Abstract: Sample Size Planning for Latent Curve Models

When designing a study that uses structural equation modeling (SEM), an important task is to decide an appropriate sample size. Historically, this task is approached from the power analytic perspective, where the goal is to obtain sufficient power to reject a false null hypothesis. However, hypothesis testing only tells if a population effect is zero and fails to address the question about the population effect size. Moreover, significance tests in the SEM context often reject the null hypothesis too easily, and therefore the problem in practice is having too much power instead of not enough power. An alternative means to infer the population effect is forming confidence intervals (CIs). A CI is more informative than hypothesis testing because a CI provides a range of plausible values for the population effect size of interest. Given the close relationship between CI and sample size, the sample size for an SEM study can be planned with the goal to obtain sufficiently narrow CIs for the population model parameters of interest. Latent curve models (LCMs) is an application of SEM with mean structure to studying change over time. The sample size planning method for LCM from the CI perspective is based on maximum likelihood and expected information matrix. Given a sample, to form a CI for the model parameter of interest in LCM, it requires the sample covariance matrix S, sample mean vector [Formula: see text], and sample size N. Therefore, the width (w) of the resulting CI can be considered a function of S, [Formula: see text], and N. Inverting the CI formation process gives the sample size planning process. The inverted process requires a proxy for the population covariance matrix Σ, population mean vector μ, and the desired width ω as input, and it returns N as output. The specification of the input information for sample size planning needs to be performed based on a systematic literature review. In the context of covariance structure analysis, Lai and Kelley (2011) discussed several practical methods to facilitate specifying Σ and ω for the sample size planning procedure.