Spatial Survey Data Modeling - Sampling Spatial Units for Agricultural Surveys - page 302

analyze survey data. Unfortunately, these methods are defined in a very general and
non-specific framework that does not consider the particular nature of the data
being investigated. In fact, standard formulations of many statistical methods
assume that the sample data are directly generated from the population model,
without considering the sampling scheme.
We have chosen to include these two apparently different topics in the same
concluding chapter of this topic, because they both effectively use modeling
assumptions to derive estimators and their properties. In fact, the properties of the
predictive (or model-based) approach for survey sampling are evaluated consider-
ing a model as a stochastic element. On the other hand, survey data can only be
appropriately analyzed by considering the model as a key factor in the procedures.
Another common element of these two topics is that they usually do not consider
the spatial component when defining the techniques. In other words, the predictive
approach to survey sampling was not extensively developed for spatially
distributed data.
The aim of this chapter is to raise some research questions that represent a huge
challenge for statisticians. We will not provide definitive answers to these ques-
tions; we only wish to show the gaps in the current literature that we hope to fill in
the near future.
Finally, we present a possible interpretation of the classical spatial interpolation
problem that can be viewed as an application of the predictive approach to spatial
finite populations.
The layout of this chapter is as follows. Section 12.2 describes the model-based
approach to survey sampling. Section 12.3 summarizes spatial interpolation as a
possible case of the predictive approach to sampling. Section 12.4 contains some
introductory ideas regarding survey data analysis. Finally, the last section con-
cludes the topic.
12.2 Model-Based Inference for Finite Populations
The prevalent methodological perspective for survey sampling that is used in this
book is the design-based approach. According to this framework, the properties of
the estimators have been evaluated under the randomization hypothesis, and so the
only stochastic element of the procedure is represented by s . In this section, we
discuss an alternative approach for survey sampling, which is based on modeling
assumptions. We use the notations and concepts from Sect. 1.3 . Here, note that the
model-based approach is considered with reference to finite populations, particu-
larly those that are spatial.
A finite population is a collection of different units such as people, business
establishments, schools, hospitals, fields, farms, or owners.
We can consider a basic descriptive statistic for these lists as the total of some
variable. The definition of the total obviously depends on the population of interest.
The total population may be the number of agricultural employees, the total