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Missing data

In statistics, missing data, or missing values, occur when no data value is stored for the variable in an observation. Missing data are a common occurrence and can have a significant effect on the conclusions that can be drawn from the data. In statistics, missing data, or missing values, occur when no data value is stored for the variable in an observation. Missing data are a common occurrence and can have a significant effect on the conclusions that can be drawn from the data. Missing data can occur because of nonresponse: no information is provided for one or more items or for a whole unit ('subject'). Some items are more likely to generate a nonresponse than others: for example items about private subjects such as income. Attrition is a type of missingness that can occur in longitudinal studies—for instance studying development where a measurement is repeated after a certain period of time. Missingness occurs when participants drop out before the test ends and one or more measurements are missing. Data often are missing in research in economics, sociology, and political science because governments or private entities choose not to, or fail to, report critical statistics, or because the information is not available. Sometimes missing values are caused by the researcher—for example, when data collection is done improperly or mistakes are made in data entry. These forms of missingness take different types, with different impacts on the validity of conclusions from research: Missing completely at random, missing at random, and missing not at random. Missing data can be handled similarly as censored data. Understanding the reasons why data are missing is important for handling the remaining data correctly. If values are missing completely at random, the data sample is likely still representative of the population. But if the values are missing systematically, analysis may be biased. For example, in a study of the relation between IQ and income, if participants with an above-average IQ tend to skip the question ‘What is your salary?’, analyses that do not take into account this missing at random (MAR pattern (see below)) may falsely fail to find a positive association between IQ and salary. Because of these problems, methodologists routinely advise researchers to design studies to minimize the occurrence of missing values. Graphical models can be used to describe the missing data mechanism in detail. Values in a data set are missing completely at random (MCAR) if the events that lead to any particular data-item being missing are independent both of observable variables and of unobservable parameters of interest, and occur entirely at random. When data are MCAR, the analysis performed on the data is unbiased; however, data are rarely MCAR. In the case of MCAR, the missingness of data is unrelated to any study variable: thus, the participants with completely observed data are in effect a random sample of all the participants assigned a particular intervention. With MCAR, the random assignment of treatments is assumed to be preserved, but that is usually an unrealistically strong assumption in practice. Missing at random (MAR) occurs when the missingness is not random, but where missingness can be fully accounted for by variables where there is complete information. Since MAR is an assumption that is impossible to verify statistically, we must rely on its substantive reasonableness. An example is that males are less likely to fill in a depression survey but this has nothing to do with their level of depression, after accounting for maleness. Depending on the analysis method, these data can still induce parameter bias in analyses due to the contingent emptiness of cells (male, very high depression may have zero entries). However, if the parameter is estimated with Full Information Maximum Likelihood, MAR will provide asymptotically unbiased estimates. Missing not at random (MNAR) (also known as nonignorable nonresponse) is data that is neither MAR nor MCAR (i.e. the value of the variable that's missing is related to the reason it's missing). To extend the previous example, this would occur if men failed to fill in a depression survey because of their level of depression.

[ "Statistics", "Data mining", "Econometrics", "Artificial intelligence", "Machine learning", "Imputation (statistics)", "Ignorability", "Inverse probability weighting", "nonignorable missingness" ]
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