Covariance of Totals :: SAS/STAT(R) 13.1 User's Guide

Covariance of Totals

The covariance matrix of the table cell totals $\widehat{N}_{rc}$ is an $rc \times rc$ matrix $\widehat{\mb {V}}(\widehat{\mb {N}})$ , which contains the pairwise table cell covariances $\widehat{\mr {Cov}}(\widehat{N}_{rc}, ~ \widehat{N}_{ab})$ , for $r = 1, \cdots , R$ ; $c = 1, \cdots , C$ ; $a = 1, \cdots , R$ ; and $b = 1, \cdots , C$ .

PROC SURVEYFREQ estimates the covariances by using the variance estimation method that you request. If you request BRR variance estimation (by specifying the VARMETHOD=BRR option in the PROC SURVEYFREQ statement), the procedure estimates the covariances by the method described in the section Balanced Repeated Replication (BRR). If you request jackknife variance estimation (by specifying the VARMETHOD=JACKKNIFE option), the procedure uses the method described in the section The Jackknife Method.

Otherwise (by default, or if you request the Taylor series method), PROC SURVEYFREQ estimates the covariance between total frequency estimates for table cells (r, c) and (a, b) as

$\widehat{\mr {Cov}}(\widehat{N}_{rc}, ~ \widehat{N}_{ab}) = \sum _{h=1}^ H { \left( \frac{n_ h(1-f_ h)}{n_ h-1} ~ \sum _{i=1}^{n_ h} (n_{rc}^{~ hi} - \bar{n}_{rc}^{~ h}) ~ (n_{ab}^{~ hi} - \bar{n}_{ab}^{~ h}) \right) }$

The SURVEYFREQ Procedure

Covariance of Totals