A missing variable imputation methodology with an empirical application

The objective of this research is to examine, validate, and recommend techniques for handling the problem of missingness in observational data. We use a rich observational data set, the Nielsen HomeScan data set, which allows us to effectively combine elements from simulated data sets: large numbers of observations, large number of data sets and variables, allowing elements of "design" that typically come with simulated data, and its observational nature. We created random 20% and 50% uniform missingness in our data sets and employed several widely used methods of single imputation, such as mean, regression, and stochastic regression imputations, and multiple imputation methods to fill in the data gaps. We compared these methods by measuring the error of predicting the missing values and the parameter estimates from the subsequent regression analysis using the imputed values. We also compared coverage or the percentages of intervals that covered the true parameter in both cases. Based on our results, the method of single regression or conditional mean imputation provided the best predictions of the missing price values with 28.34 and 28.59 mean absolute percent errors in 20% and 50% missingness settings, respectively. The imputation from conditional distribution method had the best rate of coverage. The parameter estimates based on data sets imputed by conditional mean method were consistently unbiased and had the smallest standard deviations. The multiple imputation methods had the best coverage of both the parameter estimates and predictions of the dependent variable.