Random effects estimator

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In statistics, a random effects estimator is an estimator for the coefficients in multiple comparisons model in which the effects of different classes are random. In econometrics, random effects models are used in analysis of hierarchical or panel data when one assumes no fixed effects, i.e. no individual effects. The estimation is via generalized least squares (GLS).

1 Model
2 Estimator
3 See also
4 External links

[edit] Model

$y_{it}=x_{it}\beta+\alpha_{i}+u_{it},\,$

where $y i t$ is the dependent variable, $x i t$ is the vector of regressors, $β$ is the vector of coefficients, $α i = α$ are the random effects, and $u i t$ is the error term.

[edit] Estimator

The coefficients can be estimated via

$\widehat{\beta}=(X'\Omega^{-1} X)^{-1}(X'\Omega^{-1}Y),$

$\widehat{\Omega}^{-1}=\Iota \otimes \Sigma,$

where X and Y are the matrix version of the regressor and independent variable, respectively, $Ι$ is the identity matrix, $Σ$ is the variance of $u i t$ and $α$ , and $Ω$ is the variance-covariance matrix.