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Summary topic Missing Data AMDA SPRING
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TOPIC 4: Missing dataMissing data can have significant consequences on statistical analysis and its conclusions.
Consequences of missing data:
1. Less data than planned > enough statistical power?
When designing a study, the researcher plans for a certain sample size to ensure
sufficient power. With fewer data points, the study might be unable to detect
significant effects, leading to a higher risk of type 2 errors.
(= failing to reject a false null hypothesis).
2. Biases in analysis:
Effect bias: Distortion of the estimated effect. The relations between variables
might be inaccurately estimated.
Representativity: The extent to which the sample represents the population.
This also affects the generalizability of the findings.
Appropriate confidence interval, p-values?
With missing data, CIs might become wider. This indicates there is
more uncertainty about the estimates
Statistical tests assume data is missing randomly (MAR). If this
assumption is violated, the results may be inappropriate.
Response indicator (R): This indicator denotes whether each individual's value is observed or
missing. R is always available data because you always know whether the data is present or
absent.
R = 1: Not missing, R = 0: Missing
Missing data mechanism: MCAR, MAR, NMAR
MCAR = Missing completely at random.
o The missingness is entirely unrelated to the observed and unobserved data.
o P (R=0 |Y, X) = P (R=0)
E.g., accidentally skipping the question.
= Quite a strict assumption: Normally, missing data will have an underlying pattern or
reason.
MAR = Missing at random.
o The missingness is related to the observed data but not the unobserved data
o P (R=0 | Y,X) = P (R=0|X).
For example, gender is always observed, and men have more missing data
than women.
NMAR = Not missing at random.
o The missingness is related to the unobserved data.
o People with high incomes have more missing data on variable measuring
income than people with lower incomes.
o If there are strong theoretical reasons or significant associations cannot be
explained by observed data alone.
, Asses if the type of missing data is problematic:
The missing data types for MCAR and MAR are ignorable:
The mechanisms do not bias the parameter estimates if the appropriate methods are
used
The missing data types for NMAR are nonignorable:
This type introduces bias into the parameter estimates if not properly addressed. The
missing data mechanism is related to the values that are missing. This might skew the
statistical inference
How to know which of these types of missing data it is (ChatGPT):
Look if there are patterns in the missing data. See if there is a correlation with any
observed variables.
There is an MCAR test: If it is significant, the data is not MCAR
Do a regression analysis with the missing indicator (0/1) as the Y and the observed
data as X. If the analysis shows a significant predictor from the observed data, the
data may be MAR.
Strategies to deal with missing data:
Prevention
Simple methods:
o Listwise deletion- complete-case analysis
o Pairwise deletion – available case analysis
o Mean substitution
Likelihood methods, EM
Multiple imputation
Elaboration on the ‘Simple Methods’:
1. Listwise Deletion- Complete Case Analysis:
Explanation: Missing values are excluded from the analysis.
+ Simplicity (default in SPSS)
+ Correct standard errors and significance levels when MCAR
+ Works in some special NMAR cases
- Wasteful: It deletes any observations. Reduction in N & power
- Same data- different N. Not representative of the population.
- OK under MCAR, biased under MAR, and partly NMAR
2. Pairwise deletion: Available case analysis.
Uses all available data for each specific calculation or test. Instead of excluding entire
cases (like listwise deletion), it includes observations in the analysis as long as the
required variables are present.
+ Uses all available information: Less waste
- Only works under MCAR
- Computational problems: negative variances, rank problems’
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