what is your view on the use of a single shape factor, and when can you use it? I read a paper, I believe by DUncan that posited shape factors are useful when the value of the intercept is not significant. However, in LGM with categorical variables, the baseline value is standardized to zero. Would that suggest a single shape factor is useful?
It sounds like by "shape factor" you mean a slope growth factor. I am not familiar with papers on this topic. I don't understand why you would not want an intercept growth factor, or why you would want to fix its mean to zero. The fact that with categorical outcomes Mplus fixes the intercept growth factor mean to zero has no substantive meaning but is merely because the mean of the outcome is instead picked up by a threshold parameter.
The chapter I am thinking of is in the Duncan et al. book "An introduction to latent variable growth curve modeling," 1999. They have a chapter on testing interaction effects on LGM. They propose two possible methods. One method involves the use of a single shape factor in place of intercept and trend random effects. Essentially, it looks like a simple CFA, as the factor loadings are freely estimated except one for sclae (constrained to 1). They say it is useful when the intercept factor can be eliminated. I guess it gives one less parameter to estimate?
bmuthen posted on Wednesday, May 26, 2004 - 2:03 am
I see; yes, I am aware of that approach. The factor is then a combination of an intercept and a slope factor where the factor loadings capture the shape. In my opinion, the interpretation is clearer when you work with the intercept and slope factors as in regular growth modeling.
cricket posted on Wednesday, May 26, 2004 - 10:45 am
Thanks for taking the time to respond to this question.
Anonymous posted on Tuesday, May 03, 2005 - 7:41 pm
If the mean of slope parameter is not statistically significant, can we explain this way: the average score at different time point are the same? So there is unnecessary to test the affect of the time-invarying variable to slope variable? Thanks
Yes on the first question. Re the second question, you might still be interested in seeing how time-invariant covariates explain the slope variance, but there is probably less interest in that in this case.