  We investigate model based classification with partially labelled training
data. In many biostatistical applications, labels are manually assigned by
experts, who may leave some observations unlabelled due to class uncertainty.
We analyse semi-supervised learning as a missing data problem and identify
situations where the missing label pattern is non-ignorable for the purposes of
maximum likelihood estimation. In particular, we find that a relationship
between classification difficulty and the missing label pattern implies a
non-ignorable missingness mechanism. We examine a number of real datasets and
conclude the pattern of missing labels is related to the difficulty of
classification. We propose a joint modelling strategy involving the observed
data and the missing label mechanism to account for the systematic missing
labels. Full likelihood inference including the missing label mechanism can
improve the efficiency of parameter estimation, and increase classification
accuracy.
