Hoffman, L., Hofer, S. M.,& Sliwinski, M. J. (2011). On the confounds among retest gains and age-cohort differences in the estimation of within-person change in longitudinal studies: A simulation study. Psychology and Aging, 26(4), 778-791.
Abstract: Although longitudinal designs are the only way in which age changes can be directly observed, a recurrent criticism involves to what extent retest effects may downwardly bias estimates of true age-related cognitive change. Considerable attention has been given to the problem of retest effects within mixed effects models that include separate parameters for longitudinal change over time (usually specified as a function of age) and for the impact of retest (specified as a function of number of exposures). Because time (i.e., intervals between assessment) and number of exposures are highly correlated (and are perfectly correlated in equal interval designs) in most longitudinal designs, the separation of effects of within-person change from effects of retest gains is only possible given certain assumptions (e.g., age convergence). To the extent that cross-sectional and longitudinal effects of age differ, obtained estimates of aging and retest may not be informative. The current simulation study investigated the recovery of within-person change (i.e., aging) and retest effects from repeated cognitive testing as a function of number of waves, age range at baseline, and size and direction of age-cohort differences on the intercept and age slope in age-based models of change. Significant bias and Type I error rates in the estimated effects of retest were observed when these convergence assumptions were not met. These simulation results suggest that retest effects may not be distinguishable from effects of aging-related change and age-cohort differences in typical long-term traditional longitudinal designs.
Hoffman, L. (in press). Considering alternative metrics of time: Does anybody really know what "time" is? Forthcoming in G. Hancock & J. Harring (Eds)., Advances in longitudinal methods in the social and behavioral sciences.
Abstract: The idea that people change differently over time is a cornerstone of many fields, including psychology, human development, education, and business. Statistical models of change over time often begin with two initial goals: description (i.e., to describe the average pattern of change over time and individual differences therein) and prediction (i.e., to predict those inter-individual differences in change over time; to predict remaining intra-individual variation over time). In pursuing these and more complex aims regarding change over time, however, it is implicitly assumed that one knows what “time” is. Yet in many longitudinal contexts exactly what “time” should be is both a theoretical and empirical question, in that different metrics for indexing time that reflect alternative causal models of change may yield very different conclusions. For instance, in aging research one might conceptualize change as a function of time since birth, time to death, or time in disease progression (e.g., dementia). Further, selecting a time metric can be complicated by additional choices in model specification (i.e., the different centering procedures available for distinguishing cross-sectional from longitudinal effects of time). The purpose of this chapter is to illustrate how considering alternative models for the metric of time and alternative specifications thereof can color the inferences one might draw about these fundamental aspects of change, as well as to emphasize some empirical means by which such choices can be made. Such considerations are a necessary precursor to making informed use of subsequent methodological advances for longitudinal data.