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From |
Steven Samuels <sjhsamuels@earthlink.net> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: variance when using svy: mean |

Date |
Mon, 3 Dec 2007 13:52:24 -0500 |

You are very welcome. One observation and 10 observations per psu will not give the -same- precision; increasing the number of observations will decrease the standard error, but there is a limit, depending on the relative variation within-and between- psu's. Theory can help determine the optimal balance between the number of psu's and the number of observations to take from each. The formulas take into account the relative cost of working in a new psu versus the cost of taking an additional observation once you are in the psu.

I'm still not sure that you took a simple random sample, as this requires a finite population to begin with. Still, it sounds like you are on the right track.

Good luck!

Steve

On Dec 3, 2007, at 1:26 PM, David Merriman wrote:

Thanks, I am understanding better. Within each area I took a random (iid) sample from an infinite population. The sample sizes varied for reasons that are contextual and difficult to explain without telling you all the details of the project. (Can you help me w'ith the computer code here? How do I tell stata that I took a random sample within psus?) So, if I understand you correctly the variance of my estimate of the population mean is roughly independent of how many observations I have. In other words, if I had gone to 100 different areas and collected a single sample I would estimate the population mean with about the same precision as if I had collected 10 samples within each area? I still have trouble getting my mind around that but your example with a Census of the two areas does help. Thanks again. On Dec 3, 2007 12:08 PM, Steven Joel Hirsch Samuels <sjhsamuels@earthlink.net> wrote:Thanks, David that is clearer. Was there a sampling procedure within areas? If not, you can still apply the -svy- commands, but without a sampling procedure of some kind, the observations within a single area may not 'represent' that area in any statistical sense. In any case, the major portion of the variance of sample estimates will still arise from PSU-to-PSU variation. The effective sample size is 100, the number of PSU's. Thought experiment: you take a sample of n= 2 areas and collect information about everybody (a census). Even if the number of observations is 200,000, your effective sample size is still n=2 for making inferences about the original population. As long as the two area means are different, the standard error will be nonzero. Your simulations are therefore correct in producing the same standard error for the two PSU's. If you had simulated sampling within the PSU's, then the you would the SE's to change, as the sample proportions would vary from simulation to simulation. -Steven 4. The sampling weight for a PSU On Dec 3, 2007, at 12:21 PM, David Merriman wrote:Thanks. I do have a lot of trouble with the terminology.

I selected a weighted random sample of 100 geographic areas from 930

such areas. The weights were designed so that my weighted random

sample would be representative of the population (e.g. I oversampled

areas with a high number of people). I do not think I have any strata

(I did NOT for example oversample high poverty areas). My psus are

the 100 geographic areas.

I am afraid I still do not know what to do next. It sounds like you

are saying that the variance should not differ between my two cases

but this does not make intuitive sense to me. Any help you can

provide would be appreciated.

On Dec 3, 2007 11:11 AM, Steven Joel Hirsch Samuels

<sjhsamuels@earthlink.net> wrote:

David, it doesn't sound like your study is a probability sample; if

not, you don't need -svy- commands. Instead, use non-survey

commands and assign an -iweight- or other weight variable to

properly represent your population.

If your data do arise from a probability sample, your 'areas' appear

to be strata, not primary sampling units (psu's). Strata are units

which partition a population. A psu is the highest stage unit

selected by random numbers within a stratum. Standard errors for

survey data depend mainly on the number of psu's, not on the number

of observations within them.

-Steven

On Dec 3, 2007, at 11:19 AM, David Merriman wrote:

Dear Statalisters:

I am a long time Statauser but new to svy: commands and am quite

confused.

I apologize if this is long-winded I am trying to say it as

concisely

as possible.

I have collected primary data in several geographic areas. Each of

the geographic areas has a different weight so that my entire sample

should be representative of the population. In each geographic

area I

have collected a number of observations but the number of

observations

in the area tells me nothing about the density of the activit

area. I want to estimate the population mean (for all geographic

areas) and the variance of that estimate. The problem is that

while I

get sensible means the variances do not seem to be a function of the

number of observations I have. Intuitively I think that the

variance

ought to change (fall) as the number of observations increases.

I tried using

svyset psuedo_psu [pweight=obs_weight]

svy: mean psuedo_chicago_tax_paid

where psuedo_psu is the variable indicating the primary sampling

unit,

obs_weight is the psu_weight divided by the number of

observations in

that psu and psuedo_chicago_tax_paid is the (zero-one) variable for

which I want to estimate the mean and variance.

I created a simulated data set (the real one is more complex) with 2

psus. In the first trial, each psu had 50 observations. psu 1

had a

weight of 1 and a 50 percent chance of a 1. psu 2 had a weight of 5

and a 20 percent chance of a 1. I get a sensible mean of .25 and a

standard error of .0833333.

