Package smile.feature.imputation
Data are missing for many reasons. Missing data can occur because of non-response: no information is provided for several items or no information is provided for a whole unit. Some items are more sensitive for non-response than others, for example items about private subjects such as income.
Dropout is a type of missingness that occurs mostly when studying development over time. In this type of study the 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.
Sometimes missing values are caused by the device failure or even by researchers themselves. It is important to question why the data is missing, this can help with finding a solution to the problem. If the values are missing at random there is still information about each variable in each unit but if the values are missing systematically the problem is more severe because the sample cannot be representative of the population.
All 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.
If it is known that the data analysis technique which is to be used isn't content robust, it is good to consider imputing the missing data. Once all missing values have been imputed, the dataset can then be analyzed using standard techniques for complete data. The analysis should ideally take into account that there is a greater degree of uncertainty than if the imputed values had actually been observed, however, and this generally requires some modification of the standard complete-data analysis methods. Many imputation techniques are available.
Imputation is not the only method available for handling missing data. The expectation-maximization algorithm is a method for finding maximum likelihood estimates that has been widely applied to missing data problems. In machine learning, it is sometimes possible to train a classifier directly over the original data without imputing it first. That was shown to yield better performance in cases where the missing data is structurally absent, rather than missing due to measurement noise.
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ClassDescriptionMissing value imputation by K-Medoids clustering.Missing value imputation with k-nearest neighbors.Simple algorithm replaces missing values with the constant value along each column.Missing value imputation with singular value decomposition.