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The TSCSREG Procedure |

If the effects are fixed, the models are essentially regression models with dummy variables corresponding to the specified effects. For fixed effects models, ordinary least squares (OLS) estimation is best linear unbiased.

The other alternative is to assume that the effects are random. In the one-way case, , , and

for , and is uncorrelated with
for all *i* and *t*.
In the two-way case, in addition to all of the preceding,
*E*(*e*_{t}) = 0, , and

*E*(*e*_{t} *e*_{s}) = 0 for , and the
*e*_{t} are uncorrelated with
the and the for all *i*and *t*.
Thus, the model is a variance components
model, with the variance components
and
,
as well as ,
to be estimated.
A crucial implication of such a specification is that the effects are
independent of the regressors.
For random effects models, the estimation
method is an estimated generalized least squares (EGLS) procedure that
involves estimating the variance components in the first stage and
using the estimated variance covariance matrix thus obtained
to apply generalized least squares (GLS) to the data.

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