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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. (2022) 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 1.1.0 is a minor release with new functions:

• Functions ordSelect, ordFusion updated/extended to cumulative logit model models.
• Function ordCV added, provides cross-validation for penalized regression models with ordinal predictors.
  
• Function StabilityCumu added, provides stability selection for penalized cumulative logit models.

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.

Installation & getting started

For standard use, install ordPens from CRAN:

install.packages("ordPens")

The development version of the package may be installed from GitHub:

devtools::install_git("https://github.com/ahoshiyar/ordPens", build_vignettes = TRUE)

For a detailed overview about the functionalities and given examples type:

library(ordPens)
vignette("ordPens", package = "ordPens")
vignette("ordPCA", package = "ordPens")

Issues

If you encounter any bugs or have any specific feature requests, please file an issue.

Contributions & Code of conduct

Contributions are very welcome. Interested contributors should consult the contribution guidelines prior to submitting a pull request.

Please note that the ordPens package is released with a Contributor Code of Conduct. By contributing to this project, you agree to abide by its terms.

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 (2022). Statistical inference for ordinal predictors in generalized linear and additive models with application to bronchopulmonary dysplasia. BMC research notes 15, 112.

• 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. British Journal of Mathematical and Statistical Psychology 76, 353-371.

• Hoshiyar, A., Gertheiss, L.H., and Gertheiss, J. (2023). Regularization and model selection for item-on-items regression with applications to food products’ survey data. Preprint, available from https://arxiv.org/abs/2309.16373.

• 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.

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.