Dear Thomas,

Thank you for your informative answer. We used epi.stratasize() to

estimate the required sample size per stratum. Notice in the example

below that it can select a sample size smaller than 2 in the very small

strata. Would you recommend to sample at least two items per stratum or

rather to merge some strata a priori until the sample size is at least

2? Or is there a better way to estimate the sample size per stratum?

Note that the stratification only aims to get a good geographical

coverage (the strata a geographical regions). We are not interested in

estimates per stratum.

library(epiR)

N <- c(39, 270, 1060, 1336, 118, 26, 154, 10, 3)

epi.stratasize(strata.n = N, strata.mean = 0.9, epsilon = 0.05, method =

"proportion")

$strata.sample

[1] 2 15 57 72 6 1 8 1 0

$total.sample

[1] 162

The probability of sampling was proportional with the area (larger

polygons are more likely to be selected than smaller ones). So we will

use weights = I(1/Area), as you suggested.

Best regards,

Thierry

------------------------------------------------------------------------

----

ir. Thierry Onkelinx

Instituut voor natuur- en bosonderzoek

team Biometrie & Kwaliteitszorg

Gaverstraat 4

9500 Geraardsbergen

Belgium

Research Institute for Nature and Forest

team Biometrics & Quality Assurance

Gaverstraat 4

9500 Geraardsbergen

Belgium

tel. + 32 54/436 185

[hidden email]
www.inbo.be

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say what the experiment died of.

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~ Roger Brinner

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ensure that a reasonable answer can be extracted from a given body of

data.

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> -----Oorspronkelijk bericht-----

> Van: Thomas Lumley [mailto:

[hidden email]]

> Verzonden: woensdag 7 april 2010 18:51

> Aan: ONKELINX, Thierry

> CC:

[hidden email]
> Onderwerp: Re: [R] Struggeling with svydesign()

>

> On Wed, 7 Apr 2010, ONKELINX, Thierry wrote:

>

> > Dear all,

> >

> > We are analysing some survey data and we are not sure if we

> are using

> > the correct syntax for our design.

> >

> > The population of interest is a set of 4416 polygons with different

> > sizes ranging from 0.003 to 45.6 ha, 7460 ha in total. Each polygon

> > has a binary attribute (presence/absence) and we want to

> estimate the

> > probability of presence in the population.

> >

> > We used sampling with replacement weighted by the area of

> the polygon.

> > The population was stratified using 2 variables: block and

> type. Each

> > of the 14 blocks is a 20 by 50 km geographical region. Type

> is a two

> > level factor. Not every level is present in each block.

> Each block has

> > a Status attribute with two levels: medium (9 blocks) or

> good (5 blocks).

> > Besides the overall ratio, we would like the estimate the ratio per

> > Status.

> > The samplesize per stratum was calculated with

> epi.stratasize() from

> > the epiR package. The population size in the 21 strata

> ranges from 1

> > to 1158. The sample size ranges from 0 in the blocks with very few

> > polygons (<20), 1 in blocks with a low number of polygon

> (20 - 50) and

> > up to 25 polygons in the largest strata.

>

> That sounds strange. If you have a stratified sample and

> have set the sample size in some strata to be zero, you

> cannot possibly learn anything about those strata and so you

> can't get unbiased population estimates. In order to get

> unbiased estimates and valid standard errors you need at

> least two samples per stratum.

>

> You're going to have to combine some of the strata so that

> each stratum has at least two observations. Since your

> design only makes sense if you assume the small, unsampled,

> strata are similar to some of the larger strata, it should be

> possible for you to combine them.

>

>

> > Does the syntax below represents the data structure above? Any

> > comments are welcome.

> >

> > library(survey)

> > svydesign(

> > id = ~ 1, #no clustering

> > weights = ~ Area, #weighted by the area of the polygon

> > strata = ~ Status + Block + Type,

> > nest = TRUE

> > )

>

> You want strata = ~interaction(Block,Type,drop=TRUE), which

> specifies a single stage of sampling in which the strata are

> combinations of Block and Type. The fact that you need

> drop=TRUE is a bug, which I will fix.

>

> > # Is Area a correct weighting factor? Or should we use the area

> > divided by the sum of the total area (per stratum?)

>

> It's not clear to me from your description whether the

> probability of sampling a particular region is proportional

> to its Area or inversely proportional to its Area. If the

> probability is proportional to Area, the weight would be 1/Area

>

> svydesign(

> id = ~ 1, #no clustering

> weights = ~ I(1/Area), #weighted by the area of the polygon

> strata = ~ interaction(Block, Type,drop=TRUE),

> nest = TRUE

> )

>

>

> > # The code above runs. But when we omit "Status" from the

> strata, then

> > we get an error: "a stratum has only 1 PSU". Shouldn't we

> get the same

> > error with the code above?

> >

> > #with finity population correction

> > svydesign(

> > id = ~ 1, #no clustering

> > weights = ~ Area, #weighted by the area of the polygon

> > strata = ~ Status + Block + Type,

> > fpc ~ nStatus + nBlock + nType,

> > nest = TRUE

> > )

> > #We are not sure what to use for nStatus, nBlock and nType.

> Is it the

> > number of levels of that stratum (nStatus = 2)? The number

> of levels

> > in the stratum below (nStatus = length(unique(Block)) per level of

> > Status, nType = number of polygons per Status:Block:Type)?

> The total

> > number of polygons in that stratum?

>

> This is easier when you get the right strata. There should

> be a single fpc variable, which should be equal to the number

> of polygons in the population for that stratum.

>

>

> > To call in the statistician after the experiment is done may be no

> > more than asking him to perform a post-mortem examination:

> he may be

> > able to say what the experiment died of.

> > ~ Sir Ronald Aylmer Fisher

>

> Indeed.

>

>

> -thomas

>

> Thomas Lumley Assoc. Professor, Biostatistics

>

[hidden email] University of Washington, Seattle

>

>

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