Recovering knot placements in Bayesian piecewise growth models with missing data

Abstract

Bayesian piecewise growth models (PGMs) are useful tools to capture nonlinear trends comprised of distinct developmental phases. An important parameter in Bayesian PGMs is the knot location - the time at which transitions arise between phases. While researchers can specify knot locations when they are known a priori, a more flexible approach is to estimate knot locations based on data. The Bayesian estimation of knot locations is largely affected by prior distributions and missing data; however, little is known about the impact of these two factors in recovering knot placements. In the current article, we conducted a Monte Carlo simulation study to examine the impact of different prior specifications and the presence of missing data on the recovery of knot placements in Bayesian PGMs. Simulation results indicated that in small sample sizes, knot location estimates were dictated by prior distributions. Even with larger sample sizes, the estimates remained sensitive to informative and inaccurate prior specifications. The presence of missing data complicated the recovery linked to certain priors. While negative consequences, such as bias in parameter estimates, were caused by a larger amount of missing data, this could be alleviated by informative and accurate priors. These findings emphasize the critical role and intertwined influence of prior distributions and missing data in reaching conclusions about changepoints. We present an illustrative example using real data with missing values to demonstrate the Bayesian estimation of knot locations under realistic scenarios. Recommendations for applied researchers are discussed.

Keywords: Bayesian estimation; Knot; Missing data; Piecewise growth; Prior distribution.

Fig. 1

A path diagram for the population model

Fig. 2

Prior specifications

Fig. 3

Missing data patterns

Fig. 4

Boxplots of bias for knot location estimates across simulation conditions

Fig. 5

Distributions of posterior means for knot location across simulation conditions

Fig. 6

Attrition pattern for the ECLS-K data