Sampling Designs - Sampling Spatial Units for Agricultural Surveys - page 140

Adaptive sampling designs are those in which the procedure for selecting units
depends on values of the study variable or on values of any other variable observed
during the survey (Thompson and Seber 1996 ). In this sense, adaptive sampling
designs are adaptive in that the remaining units to be sampled may change
according to previously observed units. Adaptive sampling designs have been
used in various disciplines, including ecological, epidemiological, environmental,
geographical, and social sciences.
Adaptive cluster sampling (ACS, Thompson 1990 ) is a subclass of adaptive
sampling. There has been considerable research within the adaptive sampling field,
using ACS designs and their associated estimators.
In ACS, an initial probability sample is first selected; thereafter, additional units
may be added depending on the y values observed in the initial sample. The
additional units are referred to as the adaptively sampled component. The initial
sample can be taken according to any of the usual designs, including SRS (Thomp-
son 1990 ), systematic sampling (Thompson 1991a ), stratified random sampling
(Thompson 1991b ), ps sampling (Pontius 1997 ), and even inverse sequential

sampling (Christman 2000 ). When we are dealing with spatial populations and
the rare units occur in spatially distinct groups of reasonable size, then ACS may be
an attractive candidate for estimating the parameters of the population. The avail-
ability of different sampling strategies for the initial drawing allows for a variety of
approaches that can estimate the parameters of y with an acceptable accuracy
(Christman 2009 ).
In practice, ACS follows an iterative selection criterion defined as follows:

π

1. Draw a starting sample s 1 of the observed variable y 1 .
2. Choose the rest of the sample s 2 so that the mean square error of the estimate
given what has been observed so far is minimized (Zacks 1969 ; Thompson and
Seber 1996 ; Chao and Thompson 2001 ). A typical criterion is to include all the
units contiguous to every unit k in s 1 for which y k > 0.

3. Repeat Step 2 until no contiguous unit exists, or the number of sampling units
exceeds an acceptable maximum.

Theoretically optimal designs are hard to implement, computationally complex,
and excessively dependent on model-based assumptions. Moreover, π kl are

very difficult to evaluate as they depend on the observed values. Thus, it can be
difficult to use the HT estimator. A drawback of these designs is that n is a random
variable whose realization is unknown prior to the interviewing phase, and may be
quite variable depending on the spread or spatial concentration of the population.
Recently, a new class of adaptive sampling designs called adaptive web sam-
pling has been developed (AWS, Thompson 2006 ). AWS designs are useful for
sampling in network and spatial populations. A major distinction between ACS and
AWS is that, in ACS the units in the neighborhood of a selected unit that satisfy a
predefined condition are automatically added, whereas they are not

π k and

in AWS

(Dryver 2008 ).