The SURVEYFREQ Procedure

Covariances of Frequency Estimates

The covariance matrix of the table cell frequency estimates is an r c times r c matrix that contains the pairwise cell frequency covariances. ModifyingAbove bold upper V With caret left-parenthesis ModifyingAbove bold upper N With caret right-parenthesis denotes the covariance matrix and ModifyingAbove normal upper C normal o normal v With caret left-parenthesis ModifyingAbove upper N With caret Subscript r c Baseline comma ModifyingAbove upper N With caret Subscript a b Baseline right-parenthesis denotes the pairwise covariances, for r equals 1 comma ellipsis comma upper R; c equals 1 comma ellipsis comma upper C; a equals 1 comma ellipsis comma upper R; and b equals 1 comma ellipsis comma upper C.

PROC SURVEYFREQ estimates the covariances by using the variance estimation method that you request. If you request a replication method (bootstrap, BRR, jackknife, or replicate weights), the procedure estimates the covariances as described in the section Replication Variance Estimation.

By default, or if you request Taylor series variance estimation, PROC SURVEYFREQ estimates the covariance between frequency estimates for table cells (r,c) and (a,b) as

ModifyingAbove normal upper C normal o normal v With caret left-parenthesis ModifyingAbove upper N With caret Subscript r c Baseline comma ModifyingAbove upper N With caret Subscript a b Baseline right-parenthesis equals sigma-summation Underscript h equals 1 Overscript upper H Endscripts left-parenthesis StartFraction n Subscript h Baseline left-parenthesis 1 minus f Subscript h Baseline right-parenthesis Over n Subscript h Baseline minus 1 EndFraction sigma-summation Underscript i equals 1 Overscript n Subscript h Baseline Endscripts left-parenthesis n Subscript r c Superscript h i Baseline minus n overbar Subscript r c Superscript h Baseline right-parenthesis left-parenthesis n Subscript a b Superscript h i Baseline minus n overbar Subscript a b Superscript h Baseline right-parenthesis right-parenthesis
Last updated: December 09, 2022