Estimating reliabilities and correcting for sampling error in indices of within-person dynamics derived from...

Psychology has witnessed a dramatic increase in the use of intensive longitudinal data (ILD) to study within-person processes, accompanied by a growing number of indices used to capture individual differences in within-person dynamics (WPD). The reliability of WPD indices is rarely investigated and reported in empirical studies. Unreliability in these indices can bias parameter estimates and yield erroneous conclusions. We propose an approach to (a) estimate the reliability and (b) correct for sampling error of WPD indices using "Level-1 variance-known" (V-known) multilevel models (Raudenbush & Bryk, 2002). When WPD indices are calculated for each individual, the sampling variance of the observed WPD scores is typically falsely assumed to be zero. V-known models replace this "zero" with an approximate sampling variance fixed at Level 1 to estimate the true variance of the index at Level 2, following random effects meta-analysis principles. We demonstrate how V-known models can be applied to a broad range of emotion dynamics commonly derived from ILD, including indices of the average level (mean), variability (intraindividual standard deviation), instability (probability of acute change), bipolarity (correlation), differentiation (intraclass correlation), inertia (autocorrelation), and relative variability (relative standard deviation) of emotions. A simulation study shows the usefulness of V-known models to recover the true reliability of these indices. Using a 21-day diary study, we illustrate the implementation of the proposed approach to obtain reliability estimates and to correct for unreliability of WPD indices in real data. The techniques may facilitate psychometrically sound inferences from WPD indices in this burgeoning research area.