The SURVEYREG Procedure
- Overview
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Getting Started
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Syntax
PROC SURVEYREG Statement BY Statement CLASS Statement CLUSTER Statement CONTRAST Statement DOMAIN Statement EFFECT Statement ESTIMATE Statement LSMEANS Statement LSMESTIMATE Statement MODEL Statement OUTPUT Statement REPWEIGHTS Statement SLICE Statement STORE Statement STRATA Statement TEST Statement WEIGHT Statement
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Details
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Examples
- References
Taylor Series (Linearization)
The Taylor series (linearization) method is the most commonly used method to estimate the covariance matrix of the regression coefficients for complex survey data. It is the default variance estimation method used by PROC SURVEYREG.
Use the notation described in the section Notation to denote the residuals from the linear regression as
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with 
as its elements. Let the 
matrix 
be defined as
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where
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The Taylor series estimate of the covariance matrix of 
is
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The factor 
in the computation of the matrix reduces the small sample bias associated with using the estimated function to calculate deviations (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 
parameters are estimated. By default, the procedure use this adjustment in the variance estimation. If you do not want to use this multiplier in variance estimation, you can specify the VADJUST=NONE option in the MODEL statement to suppress this factor.