  Discrete but ordered covariates are quite common in applied statistics, and
some regularized fitting procedures have been proposed for proper handling of
ordinal predictors in statistical modeling. In this study, we show how
quadratic penalties on adjacent dummy coefficients of ordinal predictors
proposed in the literature can be incorporated in the framework of generalized
additive models, making tools for statistical inference developed there
available for ordinal predictors as well. Motivated by an application from
neonatal medicine, we discuss whether results obtained when constructing
confidence intervals and testing significance of smooth terms in generalized
additive models are useful with ordinal predictors/penalties as well.
