Chapter 6: Sensitivity Analysis of Mixed-Effects Models When Longitudinal Data are Incomplete

Mixed-effects models have become a widely adopted approach to the analysis of longitudinal data. Key aspects of the methodology that make mixed-effects models well suited for longitudinal data analysis are that models may be specified to handle different types of response distributions, different mathematical functions to describe the growth trajectory, individual-specific times of measurement, and missing data (Skrondal & Rabe-Hesketh, 2004). With regard to missing data in particular, statistical inference of a mixed-effects model is considered valid when data are missing completely at random (MCAR) or missing at random (MAR). Data are MCAR whether or not data are missing (known as missingness) is independent of the missing and observed data, such as if missing data are planned in advance of data collection (see, e.g., Graham, Taylor, Olchowski, & Cumsille, 2006). Data are MAR if the missingness is related to the observed data but is independent of the missing data, such as if the probability of missing data is related to measured covariates (e.g., participant’s gender) but not to the missing data (e.g., life satisfaction measures) (Little & Rubin, 2002). Thus, mixed-effects models provide a more flexible approach in terms of the assumptions about missing data compared to methods that require complete data and so also require that data are MCAR (e.g., repeated-measures ANOVA).