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.

  H₀:   no any differences between the two groups.

  H₁:   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