I have a few (basic) questions about modelling curves in MPLUS.
First, I modelled a curve with an intercept, linear and quadratic slope as presented in the MPLUS manual. Observing my data means showed that my sample shows a combination of linear decline (timepoints 2-3) and quadratic decline 1-2 and 3-4. I see that the quadratic and linear slope is modelled together. I would like to compare the relative fit of a quadratic versus linear fit. Can I do this in MPLUS and then retain a quadratic fit if it a better overall fit? My concern is that I will be adding several covariates in subsequent analyses and I'd like to protect parsimony.
Second, am I correct in thinking that the default is to include both a linear slope and a quadratic slope factor because some individuals might show more of a linear trend while others show a quadratic shape in change over time?
Third, I have previously tested constant slopes in AMOS by restraining the variance and covariance (I - S) to 0 and comparing the model fit to an unrestrained model. I can't figure out how to restrain a variance to 0 in mplus? Also, while it is clear to me how one would compare models for a Multiple Group analaysis in MPLUS, I'm not clear on how to get a chi-square difference result (using maximum likelihood) with a single group analyses. Does M-plus provide this? The output I have seen so far does not provide the chi-square difference comparison when you have constrained parameters in a model.
In a model in which there is a decline over four time points, and you test both a quadratic slope and a linear slope- why would one growth factor be negative (slope) and the other positive(quadratic).
bmuthen posted on Thursday, May 19, 2005 - 9:01 am
There is no default growth shape in Mplus - you can specify either a linear or a quadratic curve. You can check if adding the quadratic growth factor significantly improves the fit by looking at the significance of the quadratic factor mean.
To constrain the variance of a variable - say "s" - in Mplus, you simply say "s@0;"
Chi-square differences are obtained by doing 2 analyses and comparing the chi-squares (or the log likelihood values).
Regarding your additional question about a neg linear slope and a positive quadratic slope, this simply means that the decline is not as rapid at the end as it is in the beginning - check out the plot that Mplus provides.
I am doing growth curve analysis with 2 groups and I like to test if the development over time is different for the 2 groups. First I estimate an unconstrained model. Then, should I constrain s and q simultaniously, like: [s] (1); [q] (2); Or should I first test the lin slope and then the quad slope, so separately? (I do chi-square difference testing)
You should first see if the same growth model fits well in each group separately. If not, it does not make sense to compare the parameters of the growth factors across groups. I would test them separately.