Latent Curve Detrending for Disaggregating Between-Person Effect and Within-Person Effect

Abstract

Longitudinal data analysis is gaining attention from researchers because it enables us to examine both between- and within-person effects simultaneously. Traditionally, centering has been used with multilevel models to estimate these two effects. However, recent studies found that centering could not disaggregate the between-person and within-person effects when a time-varying predictor shows time trends. This article develops methods for disaggregating the two effects in the presence of time trends using the latent curve model. The proposed methods reveal the link between centering and detrending, which are often seen as different preprocessing for different purposes. Two simulations are conducted to assess and compare the performance of the proposed and existing models. The results show that models with a slope factor behind a predictor can unbiasedly estimate the between- and within-person effects. Also, models with latent between-person predictors can unbiasedly estimate the between-person effect, while those with observed ones suffer from bias.

Keywords:

• Between-person effect and within-person effect
• centering and detrending
• latent curve detrending
• residualizing

Disclosure statement

The authors report there are no competing interests to declare.

Notes

1 Some may be familiar with this model under the name of random intercept model.

2 Hoffman (2015) proposed a trick to circumvent the software issue. Hoffman suggested stacking a predictor and an outcome in the same column in a data set and adding dummy variables to switch a dependent variable and the corresponding model from the time-varying predictor to the outcome, and vice versa. By this “doubly stacking” trick, MMD becomes a univariate three-level model, allowing us to use popular software for the mixed-effects model. However, even with this trick, it may be difficult to run MMD or equivalent univariate mixed-effects model because of a constraint of the level-1 null error variance, which cannot be available for some software and packages (e.g., lme4 package in R).