Yiannis -
You said you want "...a stratified sample of clusters with pps and then a fixed size simple random sample of cluster members." Do you really mean you want a two-stage sample, where the first stage is pps (which assumes a certain variance structure) and the second stage is a simple random sample - which is what actually applies to members within each selected cluster? (This would mean you are not actually using stratification, unless you are doing that first and the two-stage sampling applies to each stratum.) If so, then perhaps section 4.3, pages 133-144 of Särndal, CE, Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling, Springer-Verlang might be helpful. Also, Chapter 11 in Cochran, W.G(1977), Sampling Techniques, 3rd ed., John Wiley & Sons may be useful for you. - Sorry if I misunderstood, and/or you are already familiar with all of that. Perhaps someone else could point out something more applicable.
Cheers - Jim
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James Knaub
Lead Mathematical Statistician
Retired
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Original Message:
Sent: 11-26-2017 15:21
From: Yiannis Bassiakos
Subject: ICC in pps cluster sampling
Dear colleagues,
I would like to know if there is any article or book that presents the calculation of itnracluster correlation in two-stage stratified cluster sampling (i.e. a stratified sample of clusters with pps and then a fixed size simple random sample of cluster members), in a clear manner with some examples . Is the formula ICC=(variance between)/(variance between + variance within) still valid or (since the sample is pps and nor srs) something else must be done?
Yiannis C. Bassiakos
-- ************************************ ?????????????? ??. ??????????????????, ?????????????????????? ??????????????????, ??????, ???????? ???????????????????? 1, ?????????????????? 6???? ????????????, ?????????????? 611, ??????. 210.368.9491 Yiannis C. Bassiakos Associate Professor, DoE, UoA 1 Sofokleous street, 15509, Athens, GREECE tel. +30210.368.9491 mob. +30697.419.2133 Skype: yiannis.c.bassiakos