The Joint Statistical Seminars are aimed at researchers, employees, and students.
This week's seminar is given by Natalya Pya Arnqvist, Department of Mathematics and Mathematical Statistics, Umeå University.
Title: Extended generalized additive modelling with shape constraints
Abstract: Regression models that incorporate smooth functions of predictor variables to explain the relationships with a response variable have gained widespread usage and proved successful in various applications. By incorporating smooth functions of predictor variables, these models can capture complex relationships between the response and predictors while still allowing for interpretation of the results. In situations where the relationships between a response variable and predictors are explored, it is not uncommon to assume that these relationships adhere to certain shape constraints. Examples of such constraints include monotonicity and convexity. Shape-constrained additive models (SCAM) offer a general framework for fitting exponential family generalized additive models with shape restrictions on smooths. The main objective of this talk is to provide extensions of the existing framework for SCAM with a mixture of unconstrained terms and various shape-restricted terms to accommodate smooth interaction of covariates, varying coefficient terms, linear functionals with or without shape constraints as model components, and data with short-term temporal or spatial autocorrelation. The practical usage of the suggested extensions will be illustrated in several examples.
