Summary
Summary Schafer, J. & Graham, J. – Missing Data: Our view of the State of the Art
- Course
- Institution
Article by Schafer and Graham on missing data
[Show more]
Seller
Followlindawijnhoven
Reviews received
Content preview
Schafer, J. & Graham, J. – Missing Data: Our view of the State of the ArtMost data analysis are not designed for missing data. Missingness is usually a nuisance, not
the main focus of inquiry. Most researches resort to editing the data to lend an appearance
of completeness. Unfortunately this can lead to biased, inefficient, and unreliable answers.
What Is a Missing Value?
Missing values are part of the more general concept of coarsened data, which includes
numbers that have been grouped, aggregated, rounded, censored, or truncated, resulting in
partial loss of information. Latent variables are closely related to missing data, which are
unobservable quantities (e.g. intelligence) that are imperfectly measured by test of
questionnaire items.
Historical Development
Until the 1970s, missing values were handled primarily by editing. The formulation of the
EM (expectation-maximization) algorithm made it feasible to compute ML (maximum
likelihood) estimates in many missing-data problems. ML treats the missing data as random
variables to be removed from the likelihood function as if they were never sampled.
Later the idea of MI (multiple imputation) was introduced, in which each missing value is
replaced with m>1 simulated values prior to analysis.
Goals and Criteria
A missing value treatment can’t be properly evaluated apart from the modeling, estimation
or testing procedure in which it is embedded (e.g. mean substation –replacing each missing
value for a variable with the average of the observed values- may accurately predict
missing data, but distort estimated variances and correlations).
When Q is a population, and ^Q an estimated of Q based on a sample data, then if the
procedure will have ^Q close to Q. We thus want the difference, the bias, to be small. Bias/
variance are often calculated by (^Q-Q)², which is the mean square error. But this does not
yet describe the measures of uncertainty.
When missing values occur for reasons beyond our control, we must make assumptions
about the processes that create them. These are usually untestable.
Finally, one should avoid tricks that apparently solve the missing-data problem but actually
redefine the parameters or the population.
Types and Patterns of Nonresponse
Unit nonresponse is when the entire data collection procedure fails (e.g. sampled person is
not at home). Item nonresponse is when partial data available (e.g. sampled person does
not respond to certain items). Especially in longitudinal studies, both concepts are common,
which is referred to as wave nonresponse. Attrition/dropout is when one leaves the study
and does not return.
A univariate pattern is when missing values occur on an item Y, but a set of p other items
X1, X2..Xp is completely observed (see figure 1a).
A monotone pattern is when items or item groups (Y1, Y2..Yp) may be ordered in such a
way that if Yj is missing for a unit, then Yj+1 are missing as well (see figure 1b).
An arbitrary pattern is when any set of variables may be missing for any unit (see figure
1c).
The Distribution of Missingness
R is referred to as the missingness. The form of missingness depends on the complexity of
the pattern. When R=1, it indicates whether Y is observed. When R=0, it indicates whether
Y is missing.
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller lindawijnhoven. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $3.73. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
53068 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now