This website contains information about the R package ordbetareg and
general information about other implementations of the ordered beta
regression model in other statistical packages. If you just want to get
started with the R package ordbetareg, see the
vignette. The package website has further details on other implementations of the model in other statistical software packages.
Proportion data–percentiles, slider scales, visual-analog scales–have long puzzled statisticians because they combine two things: a continuous measure (the proportion) and a discrete measure (the top value of 1 or 100% and the bottom value of 0 or 0%). Conventional statistical models like the oft-used OLS regression implicitly assume these boundaries do not exist; this means an OLS regression can predict to absurd values like 115% of patients being sick or -5% of legislators being elected.
To address this issue, I developed the ordered beta regression model that combines two things: beta regression, which is defined for any bounded continuous scale, and ordered logit, which works for discrete categories. By doing this, you can fit an ordered beta regression for any percentile/proportion for both the middle continuous part and the bounds of the scale. This model can also predict within this scale as well.
I describe the model and how to do this type of modeling in this blog post. For more detail on the inner workings of the model, I refer you to the paper:
Kubinec, Robert. 2023. “Ordered Beta Regression: A Parsimonious, Well-Fitting Model for Continuous Data with Lower and Upper Bounds.” Political Analysis 31(4): 519–36. doi: http://doi.org/10.1017/pan.2022.20.
For an ungated version of the article, see the pre-publication draft on OSF:
https://osf.io/preprints/socarxiv/2sx6y
If you’ve enjoyed using the package, consider buying some ordbetareg
swag! Click the image below to go to the online store (I receive a few
dollars from each order).
At present, ordered beta regression is available in Stan (Section 3.5), R (Section 3.1), Python (Section 3.2), Stata (Section 3.3), and Julia (Section 3.4). R has the strongest support for the model with multiple implementations, but it is perfectly usable in other statistical frameworks. Below I briefly describe the available packages.
Ordered beta regression is currently available in R in two different
packages:
ordbetareg
and
glmmTMB.
The primary difference between these two packages is estimation method
and the number of ordered beta-specific functions. ordbetareg is a
package that estimates a Bayesian implementation as described in the
paper above by using brms, a powerful R package for Bayesian
regression. ordbetareg is maintained by me and you can see the full
source code here on
Github (and report an
issue with the
package if you have
one). The package includes auxiliary functions like power analysis and
plots that are specific to proportion responses—check out the package
vignette
for more details.
glmmTMB, by contrast, is a general purpose regression package that
specializes in mixed multilevel models. It implements a broad array of
regression models using maximum likelihood. This means that a model
estimated in glmmTMB will almost certainly be faster than ordbetareg
(although if you set up ordbetareg to use
cmdstanr it can get pretty fast). On
the other hand, maximum likelihood estimation has some limitations.
Arguably the most important one is that it can be tricky to fit a model
that doesn’t have observations at the bounds, i.e. either 0 (0%) or 1
(100%). The Bayesian implementation in ordbetareg has no problem doing
this.
That being said, I think glmmTMB is a fine package and believe it
works fine for many scholars’ problems. brms, which ordbetareg is
based on, offers a lot more features, including native support for
multiple imputation, time series modeling and even latent
variable/factor analysis modeling, but it does require more setup and
the models are generally slower.
For either package, I highly recommend using
marginaleffects, and in particular the
avg_slopes function, to convert the coefficient estimates in the
package to the bounded scale (i.e. between 0 and 1). This function
allows you to then interpret your model estimates as the effect of a
covariate in terms of percentage change/proportion change in the bounded
response/outcome. marginaleffects is available on
CRAN
and works great with both ordbetareg and glmmTMB.
With both of these packages available, ordered beta regression has very strong support in R. If you don’t have a preference for a particular software package and want to use this model, I would recommend R.
Ordered beta regression is implemented using the scipy package with
maximum likelihood estimation. At present, you’ll need to clone (i.e.,
download) this Github
repository to install the
package as it is not yet available with pip or conda forge. The
package includes plotting functions specific to proportion outcomes and
reports coefficient values in the untransformed (logit) scale.
marginaleffects support for this package is coming soon.
There is initial support for Stata as a set of .ado files that can be
downloaded and installed in the ado folder in your Stata machine. More
details are available on the Github
repository. This package
supports using the margins command to convert coefficients to the
bounded outcome scale, although it does not support all Stata features
as of yet. There are plans to make this package available via SSC in the
near future.
Ordered beta regression is available via the
SubjectiveScalesModels.jl
package, which offers support for a variety of regression models useful
in cognitive psychology and other fields with sliders/visual analog
scales. The package includes neat visualizations and is maintained by
Dominique Makowksi.
As is evident in the paper, the original model was written in Stan code. While I no longer am maintaining the Stan code, it is available in the paper repository and works great. If you want to incorporate the likelihood or other Stan code into your Stan model, feel free!