ordPens: Selection and/or Smoothing and Principal Components Analysis for Ordinal Variables

We provide selection, and/or smoothing/fusion of ordinally scaled independent variables using a group lasso or generalized ridge penalty. In addition, nonlinear principal components analysis for ordinal variables is offered, using a second-order difference penalty.

Also, ANOVA with ordered factors is provided by the function ordAOV; testing for differentially expressed genes can be done using ordGene. For details cf. Gertheiss (2014) and Sweeney et al. (2015), respectively.

For smoothing, selection and fusion, details may be found in Tutz and Gertheiss (2014, 2016). All functions are documented in detail in vignette("ordPens", package = "ordPens"). For smoothing only, the package also builds a bridge to mgcv::gam(), see Gertheiss et al. (2021) for further information.

For the function implementing nonlinear principal components analysis, ordPCA, details can be found in Hoshiyar et al. (2021) and vignette("ordPCA", package = "ordPens").

Version 1.0.0 is a major release with new functions:

• ordPCA applies nonlinear principal components analysis for ordinal variables. Also, performance evaluation and selection of an optimal penalty parameter provided.
  
• ordFusion fits dummy coefficients of ordinally scaled independent variables with a fused lasso penalty for fusion and selection.
• A new type of spline basis for ordered factors s(..., bs = "ordinal")is provided, such that smooth terms in the mgcv::gam() formula can be used as an alternative and extension to ordSmooth(). Additionally, generic functions for prediction and plotting are provided.

References

• Gertheiss, J. (2014). ANOVA for factors with ordered levels. Journal of Agricultural, Biological and Environmental Statistics 19, 258-277.

• Gertheiss, J., F. Scheipl, T. Lauer, and H. Ehrhardt (2021). Statistical inference for ordinal predictors in generalized linear and additive models with application to bronchopulmonary dysplasia. Preprint, available from https://arxiv.org/abs/2102.01946.

• Hoshiyar, A., H.A.L. Kiers, and J. Gertheiss (2021). Penalized non-linear principal components analysis for ordinal variables with an application to international classification of functioning core sets, Preprint.

• Sweeney, E., C. Crainiceanu, and J. Gertheiss (2015). Testing differentially expressed genes in dose-response studies and with ordinal phenotypes. Statistical Applications in Genetics and Molecular Biology 15, 213-235.

• Tutz, G. and J. Gertheiss (2014). Rating scales as predictors – the old question of scale level and some answers. Psychometrica 79, 357-376.

• Tutz, G. and J. Gertheiss (2016). Regularized regression for categorical data. Statistical Modelling 16, 161-200.