The usual procedure when using a Latent Growth Modeling with, for instance, 4 time points, is to code the intercept T1=1, T2=1, T3=1, T4=1 and the slope T1=0, T2=1, T3=2, T4=3. From my understanding, one source of misfit is to code omit T1=0 in the slope, i.e. coding the slope as follow: T2=0, T3=1, T4=2. What I cannot understand is why? Does someone knows why?
n.b.: I am using Lavaan (R)
To identify this model, two slope loadings must be fixed at two different values. Although the choice of loadings is somewhat arbitrary, the intercept factor is bound to the time scale. Shifting the loadings on the slope factor alters the scale of time, which affects the interpretation of the intercept factor mean and variance.The slope factor mean and variance differ from the intercept factor mean and variance in that changing the fixed loadings, and thereby changing the time scale, rescales the slope factor mean and variance, in this case by constants. Rescaling by constants does not change the fundamental meaning or affect significance tests of the parameters. It also does not affect the correlations between the slope factor and other predictors in the model.The slope factor mean and variance differ from the intercept factor mean and variance in that changing the fixed loadings, and thereby changing the time scale, rescales the slope factor mean and variance, in this case by constants. Rescaling by constants does not change the fundamental meaning or affect significance tests of the parameters. It also does not affect the correlations between the slope factor and other predictors in the model (Duncan & Duncan, 2009).
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Cristian Ramos-Vera ,
this is the repeated time where you insert a quotation from a different source as your own response, without making it clear that it is not your words but a quotation. In this case it is a passage from Duncan et al (2011). This is unacceptable and a form of plagiarism. Please stop this in the future. The link shows directly the passage in the book.
https://cutt.ly/orVmTjw
Holger
I'm sorry I forgot to put in the quote, even though I had already put in the quote link.
Thank you very much for your comments but it does not answer my question. What would concretly be the effect of removing the first time parameter (T1) from the calculation of the slope?
For instance, using Lavaan, what would be the difference between:
(1)
model
The intercept parameter is supposed to be the level, and the linear slope parameter the average change between two time points. In your code, you specify those two factors from the time points. You want your values to be (I ignore the residual variances for now):
T1: Level + 0X Change
T2: Level + 1x Change
T3: Level + 2x Change
...
That is basically all the growth curve does. What you do instead in your second code is to say:
T1: Level
T2: Level
T3=Level + 1x change
T4=Level + 2x change
Do you see why this is a problem? The starting point of your curve is misspecified, and so is the change.
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