A Spline Regression Model for Latent Variables

Abstract

Spline (or piecewise) regression models have been used in the past to account for patterns in observed data that exhibit distinct phases. The changepoint or knot marking the shift from one phase to the other, in many applications, is an unknown parameter to be estimated. As an extension of this framework, this research considers modeling the relation between endogenous and exogenous latent variables with a spline regression model, where each latent variable is measured by multiple observed indicators. Consequently, the spline regression model is modified to include a measurement model that explicitly expresses the relation of the observed variables to the latent constructs. Maximum likelihood estimation of the model is developed and executed on educational data to illustrate the utility of the model.