Doubly generalized shape constrained additive models

Flexible nonparametric regression modelling approaches for analyzing the relationships between a response variable and multiple predictors could be too flexible and give implausible results.

When analyzing such relationships, it might be natural to assume that some of them obey certain shape constraints, such as monotonicity and convexity.

Pya and Wood (2015) developed a general framework for shape constrained generalized additive models, SCAM, demonstrating its efficacy and practicality in numerous applications.

However, existing methods do not support complex models with large data sets, yet these are increasingly invaluable and important as technological advances across science and industry generate vast quantities of data.

Moreover, efficient and robust computation is currently possible in the standard exponential family setting, but models for beta regression, ordered categorical data, survival models require methodological development beyond the standard cases.

The project aims to address these limitations by1. developing scalable methods for fitting SCAM that can handle larger data sets than up to now been possible.2. developing methods for models with the response distribution beyond the exponential family,3. developing open source software that implements the new methods and meets the needs of scientific and industrial users.As SCAM is successfully used in various application areas, the results of this project are expected to have a very high impact.