In the second trial, I also had two psu. Psu 1 has 900 observations

and psu 2 has 100 observations. psu 1 had a weight of 1 and a 50

percent chance of a 1. psu 2 had a weight of 5 and a 20 percent

chance of a 1. I get a sensible mean of .25 but the same standard

error of .0833333 as in case 1. This does not make sense to me. I

have more observations in case 2 so I think I should get a smaller

variance.

I imagine I am not using the correct design. Can anyone help?

Below,

I show the computer code for my simulation (fake data set) but you

don't need to read this if you understand the comments above.

Thanks

so much.

#delimit ;

****************************************************************

* created the simulated data

***********************************************************;

set obs 100;

****************************************************************

* generate psu

***********************************************************;

gen psuedo_psu=1 if _n<51;

replace psuedo_psu=2 if _n>=51;

****************************************************************

* generate chicago_tax_paid

***********************************************************;

gen psuedo_chicago_tax_paid=1 if _n<=25;

replace psuedo_chicago_tax_paid=0 if _n>25 & _n<=50;

replace psuedo_chicago_tax_paid=1 if _n>50 & _n<61;

replace psuedo_chicago_tax_paid=0 if _n>=61;

****************************************************************

* generate psu weights

***********************************************************;

gen sample_weight=1 if psuedo_psu==1;

replace sample_weight=5 if psuedo_psu==2;

summarize;

****************************************************************

* generate OBSERVATION weights

***********************************************************;

sort psuedo_psu;

by psuedo_psu: gen obs_weight= sample_weight/_N;

summarize;

svyset psuedo_psu [pweight=obs_weight];

**********************************************************

* psu1 has a mean of .5 and a weight of 1

* psu2 has a mean of .2 and a weight of 5

* (5*.2)+(1*.5)=1.5

* 1.5/6=.25

*

* so the mean estimate makes sense to me

*******************************************************;

svy : mean psuedo_chicago_tax_paid;

mean psuedo_chicago_tax_paid;

*********************************************************

* do a second round with unequal size groups

*****************************************************;

clear;

#delimit ;

****************************************************************

* created the simulated data

***********************************************************;

set obs 1000;

****************************************************************

* generate psu

***********************************************************;

gen psuedo_psu=1 if _n<901;

replace psuedo_psu=2 if _n>=901;

****************************************************************

* generate chicago_tax_paid

***********************************************************;

gen psuedo_chicago_tax_paid=1 if _n<=450;

replace psuedo_chicago_tax_paid=0 if _n>450 & _n<=900;

replace psuedo_chicago_tax_paid=1 if _n>900 & _n<921;

replace psuedo_chicago_tax_paid=0 if _n>=921;

****************************************************************

* generate PSU weights

***********************************************************;

gen sample_weight=1 if psuedo_psu==1;

replace sample_weight=5 if psuedo_psu==2;

****************************************************************

* generate OBSERVATION weights

***********************************************************;

sort psuedo_psu;

by psuedo_psu: gen obs_weight= sample_weight/_N;

summarize;

svyset psuedo_psu [pweight=obs_weight];

**********************************************************

* psu1 has a mean of .5 and a weight of 1

* psu2 has a mean of .2 and a weight of 5

*

* I get the same answer for the mean in case 1 and case 2

* which I think is correct but

* I also get the same answer for the variance which I think is not

correct

*

* I think I should have a lower variance in case 2

*******************************************************;

svy : mean psuedo_chicago_tax_paid;

mean psuedo_chicago_tax_paid;

--

David Merriman

dmerrim@gmail.com

*

* For searches and help try:

* http://www.stata.com/support/faqs/res/findit.html

* http://www.stata.com/support/statalist/faq

* http://www.ats.ucla.edu/stat/stata/

Steven Samuels sjhsamuels@earthlink.net 18 Cantine's Island Saugerties, NY 12477 Phone: 845-246-0774 EFax: 208-498-7441 * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/-- David Merriman dmerrim@gmail.com * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/* * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/-- David Merriman dmerrim@gmail.com * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

* * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: variance when using svy: mean***From:*"Austin Nichols" <austinnichols@gmail.com>

**References**:**st: variance when using svy: mean***From:*"David Merriman" <dmerrim@gmail.com>

**Re: st: variance when using svy: mean***From:*Steven Joel Hirsch Samuels <sjhsamuels@earthlink.net>

**Re: st: variance when using svy: mean***From:*"David Merriman" <dmerrim@gmail.com>

**Re: st: variance when using svy: mean***From:*Steven Joel Hirsch Samuels <sjhsamuels@earthlink.net>

**Re: st: variance when using svy: mean***From:*"David Merriman" <dmerrim@gmail.com>

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