Sampling Designs - Sampling Spatial Units for Agricultural Surveys - page 133

Furthermore, this framework is also important when dealing with non-responses
(see Sect. 10.4 ), because we often consider them to be generated from a random-
ization scheme. Thus, the effective observed data can be considered as a second
sample randomly chosen, even if unintentionally, from the selected sample. The
first-phase selection can be viewed as a target sample, while the second-phase units
are the set in the target sample that have been truly observed. The inclusion
probabilities for the second-phase design are generally unknown, and need to be
estimated. A common assumption is that the second-phase sample is a stratified
Bernoulli sample, where the strata are defined by known characteristics of the
elements in the target sample (Legg and Fuller 2009 ).
There is no specific function in the sampling package that selects two-phase
random samples. They can be obtained by a series of calls to the function used to
draw samples according to the basic designs. In this example, an SRS of size
n 1 ¼ 200 was selected, and then stratified into the 4 quadrants of the study region.

Then an SRS is selected in each stratum with n h ¼ 25. The point estimates of the

total are obtained using the twophase function of the survey package. Note that
it is cumbersome to set the input parameters, because they require a list of
identifiers, possible strata codes, and inclusion probabilities for each phase. The
selected sample is mapped in Fig. 6.7 .

Fig. 6.7 Sample selected with a two-phase simple random in the first phase and stratified in the
second phase