The SURVEYSELECT Procedure

PPS Sampling with Replacement

If you specify the METHOD=PPS_WR option, PROC SURVEYSELECT selects units with probability proportional to size and with replacement. The procedure makes n Subscript h independent random selections from the stratum of upper N Subscript h units, selecting with probability upper Z Subscript h i Baseline equals upper M Subscript h i Baseline slash upper M Subscript h dot. Because units are selected with replacement, a unit can be selected for the sample more than once. The expected number of hits (selections) for unit i in stratum h is n Subscript h Baseline upper Z Subscript h i. If you specify the JTPROBS option, PROC SURVEYSELECT computes the joint expected number of hits for all pairs of selected units in each stratum. The joint expected number of hits for units i and j in stratum h is

upper P Subscript h left-parenthesis i j right-parenthesis Baseline equals StartLayout Enlarged left-brace 1st Row 1st Column n Subscript h Baseline left-parenthesis n Subscript h Baseline minus 1 right-parenthesis upper Z Subscript h i Baseline upper Z Subscript h j Baseline 2nd Column normal f normal o normal r j not-equals i 2nd Row 1st Column n Subscript h Baseline left-parenthesis n Subscript h Baseline minus 1 right-parenthesis upper Z Subscript h i Baseline upper Z Subscript h i Baseline slash 2 2nd Column normal f normal o normal r j equals i EndLayout
Last updated: December 09, 2022