What is panel data and how does it relate to other data in psychology?

What's in a term? 

In psychology, the terms 'repeated measures data' and 'repeated measures analysis' are commonly used terms, usually introduced as part of undergraduate level data analysis. By contrast, panel data or panel data models are usually less familiar terms and may seem like relatively advanced or specialised topics that are borrowed from fields like econometrics where they are more commonly used. 

In fact, repeated measures data and panel data are, at least at certain level of abstraction, essentially synonymous terms. They are also both synonymous with longitudinal data. As such, repeated measures, panel, and longitudinal data analyses are all essentially one and the same thing. 

Identifying the appropriate method of analysis 

In practice, however, exactly which method of analysis to use to analyse any given repeated measures, longitudinal, or panel data depends on the precise details of the data and, more importantly, on the precise research questions being pursued in the analysis. Depending on these details, there may be different, and better or worse, choices for the analysis. Some of these options may look like typical repeated measures analyses that are commonly used in psychology. Others may look like typical panel data analysis methods as seen in econometrics and elsewhere. Yet other methods, with names like mixed effects models, multilevel models, latent growth curve analysis, and many others, are available too. 

In this blog post, we provide a brief overview of this kind of data and its methods of analysis and how these methods are related to one another. 

Repeated measures data 

In psychology, we are very familiar with repeated measures data, particularly in the context of behavioural experiments. If, for example, in a cognitive psychology experiment, we are investigating how different types of background music, such as classical, pop, electronic, etc affect performance levels on some cognitive task, and each participant performs the task when listening to each of the different music types, then obviously for each participant, we obtain multiple observations of the dependent variable (performance of the cognitive task), one for each level of the independent variable (background music type). 

Formally, each value of the dependent variable could be written as a variable with a double subscript, such as y^jk, where j ∈ 1,2…J is the index that identifies the participant, and k ∈ 1,2…K is the index that identifies the level or condition of the music type independent variable. A typical method of analysis of this data would be a one-way repeated measures analysis of variance. 

This is a type of mixed-effect general linear model whose main equation is, for each j and k, y^jk = θ + s^j + u^k + ϵ^jk, where θ is the overall average, s^j is a random effect associated with participant j (and in effect, models the within-participant correlations), u^k is the effect associated with each level of the independent variable, and ϵ^jk is a normally distributed error term.

The main focus of this model is to see if there is a significant effect of the independent variable, which effectively tests if u¹ = ⋯ = u^k = ⋯ = u^K = 0. 

Panel data 

In econometrics and other disciplines, panel data and panel data analysis are common.

A typical example from econometrics might be where we are looking at house prices across different cities and different years and how they vary by predictor variables that may vary across cities, or across years, or across both simultaneously.

If y^jk represents the average house price in city j in year k, a model of how average house price varies by the average income in city j and year k, denoted x^jk, might be as mixed effects model as follows:

• y^jk = θ + α^j + γ^k + β^xjk + ϵ^jk, where α^j and γ^k are random effects associated with cities and years, respectively, and ϵ^jk is a normal error term

The primary focus of this analysis might be on the value of β, which tells us how average house prices change with average incomes. 

How are these methods of analysis related? 

Obviously, the task performance data in the first example and the house price data in the second are formally identical: both are variables that vary along two different indices or dimensions, participants and experimental conditions in the first example, cities and years in the second. The models used in both analyses are also similar, both being types of mixed effects linear models. 

Also obvious is that panel data is just an example of what would otherwise be called longitudinal data, which is where we have values for a set of different entities, such as cities, countries, people, etc., at different points in time. As such, panel data is just longitudinal data, and so panel data analysis is just longitudinal data analysis, and this type of data is formally identical to repeated measures data, and similar methods of analysis can be used in all of these cases. All of this is not to say that any method of analysis used for repeated measures, panel, or longitudinal data can be used as a drop-in replacement for any other. 

For example, a repeated measure analysis of variance cannot simply be used for any and all longitudinal data analysis, and some of the more complex models for longitudinal data analysis, such as latent growth analysis, would be unnecessarily complex for some repeated measures problems. 

Details concerning the nature and number of the various explanatory or covariate variables can make a difference about which method to choose, as can assumptions on how the dependent or outcomes variable vary according to these variables, as can the precise focus of the research question. In general, there are very many available options to choose from, but ultimately these methods can be seen as variants, extensions, or simplifications of one another. 

• Mark Andrews, Deputy Chair of the BPS Statistics and Research Methods Advisory Panel Nottingham Trent University, UK