A method first proposed by Satorra and Saris (1985) is utilized to compute the power estimates and applied, here, to the growth modeling framework developed by Muthen and Curran (1997).
The key technique in determining the power associated with the likelihood ratio test is based on the fact that (1) the distribution of the test statistic under the alternative hypothesis approaches a noncentral chi-square distribution; (2) the noncentrality parameter can be approximated by using existing statistical software R.
A Latent Growth Model
This is a two-level latent growth model which consists of a measurement model and a structural model with two latent variables denoted by 1, representing initial status, and 2, representing rate of change.
Modeling components of growth restricted to linear, which are the same for an individual(i) in both intervention and control groups with repeated measures (j=1,...p).
where the unique variances (variances of ), are assumed to be the same across time and correlations between components of are zero..
Modeling intervention and control differences on the latent growth variable's distributions.
Under normality, it is equivalent to.
where 2.1 is the residual variance after regressing 2 on 1..
Click here for the joint distribution of 1 and 2.