serp R package fits cumulative link models (CLMs) with the
smooth-effect-on-response penalty (SERP). The
developed by McCullagh (1980) is probably the most frequently used
ordinal model in empirical studies. However, the stochastic ordering
property of the general form of the model poses a very serious challenge
in most empirical applications of the model. For instance, unstable
likelihoods with ill-conditioned parameter space are frequently
encountered during the iterative process.
serp implements a unique
regularization method for CLMs that provides the means of smoothing the
adjacent categories in the model. At extreme shrinkage, SERP causes all
subject-specific effects associated with each variable in the model to
shrink towards unique global effects. Fitting is done using a modified
Newton’s method. Several standard model performance and descriptive
methods are also available. See Ugba,
2021, Ugba et al.,
2021 and Tutz and Gertheiss,
2016 for further details on
the implemented penalty.
Consider the cumulative logit model of the wine dataset, where the rating of wine bitterness is predicted with the two treatment factors, 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)
or the development version from GitHub with:
if (!require("devtools")) install.packages("devtools") devtools::install_github("ejikeugba/serp")
serp into R environment with:
Pull requests are welcomed! Please submit your contributions to
through the list of
Pull Requests, following the contributing
report issues and/or seek support, please file a new ticket in the
issue tracker, and expect a
Please note that
serp is released with a Contributor Code of
By contributing to this project, you agree to abide by its terms.
McCullagh, P. (1980). Regression Models for Ordinal Data. Journal of the 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 linear model. Biometrical Journal, 31, 781–793. https://doi.org/10.1002/bimj.4710310703
Tutz, G. and Gertheiss, J. (2016). Regularized Regression for Categorical Data (With Discussion and Rejoinder). Statistical Modelling, 16, 161-260. https://doi.org/10.1177/1471082X16642560
Ugba, E. R., Mörlein, D. and Gertheiss, J. (2021). Smoothing in Ordinal Regression: 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 ordinal regression Journal of Open Source Software, 6(66), 3705. https://doi.org/10.21105/joss.03705
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