Panel analysis

Panel (data) analysis is a statistical method, widely used in social science, epidemiology, and econometrics, which deals with two and "n"-dimensional (in and by the - cross sectional/times series time) 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 ${\displaystyle y_{it}=a+bx_{it}+\epsilon _{it}}$, where y is the dependent variable, x is the independent variable, a and b are coefficients, i and t are indices for individuals and time. The error ${\displaystyle \epsilon _{it}}$ 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, ${\displaystyle \epsilon _{it}}$ 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, ${\displaystyle \epsilon _{it}}$ is assumed to vary stochastically over ${\displaystyle i}$ or ${\displaystyle t}$ requiring special treatment of the error variance matrix.

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