Multiple Estimators for Longitudinal Data
Multilevel Models, Random Effects, Fixed Effects, and Correlated Random Effects
All estimators use essentially the same equation:
\[y_{it} = \beta_0 + \beta_1 x_{it} + \beta_2 z_{it} + u_{0i} + e_{it} \tag{1}\]
Some estimators divide \(x_{it}\) into a within component (\(x_{it} - \overline{x}_i\)), and a between (\(\overline{x}_i - \overline{x}\)) component.
Multilevel Models estimate Equation 1. Both within and between variation is included in the estimates of \(\beta\).
Random Effects Models estimate Equation 1. Both within and between variation is included in the estimates of \(\beta\).
Between Effects Models (rarely used) estimate Equation 1. Only between variation is included in the estimates of \(\beta\).
Fixed Effects Models estimate Equation 1. Only within variation is included in the estimates of \(\beta\).
Correlated Random Effects Models estimate Equation 1. Separate \(\beta\) parameters are provided for within and between variation.