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Theserp R package fits cumulative link models (CLMs) with thesmooth-effect-on-response penalty (SERP). Thecumulative modeldeveloped by McCullagh (1980) is probably the most frequently usedordinal model in empirical studies. However, the stochastic orderingproperty of the general form of the model poses a very serious challengein most empirical applications of the model. For instance, unstablelikelihoods with ill-conditioned parameter space are frequentlyencountered during the iterative process.serp implements a uniqueregularization method for CLMs that provides the means of smoothing theadjacent categories in the model. At extreme shrinkage, SERP causes allsubject-specific effects associated with each variable in the model toshrink towards unique global effects. Fitting is done using a modifiedNewton’s method. Several standard model performance and descriptivemethods are also available. SeeUgba,2021,Ugba et al.,2021 andTutz and Gertheiss,2016 for further details onthe implemented penalty.

Consider the cumulative logit model of thewinedataset, wherethe rating of wine bitterness is predicted with the two treatmentfactors, temperature and contact.

## The unpenalized non-proportional odds model returns unbounded estimates, hence,## not fully identifiable.f1<- serp(rating~temp+contact,slope="unparallel",reverse=TRUE,link="logit",data=wine)coef(f1)

## The penalized non-proportional odds model with a user-supplied lambda gives## a fully identified model having bounded estimates. A suitable tuning criterion## could as well be used to select lambda (e.g., aic or cv)f2<- serp(rating~temp+contact,slope="penalize",link="logit",reverse=TRUE,tuneMethod="user",lambda=1e1 ,data=wine)coef(f2)

## A penalized partial proportional odds model with one variable set to## global effect is also possible.f3<- serp(rating~temp+contact,slope="penalize",reverse=TRUE,link="logit",tuneMethod="user",lambda=2e1,globalEff=~temp,data=wine)coef(f3)

## The unpenalized proportional odds model with constrained estimates.## Under estreme shrinkage, estimates in f2 equal those in this model.f4<-  serp(rating~temp+contact,slope="parallel",reverse=FALSE,link="logit",data=wine)summary(f4)

Before installingserp, it is encouraged to have a recent version ofR installed. Thereleased version ofserp can be installed fromCRAN with:

install.packages("serp")

or the development version fromGitHub with:

if (!require("devtools")) install.packages("devtools")devtools::install_github("ejikeugba/serp")

Loadserp into R environment with:

library(serp)

Pull requests are welcomed! Please submit your contributions toserpthrough the list ofPull Requests, following thecontributingguidelines. Toreport issues and/or seek support, please file a new ticket in theissue tracker, and expect afeedback ASAP!

Please note thatserp is released with aContributor Code ofConduct.By contributing to this project, you agree to abide by its terms.

McCullagh, P. (1980). Regression Models for Ordinal Data.Journal ofthe Royal Statistical Society. Series B (Methodological), 42, 109-142.https://doi.org/10.1111/j.2517-6161.1980.tb01109.x

Randall, J (1989). The analysis of sensory data by generalized linearmodel.Biometrical Journal, 31, 781–793.https://doi.org/10.1002/bimj.4710310703

Tutz, G. and Gertheiss, J. (2016). Regularized Regression forCategorical Data (With Discussion and Rejoinder).StatisticalModelling, 16, 161-260.https://doi.org/10.1177/1471082X16642560

Ugba, E. R., Mörlein, D. and Gertheiss, J. (2021). Smoothing in OrdinalRegression: An Application to Sensory Data.Stats, 4, 616–633.https://doi.org/10.3390/stats4030037

Ugba, E. R. (2021). serp: An R package for smoothing in ordinalregressionJournal of Open Source Software, 6(66), 3705.https://doi.org/10.21105/joss.03705