Spatial Survey Data Modeling - Sampling Spatial Units for Agricultural Surveys - page 301

Chapter 12
Spatial Survey Data Modeling

12.1 Introduction

Design-based inference has been the most popular sampling method for many
years. This approach has been extensively discussed in this topic. A different
framework has been developed to apply models to survey sampling and practice.
This model-based inference approach can be considered as an alternative to the
classical design-based theory.
A polarization occurred around four decades ago, and inference theories split
into design-based and model-based. These terms were not in common use before
1970. Today, they are used as standard among survey sampling specialists and other
scientists. After all these years, the debate continues; neither side has been shown to
be superior.
It is well known that the principal difference between the two philosophies lies in
the element of randomness, which is used to give stochastic structure to the
inference (S ¨ rndal 1978 ).
In a design-based approach, the primary sources of randomness are the proba-
bilities attributed by the sampling design to the various subsets of the finite
population. Godambe ( 1955 , 1965 , 1975 ) formalized the design-based approach
using traditional concepts of statistical inference for survey sampling.
Conversely, the model-based approach derives inferences by considering that
the values associated with the N units of the population, y ¼

t , are

ð y 1 y 2 ... y N Þ

t . The

¼ ð Y 1 Y 2 ... Y N Þ

the realized outcomes of the random variables Y

random vector Y has an N -dimensional joint distribution , which is called the

superpopulation. This model reflects any available background knowledge (see
Sect. 1.3 ). Model-based survey sampling methods are also called predictive
approaches. For some comparisons of design-based and model-based inference
for survey sampling, see Cassel et al. ( 1977 ).
Several statistical methods are now used to analyze sampled survey data. For
example, an extensive number of regression techniques are frequently used to

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