As almost any researcher can
attest, missing data are a widespread problem. Data from surveys,
experiments, and secondary sources are often missing some data. The
impact of the missing data on the results of statistical analysis
depends on the mechanism which caused the data to be missing and the
way in which the data analyst deals with it. This is the first in a
series of three articles that discusses issues surrounding missing
data. This article outlines the mechanisms of missing data and some of
their impacts. Subsequent articles will explain common but problematic
solutions to missing data, new and better solutions, and the software
available for implementing these solutions.
Data are missing for many
reasons. Subjects in longitudinal studies often drop out before the
study is completed because they have moved out of the area, died, no
longer see personal benefit to participating, or do not like the
effects of the treatment. Surveys suffer missing data when participants
refuse, or do not know the answer to or accidentally skip an item. Some
survey researchers even design the study so that some questions are
asked of only a subset of participants. Experimental studies have
missing data when a researcher is simply unable to collect an
observation. Bad weather conditions may render observation impossible
in field experiments. A researcher becomes sick or equipment fails.
Data may be missing in any type of study due to accidental or data
entry error. A researcher drops a tray of test tubes. A data file
becomes corrupt. Most researchers are very familiar with one (or more)
of these situations.
Missing data are problematic
because most statistical procedures require a value for each variable.
When a data set is incomplete, the data analyst has to decide how to
deal with it. The most common decision is to use complete case analysis
(also called listwise deletion)--analyzing only the cases with complete
data. Individuals with data missing on any variables are dropped from
the analysis. It has advantages--it is easy to use, is very simple, and
is the default in most statistical packages. But it has limitations. It
can substantially lower the sample size, leading to a severe lack of
power. This is especially true if there are many variables involved in
the analysis, each with data missing for a few cases. It can also lead
to biased results, depending on why the data are missing.
All of the causes for missing
data fit into four classes, which are based on the relationship between
the missing data mechanism and the missing and observed values. These
classes are important to understand because the problems caused by
missing data and the solutions to these problems are different for the
four classes.
The first is Missing Completely
at Random (MCAR). MCAR means that the missing data mechanism is
unrelated to the values of any variables, whether missing or observed.
Data that are missing because a researcher dropped the test tubes or
survey participants accidentally skipped questions are likely to be
MCAR. If the observed values are essentially a random sample of the
full data set, complete case analysis gives the same results as the
full data set would have. Unfortunately, most missing data are not
MCAR.
At the opposite end of the
spectrum is Non-Ignorable (NI). NI means that the missing data
mechanism is related to the missing values. It commonly occurs when
people do not want to reveal something very personal or unpopular about
themselves. For example, if individuals with higher incomes are less
likely to reveal them on a survey than are individuals with lower
incomes, the missing data mechanism for income is non-ignorable.
Whether income is missing or observed is related to its value. Complete
case analysis can give highly biased results for NI missing data. If
proportionally more low and moderate income individuals are left in the
sample because high income people are missing, an estimate of the mean
income will be lower than the actual population mean.
In between these two extremes
are Missing at Random (MAR) and Covariate Dependent (CD). Both of these
classes require that the cause of the missing data is unrelated to the
missing values, but may be related to the observed values of other
variables. MAR means that the missing values are related to either
observed covariates or response variables, whereas CD means that the
missing values are related only to covariates. As an example of CD
missing data, missing income data may be unrelated to the actual income
values, but are related to education. Perhaps people with more
education are less likely to reveal their income than those with less
education.
A key distinction is whether
the mechanism is ignorable (i.e., MCAR, CD, or MAR) or non-ignorable.
There are excellent techniques for handling ignorable missing data.
Non-ignorable missing data are more challenging and require a different
approach.
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