A word on standardization in longitudinal studies: don't.

Abstract

Z-standardization is a widely used procedure, applied for getting rid of acquiescence and other response biases, bringing variables of different metrics to the same metric, and emphasizing differences between groups in graphs. In longitudinal data and analyses of subgroups of observations, z-standardization leads to a number of problems. It changes in often undesirable ways the distances between observations, and the multivariate distributions of cross-sectional and longitudinal data. The psychological literature is rich in examples of misinterpreted z-scores, some of which were described in this article. While many pitfalls are known for cross-sectional studies, longitudinal studies add further problems, due to confounded frames of reference (the original response scale, the intra-individual distribution, the inter-individual distribution within given time points, the inter-individual distribution across different time points, the variation within vs. between cohorts, and any combinations of these). Generally, it is not insightful to first standardize variables within units (individuals, cohorts, states, organizations) and then compare mean scores across these units that gave the reference frame for standardization. This should be trivial, but can often be observed in the current research, and is easily overseen or mishandled the more units and reference frames are added to the data structure. Modeling common-method factors is a useful alternative to account for response biases while avoiding the downsides of ipsatization. Alternative easy monotonous scale transformations are available to get items with different response scales to the same metric (Cohen et al., 1999; Little, 2013). Given the ease and wide acceptance of standardization in the psychological literature, it seems necessary to emphasize the risks and possible misinterpretations during the methodological training, writing and review processes in psychology. As Little (2013) pointed out, it seems wise to avoid standardization in longitudinal data analyses and person-oriented analyses, unless the researcher is fully aware of and able to avoid undesirable consequences. There are many good uses for these procedures, but also many risks.