Graphics Reference
In-Depth Information
4.2 Assumptions and Missing Data Mechanisms
It is important to categorize the mechanisms which lead to the introduction of
MVs [
54
]. The assumptions we make about the missingness mechanism and the
MVs pattern of MVs can affect which treatment method could be correctly applied,
if any.
When thinking about the missing data mechanism the probability distributions
that lie beneath the registration of rectangular data sets should be taken into account,
where the rows denote different registers, instances or cases, and the columns are the
features or variables. A common assumption is that the instances are all independent
and identically distributed (i.i.d.) draws of some multivariate probability distribution.
This assumption is also made by Schafer in [
82
] where the schematic representation
followed is depicted in Fig.
4.1
.
X
being the
n
m
rectangular matrix of data, we usually denote as
x
i
the
i
th row
of
X
. If we consider the i.i.d. assumption, the probability function of the complete
data can be written as follows:
×
n
P
(
X
|
θ)
=
f
(
x
i
|
θ),
(4.1)
i
=
1
Fig. 4.1
Data set with MVs denoted with a '?'
