A comparison of imputation techniques for internal preference mapping, using Monte Carlo simulation

The usual algorithm for internal preference mapping requires a complete set of observations, meaning the technique cannot be used to analyse trials based on incomplete block designs. A simulation study was carried out to compare techniques for imputing missing values under various conditions. Sets of simulated preference data with different characteristics were constructed. Monte Carlo simulation was used to create missing observations in these sets; the imputation techniques were applied to the data; and the results of preference mapping based on the imputed data compared to those from the complete data set. Convergence problems were found with two techniques. Analysis of variance revealed that effects on performance were dominated by the proportion of data missing, the level of noise in the data, and the size of the data set. Differences in performance among the three convergent imputation techniques were small; mean substitution is recommended, as it performed as well as more complex iterative techniques. The results were broadly confirmed by a similar study on a genuine set of preference data.