How to state 'fpc' in Stata with multistage sampling with PPS?

[Deepani Siriwardhana]

Hello!

I'm having problems with stating fpc in three stage sampling design. I went through the example given in the Stata manual; Example 2: Multistage survey data (use http://www.stata-press.com/data/r15/multistage) and it seems they have used random sampling to select PSUs and SSUs in two-stage sampling design.

I used Probability Proportionate to Size technique to select PSUs and SSUs (stage 1 and stage 2) and stratified random sampling at stage 3. I wonder how to specify the fpc in my case. Much appreciated your input.

Please see below for detailed explanation of my sampling technique.

I managed to recruit 746 participants using a three stage sampling design. My targeted sample was 750 participants.

Stage 1 – Selected 6 DS areas (PSUs) from 11 DS areas using probability proportionate to size technique (PPS) (the total population in 11 DS areas and 6 selected DS areas are 125069 and 72704 respectively)
These selected 6 DS areas comprised of 327 GN areas and each DS areas has varying number of GN areas.
Stage 2- Selected 50 GN areas (SSUs) out of 327 GN areas using PPS technique (the total population in 327 GN areas and 50 selected GN areas are 72704 and 12185 respectively)

Stage 3- Selecting 15 individuals using stratified random sampling from each GN area. These individuals were selected from 10 strata (age bands; (60-64, 65-69, 70-74, 75-79, 80+ by sex).

I calculated the sampling weight for each participant considering their selecting probabilities at each stage and adjusted by sex and age bands using post-stratification option.

However, I wonder how to specify the fpc for each stage. I have come up with 3 different options

Stage 1
fpc1=72704/125069 (or fpc1 should be 6/11 or 11???)

Stage 2
fpc2=12185/72704 (or fpc2 should be 50/327 or total no of SSUs in a given PSU so 6 different fpc values???)

Stage 3
fpc3=750/12185 or total number of participants in a given SSU so 50 different fpc values


I look forward to hearing from you.

Thanks.

Deepani

[Steve Samuels]

Stata requires that there be a single fpc value in each stratum, so your "6 different fpc values" wouldn't work-you have only one stratum for the first stage. Ouyang, Schreuder, and Boes (1997, p 3)) state that \(fpc = \dfrac{n}{N}\) is a conservative compromise for a single stage sample. I recommend that you use that at each stage. So: 6/11 at Stage 1 and so on.

Reference:
Ouyang, Z., Schreuder, H. T., & Boes, D. C. (1997). Finite population corrections of the Horvitz-Thompson estimator and their application in estimating the variance of regression estimators. USDA Forest Service Research Paper, RM-RP-329

https://ia802701.us.archive.org/14/items/IND20577930/IND20577930.pdf.

[Deepani Siriwardhana]

Thanks for the clear explanation and reference Steve.