finnigan posted on Thursday, February 26, 2009 - 8:53 am
I was going through the above example and would like to ask how the degrees of freedom 34 and 36 were calculated.
For example in a CFA model using rules of path diagrams one counts factor loadings, residual variances, any factor covariances ,but not the factor intercepts and factor means. The number of these parametres is then subtracted from p(p+1)/2) to get the Degres of freedom. Iassume that in invariance testing under CFA that fctor intercepts
Is there a particular way that the degrees of freedom are calculated in the multiple indicator growth model that uses a similar approach to that in SEM.
The degrees of freedom for Example are computed in the regular way. There are 45 variances and covariances and 9 means for a total of 54 sample statistics. 54 minus 21 free parameters in the H0 model results in 33 degrees of freedom. The Baseline model has free parameters of nine means and nine variances. 54 minus 18 free parameters is 36 degrees of freedom.
finnigan posted on Friday, February 27, 2009 - 6:53 am
The trouble I am having is identifying and separating the variances, covariances and means included in 54(45+9) and free parametres which constitute the 21 and 18 under the Ho and baseline model Please excuse the rooky questions. Ho model 45 variances and covariances I counted 9 residual variancese 3 factor residual variances 1 slope residual variance 1 intercept residual variance 1 slope variance 1 intercept variance 0 correlated residuals by default 1 covariance between I and S
Total 17: clearly I am missing 28 items!
Means Do the 9 means refer to indicator intercepts; what do they include?
The intercepts of the first-order factor indicators are in nu. They are held equal across time as part of the growth model parameterization. See page 546 of the Mplus User's Guide for the BY language for this model specification. See also the Topic 4 course handout.
One further comment about TECH1. The numbers are simply numbers assigned to each parameter. These numbers are used in error messages. Starting values are given in the second part of TECH1. See pages 586-588 of the Mplus User's Guide.
finnigan posted on Tuesday, March 03, 2009 - 8:23 am
Linda, Many thanks for this.
I took a look at the topic four course handout about the estimation of the multiple indicator growth model.
I assume that the EFA at each time point is done to see what indicators load on what first order factors. Why is an efa using all time points not done? Why is the growth model part done before the CFA ?
I 'd like to ask if there is a set of references available to explain the logic of each step and if there is a longitudinal CFA example available.
EFA at each time point is done to determine that at a minimum the same number of factors is represented. If not, it would not make sense to go on to the CFA. The growth model is the last step after CFA.
I know of no set of references that explicitly discusses the strategy we recommend. Slides 77-96 of short course Topic 4 show the steps and the inputs involved. Example 6.14 is also multiple indicator growth.