Comparing Single and Multiple Imputation Approaches for Missing Values in Univariate and Multivariate Water Level Data

Abstract

Missing values in water level data is a persistent problem in data modelling and especially common in developing countries. Data imputation has received considerable research attention, to raise the quality of data in the study of extreme events such as flooding and droughts. This article evaluates single and multiple imputation methods used on monthly univariate and multivariate water level data from four water stations on the rivers Benue and Niger in Nigeria. The missing completely at random, missing at random and missing not at random data mechanisms were each considered. The best imputation method is identified using two error metrics: root mean square error and mean absolute percentage error. For the univariate case, the seasonal decomposition method is best for imputing missing values at various missingness levels for all three missing mechanisms, followed by Kalman smoothing, while random imputation is much poorer. For instance, for 5% missing data for the Kainji water station, missing completely at random, the Kalman smoothing, random and seasonal decomposition methods had average root mean square errors of 13.61, 102.60 and 10.46, respectively. For the multivariate case, missForest is best, closely followed by k nearest neighbour for the missing completely at random and missing at random mechanisms, and k nearest neighbour is best, followed by missForest, for the missing not at random mechanism. The random forest and predictive mean matching methods perform poorly in terms of the two metrics considered. For example, for 10% missing data missing completely at random for the Ibi water station, the average root mean square errors for random forest, k nearest neighbour, missForest and predictive mean matching were 22.51, 17.17, 14.60 and 25.98, respectively. The results indicate that the seasonal decomposition method, and missForest or k nearest neighbour methods, can impute univariate and multivariate water level missing data, respectively, with higher accuracy than the other methods considered.