What is/are the difference(s) between a longitudinal design and a time series?
I will add that in time series context it is usually assumed that data observed is a realisation of stochastic process. Hence in time series a lot of attention is given to properties of stochastic processes, such as stationarity, ergodicity, etc. In longitudinal context in my understanding data comes from usual samples (by sample I mean sequence of iid variables) observed at different points in time, so classical statistic methods are applied, since they always assume that sample is observed.
For short answer, one might say that time series are studied in econometrics, longitudinal design -- in statistics. But that does not answer the question, just shifts it to another question. On the other hand a lot of short answers do exactly that.
If we think of designs made up of $n$ cases measured on $k$ occasions, then the following loose definition seems to me to be descriptive of the distinction:
- longitudinal designs: high $n$, low $k$
- time series: low $n$, high $k$
Of course, this raises the question of what is high and what is low. Summarising my own rough sense of these fuzzy definitions, prototypical examples of:
- time series might have $n$ = 1, 2, or 5 and $k$ = 20, 50, 100, or 1000, and
- longitudinal designs might have $n$ = 10, 50, 100, 1000 and $k$ = 2, 3, 5, 10, 20
Update: Following up on Dr Who's question about what is the purpose of the distinction, I don't have an authoritative answer, but here are a few thoughts:
- terminology evolves in disciplines concerned with particular substantive problems
- time series
- often concerned with forecasting future time points
- often concerned with modelling various cyclical and trend processes
- often concerned with describing temporal dynamics in great detail
- often studies phenomena where the particular thing measured is of specific interest (e.g., unemployment rate, stock market indices, etc.)
- temporal indices are often pre-existing
- longitudinal designs:
- often use samples of cases as exemplars of a population in order to make inferences about the population (e.g., sample of children to study how children change in general)
- often concerned with fairly general temporal processes like growth, variability and relatively simple functional change models
- study is often specifically designed to have a given number of time points.
- often interested in variation in change processes
Given the differences in the actual temporal dynamics, and the particular combination of $k$ and $n$ this creates different statistical modelling challenges. For example, with high $n$ and low $k$ multilevel models are often used that borrow strength from the typical change process to describe the individual change process. These different disciplines, modelling challenges, and literatures encourage the creation of distinct terminology.
Anyway, that's my impression. Perhaps others have greater insight.
A time series is simple a sequence of data points spaced out over time, usually with regular time intervals. A longitudinal design is rather more specific, keeping the same sample for each observation over time.
An example of a time series might be unemployment measured every month using a labour force survey with a new sample each time; this would be a sequence of cross-sectional designs. But it could be anything such as your personal savings each year, which would also be longitudinal. Or it might simply follow a particular cohort of people growing older, such as the television documentary Seven Up! and the sequels every seven years after that - the latest was 49 Up in 2005, so there should be another edition next year. Longitudinal designs tend to tell you more about ways in which typical individuals change over time, but might (depending on the details of the design and whether the sample is refreshed) say less about how the population as a whole changes.
Time-series data are assessed at regular intervals for a long period of time. Whereas longitudinal data are not: the repeated measures are for a short period of time. That is data collection can stop / be terminated at a certain point in time to do the analysis or when the measures satisfies the researcher in terms of behavioural change.