What is/are the difference(s) between a longitudinal design and a time series?
Longitudinal Design vs Time Series – Understand Key Differences
panel datatime series
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I doubt there are strict, formal definitions that a wide range of data analysts agree on.
In general however, time series connotes a single study unit observed at regular intervals over a very long period of time. A prototypical example would be the annual GDP growth of a country over decades or even more than a hundred years. For an analyst working for a private company, it might be monthly sales revenues over the life of the company. Because there are so many observations, the data are analyzed in great detail, looking for things like seasonality over different periods (e.g., monthly: more sales at the beginning of a month just after people have been paid; yearly: more sales in November and December, when people are shopping for the Christmas season), and possibly regime shifts. Forecasting is often very important, as @StephanKolassa notes.
Longitudinal typically refers to fewer measurements over a larger number of study units. A prototypical example might be a drug trial, where there are hundreds of patients measured at baseline (before treatment), and monthly for the next 3 months. With just 4 observations of each unit in this example, it is not possible to try to detect the kinds of features time series analysts are interested in. On the other hand, with patients presumably randomized into treatment and control arms, causality can be inferred once the non-independence has been addressed. As that suggests, often the non-independence is considered almost a nuisance, rather than the primary feature of interest.
Usually you want to forecast the behaviour of a system to improve your reaction to and interaction with that system. But at the end of the day, forecasting is only a last resort, if it is not feasible to control the system. Moreover, forecasting with nothing but time series is something you usually only do if your system is so complex that you cannot incorporate any useful other knowledge about it into your forecasts.
Time-series analysis gives you a lot of methods to understand the inner workings of a system, which in turn may be the first step to controlling it. For example, it may yield the following information:
- What are the internal rhythms of the system and what is their relevance to my observable?
- To what extent is my system noise-dominated and how does that noise look like?
- Is the system stationary or not – the latter being an indicator for long-term changes of external conditions influencing the system.
- If I regard my system as a dynamical system, what are the features of the underlying dynamics: Is it chaotic or regular? How does it react to perturbations? How does its phase space look like?
- For a system with multiple components: Which components interact with each other?
- How do I model my system if I want my model to do more than just reproduce certain features of observed time series, such as yielding an understanding of the system, properly describing situations that are not comparable to anything that has been observed in the past at all, e.g., when I actively manipulate the system or an extreme event happens (such as in a disaster simulation). All of the above points can play into this and moreover, time-series analysis can be used to verify a model by comparing the time series of the original and the model.
Some practical examples:
- Climate research employs a lot of time-series analysis but is not only good for forecasting climate but also tries to answers the important question of how we influence our climate.
- If you have a time series related to the illness of an individual female patient and you find a strong frequency component of roughly one month, this is a strong hint to the menstrual cycle being somehow involved. Even if you fail to understand this relation, and can only treat the symptoms by giving some medication at the right time, you can benefit from taking the actual menstrual cycle of that patient into account (this is an example were you forecast with more than just time series).
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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.