General Variance Covariance Structures in Two-Way Random Effects Models

Carlos De Porres, Jaya Krishnakumar
2013 Applied Mathematics  
This paper examines general variance-covariance structures for the specific effects and the overall error term in a twoway random effects (RE) model. So far panel data literature has only considered these general structures in a one-way model and followed the approach of a Cholesky-type transformation to bring the model back to a "classical" one-way RE case. In this note, we first show that in a two-way setting it is impossible to find a Cholesky-type transformation when the error components
more » ... e a general variance-covariance structure (which includes autocorrelation). Then we propose solutions for this general case using the spectral decomposition of the variance components and give a general transformation leading to a block-diagonal structure which can be easily handled. The results are obtained under some general conditions on the matrices involved which are satisfied by most commonly used structures. Thus our results provide a general framework for introducing new variance-covariance structures in a panel data model. We compare our results with [1] and [2] highlighting similarities and differences. 1 We show that these conditions are satisfied in almost all usually assumed structures and these conditions do not imply a rewriting of the three component variance matrix as a two component one. Thus we do go beyond a two component structure. C. DE PORRES, J. KRISHNAKUMAR 616 2 Note that given in this lemma represents the variance-co-, ,N   Ω variance matrix of an equicorrelated error structure.
doi:10.4236/am.2013.44086 fatcat:btfqk4mj7za2fjyrpxnajpwilm