[R] Struggeling with svydesign()

[Thomas Lumley]

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 at u.washington.edu	University of Washington, Seattle