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st: Jackknife with clustered survey data

From   "James Shaw" <>
Subject   st: Jackknife with clustered survey data
Date   Sat, 24 Mar 2007 13:28:06 -0400

I have a question about variance estimation with survey data. The -svr- commands in Stata can be used to analyze complex survey data with replication methods such as the jackknife. I am working with a multi-stage sample of the US population. The first-stage sampling was performed without replacement (WOR). Since the sampling fraction was small (<10%), I should be able to analyze the data as though sampled with replacement (WR). The first stage units were also selected with unequal probabilites using a probability proportional to size (PPS) algorithm. The second-stage units (survey respondents) were selected randomly, and there is no stratification.

I have read (in the manual for SUDAAN) that the jackknife variance estimator is applicable when:

(1) WR sampling is used at the first stage or the sampling fraction is small in every first-stage stratum.
(2) WR or WOR sampling is used at subsequent stages.
(3) Sampling is performed with equal or unequal probabilities of selection at both the first and subsequent stages.

I thought that the jackknife assumes WR sampling AND equal probabilities of selection. Can anyone tell me why the jackknife would still be applicable when the first stage sampling was done using PPS (with unequal selection probabilities in a single first-stage stratum)? Thanks!

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