The witch tapped her broomstick, and _whoosh!_ they were gone
Julia Donaldon. 2003. Room on the Broom
People do not respond to survey (or specific questions in a survey).
Species are rare and cannot be found or sampled.
The individual dies or drops out before sampling.
Some things are easier to measure than others.
Data entry errors.
.. And many others!
Missingness completely at random
Missingness at random
Missingness that depends on unobserved predictors
Missingness that depends on the missing value itself
The reason for missingness is totally independent of the predictors and response.
i.e., the probability of missingness is the same for each unit in your sample.
The data sample with complete cases remains an unbiased sample of the population.
Can analyse these complete cases, but loss of power.
Data rarely MCAR.
Missingness depends only on other available information (e.g., other predictors).
E.g., different social groups have different response rates to a survey:
if sex, race, education, and age are recorded for all people in the survey, then “earnings” is missing at random if the probability of nonresponse to this question depends only on these other, fully recorded variables.
The data sample with complete cases is a biased sample of the population.
But, this is ok if the regression controls for all the variables that affect the probability of missingness.
E.g., need to include sex, race, education, and age in the model.
depends on information that has not been recorded and
this information also predicts the missing values,
e.g., if a particular treatment causes discomfort, a patient is more likely to drop out of the study (and ‘discomfort’ is not measured).
Data sample is biased, therefore you need to explicitly model it. (Or accept bias).
Missingness depends on the (potentially missing) variable itself
E.g., people with higher earnings are less likely to reveal them.
Censoring occurs when a particular value of information leads to missingess
everyone earning >$100k does not respond,
lighter weight chicks die before they can be sampled,
smaller seeds do not germinate.
Model the missing data.
Include more predictors.
Red is missing data in the y-variable.
Blue is observed data.
Source: Nakagawa & Freckleton (2008)
(a) Missing At Random
(b) Missing Not At Random
(c) Missingness Completely At Random
Cannot be sure that data are MCAR, MAR, or MNAR
Because unobserved predictors (lurking variables) are unobserved.
So, we can never rule them out
The best solution to handle missing data is to have none.
– R.A. Fisher
See references for specific details.
Use a value that is:
Compatible with (most) software.
Unlikely to cause errors in analysis.
|0||Indistinguishable from a true zero||Never use|
|Blank||Hard to tell values that are missing from those overlooked on data entry. Hard to tell blanks from spaces (behave differently)||R, Python, SQL||Best option|
|-999, 999||Not recognized as null by many programs without user input. Can be inadvertently entered into calculations.||Avoid|
|NA, na||Also an abbreviation (e.g., North America). Can cause problems with data type (turn a numerical column into a text column). NA is more common than na||R||Good option|
|N/A||An alternate form of NA, but often not compatible with software||Avoid|
|NULL||Can cause problems with data type. Variable use in R||SQL||Good option|
|None||Uncommon. Can cause problems with data type||Python||Avoid|
|No data||Uncommon. Can cause problems with data type. Contains a space||Avoid|
|Missing||Uncommon. Can cause problems with data type||Avoid|
|-, +, .||Uncommon. Can cause problems with data type||Avoid|
Table 1 Commonly used null values, limitations, compatibility with common software. From: White et al. 2013
When you read data in to R, it will convert blank cells to NA.
‘NA’ are the only characters permitted in non-character vectors.
x <- c(1, 2, 3, 4, NA, 6, 7, 8, NA, 10) x #  1 2 3 4 NA 6 7 8 NA 10 is.numeric(x) #  TRUE is.character(x) # FALSE
Some functions will fail with missing data.
# generate vector of integers with an NA x <- c(1:10, NA) # calculate mean of x mean(x) #  NA
Include ‘na.rm = TRUE’
mean(x, na.rm = TRUE) #  5.5
Gelman, A. & Hill J. 2006. Missing data imputation. Chapter 25, In: Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press, UK. pp 529–543.
Nakagawa, S. 2015. Missing data: mechanisms, methods, and messages. In: Fox, Negrete-Yankelevich, and Sosa (eds). Ecological Statistics: Contemporary theory and application. Oxford University Press, UK.
Nakagawa, S. and Freckleton, R.P. 2008. Missing inaction: The dangers of ignoring missing data. Trends in Ecology & Evolution 23, 592–596.