Methods for imputation of missing values in air quality data sets

Methods for data imputation applicable to air quality data sets were evaluated in the context of univariate (linear, spline and nearest neighbour interpolation), multivariate (regression-based imputation (REGEM), nearest neighbour (NN), self-organizing map (SOM), multi-layer perceptron (MLP)), and hybrid methods of the previous by using simulated missing data patterns. Additionally, a multiple imputation procedure was considered in order to make comparison between single and multiple imputations schemes. Four statistical criteria were adopted: the index of agreement, the squared correlation coefficient ( R 2), the root mean square error and the mean absolute error with bootstrapped standard errors. The results showed that the performance of interpolation in respect to the length of gaps could be estimated separately for each variable of air quality by calculating a gradient and an exponent α (Hurst exponent). This can be further utilised in hybrid approach in which the imputation has been performed either by interpolation or multivariate method depending on the length of gaps and variable under study. Among the multivariate methods, SOM and MLP performed slightly better than REGEM and NN methods. The advantage of SOM over the others was that it was less dependent on the actual location of the missing values. If priority is given to computational speed, however, NN can be recommended. The results in general showed that the slight improvement in the performances of multivariate methods can be achieved by using the hybridisation and more substantial one by using the multiple imputations where a final estimate is composed of the outputs of several multivariate fill-in methods.