![]() ![]() The τ 2 parameter is also called the intraclass correlation coefficient. These " expected mean squares" can be used as the basis for estimation of the "variance components" σ 2 and τ 2. Let Y ij be the score of the jth pupil at the ith school. Their scores on a standard aptitude test are ascertained. Suppose also that n pupils of the same age are chosen randomly at each selected school. Suppose m large elementary schools are chosen randomly from among thousands in a large country. If the random effects assumption holds, the random effects estimator is more efficient than the fixed effects model. The fixed effect assumption is that the individual specific effect is correlated with the independent variables. The random effects assumption is that the individual unobserved heterogeneity is uncorrelated with the independent variables. Two common assumptions can be made about the individual specific effect: the random effects assumption and the fixed effects assumption. This constant can be removed from longitudinal data through differencing, since taking a first difference will remove any time invariant components of the model. Random effect models assist in controlling for unobserved heterogeneity when the heterogeneity is constant over time and not correlated with independent variables. Not to be confused with Random coefficient model. ![]()
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