The AT option requires using |. But you could turn the model into a 2-level model and let time be a variable, regressing the outcome on time with a random intercept and a random slope.
Jon Heron posted on Monday, March 23, 2009 - 11:22 am
Ahh, thanks Bengt
Jon Heron posted on Tuesday, April 07, 2009 - 11:48 am
I have fitted my piecewise linear 2nd order growth model on 3 time points of data by constraining the first order residual variances to be zero.
My manifest scales are very skewed and hence the estimated covariate effects on my 2nd order growth factors are rather small. Consequently, I have coverted my manifests into ordinal variables to see what effect this will have.
A linear (2 growth factors) model is estimable in this situation, however I run into problems when I attempt my piecewise (3 growth factor) model - I am unable to constrain my first order residual variances to be zero.
Having read (i.e. struggled) through mplus notes #4, I now think that such a model may not be possible due to the relationship between the residual variances of the manifests and 1st order factors (theta and psi)
I think I have more questions than answers here - I am perhaps not understanding the setting.
I assume when you say "first order residual" that you refer to residuals of the first piece of the piece-wise growth modeling?
I am not quite sure how you identify a piece-wise model from only 3 time points. You have to impose restrictions.
When you do the ordinal version you say you have problems restricting your first order residual variances to zero - but I don't understand why do you want residual variances to be zero. One may want to restrict them to be equal over time. Note that ML estimation of such growth models do not have free residual variance parameters, but essentially says they are equal over time. So using WLSMV one may want to restrict them to be say 1 at all time points. But I think piece-wise growth modeling for ordinal outcomes using only 3 time points draws on too little information relative to its parameters.
Jon Heron posted on Wednesday, April 08, 2009 - 2:48 pm
I'm constraining to zero the residual variances for the three factors at the first level - i.e. the level between the growth factors and the manifests. This is to enable me to fit a piecewise model on 3 time points (this constraint was suggested in a paper on 2nd order growth models from the Teacher's Corner bit of the SEM journal)
Incidentally, in said SEM paper, the author used likert scales as if they were continuous - so he really should have done what I am attempting to do!
I see, you have a multiple indicator growth model. I am not familiar with this SEM article or this approach (what's the exact ref.?), but it seems strange to me to restrict the residual variances to zero for the essential outcome of the growth model.
Jon Heron posted on Thursday, April 09, 2009 - 6:30 am
Teacher's Corner: An Illustration of Second-Order Latent Growth Models Gregory R. Hancock, Wen-Ling Kuo, Frank R. Lawrence Structural Equation Modeling: A Multidisciplinary Journal, Volume 8, Issue 3 July 2001 , pages 470 - 489
I don't have the article in front of me, but if I remember correctly, the constraint described results in a model akin to a repeated measures ANOVA. This constraint is not the main focus of the paper - merely a comment in the discussion.
Jon Heron posted on Thursday, April 16, 2009 - 5:58 am
I think I might be worrying about non-normality unnecessarily as I can stick with continuous use MLR
My measures are either 9 or 12 point scales (typical dist'ns shown below). Do you think i would scrape through with MLR? I'm under a bit of time pressure now and don't feel I have the breathing space to start playing with a zero-inflated approach such as Olsen/Schafer.
Categorical variables with strong floor effects like the ones you show should not be treated as continuous using MLR. The robustness to non-normality is not sufficient in this case. Instead, they should be treated as ordered categorical or a two-part model as shown in Example 6.16 could be considered.
Jon Heron posted on Sunday, April 19, 2009 - 11:43 am
I think I've established that the constraints I want to impose are not possible with the ordinal approach (earlier up this message).
Is the two part model compatible with multiple indicator growth? Can't quite get my head round that at the minute!
I see there is also a third option - mixtures with a constrained symptom-free class.
You can recode the age variables to any non-missing value if the dependent variable is missing. Then they will not be deleted. Because the dependent variable is missing, this does not affect the results.
Jon Heron posted on Wednesday, November 21, 2012 - 7:00 am