The factor in the computation of the matrix reduces the small sample bias associated with using the estimated function to calculate deviations (Morel, 1989; Hidiroglou, Fuller, and Hickman, 1980). For simple random sampling, this factor contributes to the degrees-of-freedom correction applied to the residual mean square for ordinary least squares in which p parameters are estimated. By default, the procedure uses this adjustment in Taylor series variance estimation. It is equivalent to specifying the VADJUST=DF option in the MODEL statement. If you do not want to use this multiplier in the variance estimation, you can specify the VADJUST=NONE option in the MODEL statement to suppress this factor.
In addition, you can specify the VADJUST=MOREL option to request an adjustment to the variance estimator for the model parameters , introduced by Morel (1989):
where for given nonnegative constants and ,
The adjustment does the following:
reduces the small sample bias reflected in inflated Type I error rates
guarantees a positive-definite estimated covariance matrix provided that exists
is close to zero when the sample size becomes large
In this adjustment, is an estimate of the design effect, which has been bounded below by the positive constant . You can use DEFFBOUND= in the VADJUST=MOREL option in the MODEL statement to specify this lower bound; by default, the procedure uses . The factor converges to zero when the sample size becomes large, and has an upper bound . You can use ADJBOUND= in the VADJUST=MOREL option in the MODEL statement to specify this upper bound; by default, the procedure uses .