Panel (data) analysis is a statistical method, widely used in social science, epidemiology, and econometrics to analyze two-dimensional (typically cross sectional and longitudinal) panel data. The data are usually collected over time and over the same individuals and then a regression is run over these two dimensions. Multidimensional analysis is an econometric method in which data are collected over more than two dimensions (typically, time, individuals, and some third dimension).

A common panel data regression model looks like ${\displaystyle y_{it}=a+bx_{it}+\varepsilon _{it}}$, where ${\displaystyle y}$ is the dependent variable, ${\displaystyle x}$ is the independent variable, ${\displaystyle a}$ and ${\displaystyle b}$ are coefficients, ${\displaystyle i}$ and ${\displaystyle t}$ are indices for individuals and time. The error ${\displaystyle \varepsilon _{it}}$ is very important in this analysis. Assumptions about the error term determine whether we speak of fixed effects or random effects. In a fixed effects model, ${\displaystyle \varepsilon _{it}}$ is assumed to vary non-stochastically over ${\displaystyle i}$ or ${\displaystyle t}$ making the fixed effects model analogous to a dummy variable model in one dimension. In a random effects model, ${\displaystyle \varepsilon _{it}}$ is assumed to vary stochastically over ${\displaystyle i}$ or ${\displaystyle t}$ requiring special treatment of the error variance matrix.

Panel data analysis has three more-or-less independent approaches:

• independently pooled panels;
• random effects models;
• fixed effects models or first differenced models.

The selection between these methods depends upon the objective of the analysis, and the problems concerning the exogeneity of the explanatory variables.