RegressionsImputation

Regression imputation is a method used in statistics to estimate missing data points within a dataset. It works by establishing a relationship between the variable with missing values and other variables in the dataset that are complete. This relationship is typically modeled using regression analysis.

The process involves building a regression model where the variable with missing values is the dependent variable, and other complete variables are the independent variables. Once the regression equation is determined, it is used to predict the missing values based on the observed values of the independent variables for those specific observations. For example, if age is missing for some individuals, and income and education level are available and correlated with age, a regression model can be built using the complete cases to predict the missing ages.

While regression imputation can preserve the relationships between variables better than simpler methods like mean imputation, it has drawbacks. It tends to underestimate the variance of the variable being imputed, as it replaces missing values with predicted values that lie exactly on the regression line, effectively reducing variability. It also assumes a linear relationship between the variables and may not perform well if the relationships are non-linear or if there are complex interactions. Furthermore, it does not account for the uncertainty associated with the imputed values. More advanced techniques, such as multiple imputation, are often preferred as they address some of these limitations by creating multiple plausible imputed datasets.