2.2. Handling Missing Values

• MCAR – Missing Completely At Random • MAR – Missing At Random • MNAR – Missing Not At Random

There are three main types of missingness when dealing with missing data:

1. MCAR (Missing Completely At Random): This occurs when the reason for the missing data is random and has no relationship with any other variable. For example, if a survey respondent skips a question about their age purely by chance, their data would be considered MCAR.
2. MAR (Missing At Random): In this case, the missingness is related to some observed data but not the missing data itself. For instance, if older participants are less likely to respond to a survey, the missing age data is MAR because the age variable can be inferred from the observed responses of younger participants.
3. MNAR (Missing Not At Random): This is when the reason for missing data is related to the value of the missing data itself. For example, if wealthier individuals choose not to disclose their income, this creates a scenario where missingness is directly related to the variable in question.

Imagine a high school survey about student lunch preferences. If a student forgets to fill in their choice and misses that question at random, that's MCAR. If students from specific grades tend to skip the survey altogether but respond honestly about food options, that's MAR. If wealthier students tend to avoid answering about how much they spend on food, that would be MNAR.

• Deletion: Remove rows/columns with missing values (if few). • Imputation: o Mean/Median/Mode imputation o K-Nearest Neighbors (KNN) o Multivariate imputation (MICE) • Predictive Models: Use regression or classification to estimate missing values.

There are several techniques to manage missing data, which can significantly impact the analysis:

1. Deletion: This method involves removing rows or columns with missing values. It's effective when the amount of missing data is minimal, ensuring that the remaining dataset remains usable without significant loss of information.
2. Imputation: Instead of deleting missing values, imputation involves filling in missing data:
   • Mean/Median/Mode imputation: This technique replaces missing values with the mean (average), median (middle value), or mode (most common value) of the column. It's simple but can introduce bias if the distribution is skewed.
   • K-Nearest Neighbors (KNN): This method uses the attributes of the closest data points to predict and fill in the missing values, making it a more sophisticated imputation method that considers relationships among variables.
   • Multivariate Imputation (MICE): This advanced technique involves using multiple imputation methods to estimate missing data based on other observed data, providing a more robust solution.
3. Predictive Models: In this approach, regression or classification algorithms are utilized to predict and estimate the values of missing data, considering the patterns within the dataset.

Think about a classroom setting where students occasionally forget to submit homework. If only a few students are missing assignments, the teacher might choose to ignore those while grading (deletion). If instead, the teacher knows most students typically score similarly, she might estimate a missing score based on the average scores (mean imputation). For more thoughtful predictions, the teacher could consider past scores and friends' performance in calculating a likely score using a method like KNN. For high-stakes testing, she might leverage multiple exams to guess a student's potential score more accurately using approaches like MICE.

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