In search of the lost individual: Four theorems regarding the aggregation of processes

Based on the formulation of four theorems, the aim of this article is to discuss problems of the aggregation/disaggregation of processes and to point to possible solutions. Theorem 1 shows that in most cases one cannot draw valid conclusions from univariate aggregate curves to the underlying individual trajectories. Theorem 2, dealing with synchronous bivariate processes, points to differences between intra- and interindividual relationships. A formula describes the relation between both kinds of correlations. Theorem 3 deals with asynchronous relationships. It is demonstrated that the results of cross-lagged-panel analyses in longitudinal studies can be very different compared to the individual asynchronous relationships. Theorem 4 about the sequence of aggregation and prediction is presented to underline the priority of an microanalytic (intraindividual) approach in comparison with a macroanalytic (interindividual) approach. In conclusion, it is argued that research designs combining idiographic and nomothetic strategies could offer a solution to the aggregation problems described.