Reply to Hamaker and Ryan:Within-sample temporal instability in cross-sectional estimates

We offer our sincere gratitude to Hamaker and Ryan (2019) for their comment on our manuscript (Fisher et al., 2018). The generalization issue in question is a key problem in human subject research methodology and requires effort from all quarters to resolve. We agree "that we should interpret measures in terms of what they are meant to represent." This is perhaps the most important point to be taken from our paper, that understanding individuals requires measuring and analyzing individuals. Thus, it may be fair to argue that comparisons between idiographic and nomothetic data structures offer limited value. To this end, we do not diverge from Hamaker and Ryan's position. However, we should clarify that the repeated sampling paradigm we used explicitly avoids the problem of an asymptotically error-free estimate under infinite sampling conditions. The variability around the cross-sectional correlation estimate is the degree to which that estimate varies within the sampled population over time. Taken to the extreme, measuring a bivariate correlation in the entire human population at one time point would return a cross-sectional estimate without error. However, measuring the same bivariate correlation in the entire human population repeatedly would produce a distribution of estimates with a central tendency and a non-zero SD-the degree to which each measurement varied from the average across time points. Consequently , our estimate is not a proxy for the SE of the cross-sectional correlation estimate or for within-individual correlations, but a third representation, which estimates within-sample temporal instability in cross-sectional estimates