serp
Smooth Effects on Response Penalty for CLM
Implements a regularization method for cumulative link models using the
Smooth-Effect-on-Response Penalty (SERP). This method allows flexible
modeling of ordinal data by enabling a smooth transition from a general
cumulative link model to a simplified version of the same model. As the
tuning parameter increases from zero to infinity, the subject-specific
effects for each variable converge to a single global effect.
The approach addresses common issues in cumulative link models, such as
parameter unidentifiability and numerical instability, by maximizing a
penalized log-likelihood instead of the standard non-penalized version.
Fitting is performed using a modified Newton's method. Additionally, the
package includes various model performance metrics and descriptive tools.
For details on the implemented penalty method, see
Ugba (2021)
serp 
Overview
The serp R package fits cumulative link models (CLMs) with the
smooth-effect-on-response penalty (SERP). The cumulative model
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.
Example
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)
Installation and Use
Before installing serp, it is encouraged to have a recent version of
R installed. The
released version of serp can be installed from
CRAN with:
install.packages("serp")
or the development version from GitHub with:
if (!require("devtools")) install.packages("devtools")
devtools::install_github("ejikeugba/serp")
Load serp into R environment with:
library(serp)
Community Guidelines
Pull requests are welcomed! Please submit your contributions to serp
through the list of Pull Requests, following the contributing
guidelines. To
report issues and/or seek support, please file a new ticket in the
issue tracker, and expect a
feedback ASAP!
Code of Conduct
Please note that serp is released with a Contributor Code of
Conduct.
By contributing to this project, you agree to abide by its terms.
References
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