Sample Size and Sample Allocation - Sampling Spatial Units for Agricultural Surveys - page 211

The results change because they need to respect all three constraints, and not just
one. We can calculate the univariate allocation for each variable of interest to see if
they are still dominated by one variable (i.e., the first variable var_yobs).

> stratsize < - matrix(0,nrow(b1),3)
> for (i in 1:3)
+{
+ numvar1 < - sqrt(b1[,1+i]*(b1[,5])^2)
+ numvar1 < - numvar1*sum(numvar1)
+ numvar2 < - b1[,1+i]*(b1[,5])
+ div < - b2[i,1]^2*b2[i,2]^2+sum(numvar2)
+ stratsize[,i] ¼ pmax(ceiling(numvar1/div),b1[,7])
+}
> stratsize < - cbind(stratsize,b3[,2],apply(stratsize,1,max))
> stratsize < - rbind(stratsize,apply(stratsize,2,sum))
> colnames(stratsize) < - c("ss_yobs","ss_yobs2","ss_yobs3",
+ "bth_all","max_all")
> rownames(stratsize) < - c("stratum1","stratum2","stratum3",
+

"samplesize")

> stratsize

ss_yobs ss_yobs2 ss_yobs3 bth_all max_all

stratum1 64 117 45 98 117

stratum2 74 97 86 97 97

stratum3 71 47 113 86 113

samplesize 209 261 244 281 327

Obviously, the compromise (i.e., multipurpose) allocation always results in a
loss of precision when compared with the individual optimal allocations. However,
it uses less sampling units than the heuristic solution that uses the maximum sample
size for each stratum.

8.5 Modeling Auxiliary and Survey Variables: The
Anticipated Moment Approach

The margins of error c (i.e., the threshold for the coefficient of variation) typically
relate to auxiliary variables (X) from past surveys or administrative and remotely
sensed data, rather than to the survey variables Y. The underlying assumption is that
the optimal sample design based on specifying target levels of precision for a set of
auxiliary variables will lead to a design that achieves the required target precision
( c v ) for each survey variable v . However, the solution will be sub-optimal if there
are considerable differences between the auxiliary and survey variables. In practice,
it is well known that this assumption is only an approximation of the true situation,