  High-cardinality categorical features are pervasive in actuarial data (e.g.
occupation in commercial property insurance). Standard categorical encoding
methods like one-hot encoding are inadequate in these settings.
  In this work, we present a novel _Generalised Linear Mixed Model Neural
Network_ ("GLMMNet") approach to the modelling of high-cardinality categorical
features. The GLMMNet integrates a generalised linear mixed model in a deep
learning framework, offering the predictive power of neural networks and the
transparency of random effects estimates, the latter of which cannot be
obtained from the entity embedding models. Further, its flexibility to deal
with any distribution in the exponential dispersion (ED) family makes it widely
applicable to many actuarial contexts and beyond.
  We illustrate and compare the GLMMNet against existing approaches in a range
of simulation experiments as well as in a real-life insurance case study.
Notably, we find that the GLMMNet often outperforms or at least performs
comparably with an entity embedded neural network, while providing the
additional benefit of transparency, which is particularly valuable in practical
applications.
  Importantly, while our model was motivated by actuarial applications, it can
have wider applicability. The GLMMNet would suit any applications that involve
high-cardinality categorical variables and where the response cannot be
sufficiently modelled by a Gaussian distribution.
