture of it I could attach or send if necessary.
Hello Dr. Muthen, I am using growth curve modeling with multiple indicators. As suggested in your notes I am trying to run growth curve of each indicator and compare if the fitted curves for the indicators are the same. My question is how do you compare two curves and decide if the fits are the same? If I have two indicators measured longitudinally with different time scores estimated for the trajectories do I have to do statistical test if these time scores are the same for the two curves? Thank you.
I try to estimate a multiple indicator growth model. Three of my indicators are available every 5 years, while the forth indicator is available every 10 years only. I have missing data. I was planning to impute the missing data using a linear interpolation. For example I65=(I60+I70)/2, where I65 was previously missing, and I have the decades data I60 and I70. This type of linear interpolation imputation will make some of the indicators linearly dependent. I am not sure, but I am guessing: Mplus, and any Structural Equation Modeling software for that matter, will not be happy with linearly dependent indicators. Is that correct? Thank you.
Dear Dr. Muthen, We want to fit a growth model with multiple indicators to our data but before we would like to ask few questions. a) Can we do this type of analysis with differents raters? For instance, in our case we have self, teacher and parents ratings items. b) In one of your short classes you gave steps to follow for this analysis. The second step is to "determine the shape of the growth curve for each indicator and the sum of indicators". In the different raters case do we need to perform the same analysis for each rater in addition to the analysis which combine all raters?
We are estimating a growth model with multiple indicators to our data and one of our interest is the magnitude of the growth parameter estimates (in a Cohen's d metric, for instance). I guess one way of doing is to establish a standardized metric for the latent variables with reference to a given time point. So, in addition to fixing the intercepts of first order factors to zero, I fixed the SD of the latent variable at time 1 to one, f1 in example 6.14 from the UG. Questions: a) Is that correct? b) If not, what parametrization should I use? Any reference for that? C) Or, perhaps is there another way of assessing the magnitude of change in this context, without standardizing the latent variable? Thank you very much for your help.
refers to the residual variance of f1, not its variance.
If you want to know how big a slope growth factor mean really is in Cohen-like terms, it seems like a more direct approach is to use Model parameter labels to express the mean and variance of say f2 using New parameters in Model Constraint and also define the New parameter cohen,
cohen = meanf2/sqrt(varf2);
In this linear growth example with centering at the first time point, "cohen" gives you the standardized mean change in the factor from t1 to t2 as a function of the slope growth factor mean.
Dear Dr Muthén, I realized that my last posting was not clear enough, so I would like to re-express what I had in mind. I was thinking using the alternative parameterization you introduced in topic 1, from Mplus Short courses (2009). Then Ex 6.14 would become:
MODEL: f1 BY y11* y21 y31 (1-3); f2 BY y12* y22-y32 (1-3); f3 BY y13* y23 y33 (1-3); [y11 y12 y13] (4); [y21 y22 y23] (5); [y31 y32 y33] (6); f1-f3@1;
Under this specification, the latent variable at Time 1 has a mean of 0 and SD of 1. Is this approach correct to express the magnitude of the growth parameter estimates. Thank you very much for your help.
But note that f1-f3@1 does not set the variance of the factors to one. The factors are dependent variables, influenced by i and s, so you are setting their residual variances to one. You see this in Tech4.
Note also that your setup forces the factor variances to be the same across time, which is not what you want.