[R] Struggeling with svydesign()

[ONKELINX, Thierry]

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
Thierry.Onkelinx op inbo.be
www.inbo.be

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

The plural of anecdote is not data.
~ Roger Brinner

The combination of some data and an aching desire for an answer does not
ensure that a reasonable answer can be extracted from a given body of
data.
~ John Tukey
  

> -----Oorspronkelijk bericht-----
> Van: Thomas Lumley [mailto:tlumley op u.washington.edu] 
> Verzonden: woensdag 7 april 2010 18:51
> Aan: ONKELINX, Thierry
> CC: r-help op r-project.org
> 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
> tlumley op u.washington.edu	University of Washington, Seattle
> 
> 

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