Estimation of missing data using latent variable methods with auxiliary information

Estimating missing data in a matrix is often done with methods, such as the EM algorithm, using the existing data in that matrix. However, if auxiliary data that is related to the missing measurements is available, it can help to estimate the missing values. This paper presents latent variable approaches that exploit an auxiliary data information matrix, as well as the data matrix itself, for estimating missing data on raw material properties of rubbers used in formulating industrial polymer blends. The use of auxiliary information is most useful when the percentage of missing data is high, and when there exist certain combinations of missing data that show little correlation with the data that are present. Two approaches to incorporating the auxiliary information are presented: a multi-block approach and a novel two-stage projection approach. The latter approach is shown to be more flexible and to provide slightly better estimates in two industrial polymer blending problems. However, in both cases, the addition of the auxiliary information is shown to significantly improve the estimates.