Power Calculations for Latent Growth Modeling

(the 2nd version)


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.

  1. A Measurement Model:

    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.

  2. A Structural Model:

    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.


Four Tests

  Case 1:   Mean change in growth rates differs by the intervention group.

  Case 2:   Variance in growth rates differs by the intervention group.

  Case 3:   Mean and variance in growth rates differ by the intervention group.

  Case 4:   Mean, variance in growth rates and interaction with baseline level differ by the intervention group.

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Last updated: 04/18/98