Curve of Factors Model: A Latent Growth Modeling Approach for Educational Research.

A first-order latent growth model assesses change in an unobserved construct from a single score and is commonly used across different domains of educational research. However, examining change using a set of multiple response scores (e.g., scale items) affords researchers several methodological benefits not possible when using a single score. A curve of factors (CUFFS) model assesses change in a construct from multiple response scores but its use in the social sciences has been limited. In this article, we advocate the CUFFS for analyzing a construct's latent trajectory over time, with an emphasis on applying this model to educational research. First, we present a review of longitudinal factorial invariance, a condition necessary for ensuring that the measured construct is the same across time points. Next, we introduce the CUFFS model, followed by an illustration of testing factorial invariance and specifying a univariate and a bivariate CUFFS model to longitudinal data. To facilitate implementation, we include syntax for specifying these statistical methods using the free statistical software R.