Intensive Longitudinal Methods

Intraindividual Variation (IAV) Versus Interindividual Variation (IEV)

The availability of many repeated observations obtained in intensive longitudinal designs raises the issue of the relation between IAV and IEV. Here, IAV refers to variation within a person, and IEV refers to variation between persons. These two kinds of variation are logically independent, as is clear in a thought experiment. Consider a circadian (showing a 24-hour rhythm) process that undergoes periodic ups and downs, always peaking at noon or midnight. The IAV is substantial because there are large changes within the individual, but the IEV is zero as all individuals change in synchrony. In contrast, consider an individual difference trait that is invariant or equivalent across time; the IAV is zero because the trait does not vary within a person, but the IEV is substantial because different people possess different levels of this stable trait.

These thought experiments give rise to an important question: What is the relation between results obtained in analysis of IEV and analysis of IAV of the same replicated time series data obtained in an intensive longitudinal study? The analysis of IEV would pool across replications, whereas in an analysis of IEV, each replication would be [Page 1177]considered separately. Ergodic theory, a branch of mathematics dealing with statistical physics and equivalence of processes, can be used to determine whether these different levels of analysis are equivalent. Only if a process obeys, strict criteria are results obtained in analysis of IEV and IAV equivalent. For normally distributed processes, there are two criteria. First, the process has to have a constant level, constant variance, and sequential dependencies that are constant for time intervals of same length; this equivalence across time is called stationarity. Second, each replication should obey the same dynamic model; this equivalence across people is called homogeneity. Most processes fail to obey one or both of these criteria and therefore are referred to as nonergodic because they have inequivalent processes.

Results obtained in analysis of IEV apply at the level of the populations sampled; analogous results obtained in analysis of IAV apply at the level of individuals. The goal of intensive longitudinal data analysis is to obtain results that validly apply at both levels. For nonergodic processes, this generalizability of results to both levels requires the application of special techniques (summarized in the following).

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