A note on estimating single-class piecewise mixed-effects models with unknown change points

Abstract

Piecewise mixed-effects models are useful for analyzing longitudinal educational and psychological data sets to model segmented change over time. These models offer an attractive alternative to commonly used quadratic and higher-order polynomial models because the coefficients obtained from fitting the model have meaningful substantive interpretation. The current study thus focuses on the estimation of piecewise mixed-effects model with unknown random change points using maximum likelihood (ML) as described in Du Toit and Cudeck (2009). Previous simulation work (Wang & McArdle, 2008) showed that Bayesian estimation produced reliable parameter estimates for the piecewise model in comparison to frequentist procedures (i.e., first-order Taylor expansion and the adaptive Gaussian quadrature) across all simulation conditions. In the current article a small Monte Carlo simulation study was conducted to assess the performance of the ML approach, a frequentist procedure, and the Bayesian approach for fitting linear–linear piecewise mixed-effects model. The obtained findings show that ML estimation approach produces reliable and accurate estimates under the conditions of small residual variance of the observed variables, and that the size of the residual variance had the most impact on the quality of model parameter estimates. Second, neither ML nor Bayesian estimation procedures performed well under all manipulated conditions with respect to the accuracy and precision of the estimated model parameters.