### Power Calculations for Latent Growth Modeling

(Simplified Data Entry)

**Introduction**

Our primary interest in power estimation is to detect a given
main effect of intervention.

Two latent variables (that cannot be measured directly), *individual-specific
growth parameters,* are typically concerned here:

- an
*intercept* parameter, representing *initial
status*;
- a
*slope *parameter, representing *rate of change*.

The following figure is a graphical illustration of growth
curve modeling for both intervention and control groups.

Each dot represents the outcome value of each individual at a
specific timepoint. In this case, the two groups start with the
same initial values of the outcome. The intercept and slope of
each individual are the latent variables. The intervention effect
can be reflected by the slopes of the two curves.

**Power Calculation:** Mean change
in growth rates differs by the intervention group.

H_{0}: no any differences between the
two groups.

H_{1}: only the mean of individual
growth rates is different between the two groups.

The power corresponds to detect the overall difference in
growth between intervention and control groups across time.

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Last Updated 10/28/98