Additive interaction modelling using I-priors
This work addresses difficulties in statistical modeling for researchers and practitioners dealing with interaction terms, though it appears incremental as an extension of existing I-prior methods.
The authors tackled the challenges of estimation and model selection in additive regression models with interactions by extending the I-prior methodology to multiple covariates, resulting in a parsimonious specification that reduces scale parameters and enables straightforward model selection based on marginal likelihood.
Additive regression models with interactions are widely studied in the literature, using methods such as splines or Gaussian process regression. However, these methods can pose challenges for estimation and model selection, due to the presence of many smoothing parameters and the lack of suitable criteria. We propose to address these challenges by extending the I-prior methodology (Bergsma, 2020) to multiple covariates, which may be multidimensional. The I-prior methodology has some advantages over other methods, such as Gaussian process regression and Tikhonov regularization, both theoretically and practically. In particular, the I-prior is a proper prior, is based on minimal assumptions, yields an admissible posterior mean, and estimation of the scale (or smoothing) parameters can be done using an EM algorithm with simple E and M steps. Moreover, we introduce a parsimonious specification of models with interactions, which has two benefits: (i) it reduces the number of scale parameters and thus facilitates the estimation of models with interactions, and (ii) it enables straightforward model selection (among models with different interactions) based on the marginal likelihood.