| Title: | Implements Pseudo-R2D2 Prior for Ordinal Regression |
| Version: | 1.0.1 |
| Description: | Implements the pseudo-R2D2 prior for ordinal regression from the paper "Psuedo-R2D2 prior for high-dimensional ordinal regression" by Yanchenko (2025) <doi:10.48550/arXiv.2502.17491>. In particular, it provides code to evaluate the probability distribution function for the cut-points, compute the log-likelihood, calculate the hyper-parameters for the global variance parameter, find the distribution of McFadden's coefficient-of-determination, and fit the model in 'rstan'. Please cite the paper if you use these codes. |
| License: | MIT + file LICENSE |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.3.2 |
| Biarch: | true |
| Depends: | R (≥ 3.5.0) |
| Imports: | extraDistr (≥ 1.10.0), GIGrvg (≥ 0.8), LaplacesDemon (≥ 16.1.6), methods, Rcpp (≥ 0.12.0), RcppParallel (≥ 5.0.1), rstan (≥ 2.18.1), rstantools (≥ 2.4.0) |
| LinkingTo: | BH (≥ 1.66.0), Rcpp (≥ 0.12.0), RcppEigen (≥ 0.3.3.3.0), RcppParallel (≥ 5.0.1), rstan (≥ 2.18.1), StanHeaders (≥ 2.18.0) |
| SystemRequirements: | GNU make |
| Suggests: | knitr, rmarkdown, ggplot2, dplyr |
| VignetteBuilder: | knitr |
| NeedsCompilation: | yes |
| Packaged: | 2025-03-18 06:15:53 UTC; ericyanchenko |
| Author: | Eric Yanchenko [aut, cre] |
| Maintainer: | Eric Yanchenko <eyanchenko@aiu.ac.jp> |
| Repository: | CRAN |
| Date/Publication: | 2025-03-18 11:20:09 UTC |
The 'R2D2ordinal' package.
Description
This package implements the methods from "Pseudo-R2D2 prior for high-dimensional ordinal regression" by Eric Yanchenko.
Author(s)
Maintainer: Eric Yanchenko eyanchenko@aiu.ac.jp
PDF of cut-points
Description
This function computes the value of the probability density function for the cut-points. The distribution is induced by a Dirichlet distribution on the prior probabilities of the response.
Usage
dcut(tau, W, alpha, log = FALSE)
Arguments
tau |
cut-points |
W |
global variance |
alpha |
concentration parameters for prior probabilities of Y |
log |
logical; if TRUE, returns log pdf |
Value
value of pdf at tau
Examples
tau = c(-1,1) # set cut points
W = 1 # set value of global variance
alpha = c(1,1,1) #concentration parameters
dcut(tau, W, alpha, log=FALSE)
Find optimal GIG parameters for W prior
Description
This function finds the optimal GIG parameters for the prior on W which induces a beta prior distribution on McFadden's R2.
Usage
find_param(
a,
b,
n,
K,
alpha = rep(1, K),
nsims = 1000,
nreps = 5,
no_cores = 10
)
Arguments
a |
hyper-parameter of prior for R2 ~ Beta(a,b) |
b |
hyper-parameter of prior for R2 ~ Beta(a,b) |
n |
number of observations |
K |
number of response categories |
alpha |
prior hyper-parameters for prior Dirichlet distribution on response probabilities |
nsims |
number of times to simulate data |
nreps |
number of times to run the algorithm (default = 5) |
no_cores |
number of cores to parallelize data-generation process |
Value
Optimal GIG parameters
Examples
a = 1
b = 5
n = 100
K = 3
find_param(a, b, n, K, no_cores=1)
Log-Likelihood for ordinal regression
Description
This function evaluates the log-likelihood of the response for a given value of the parameters.
Usage
llike(Y, W, tau)
Arguments
Y |
ordinal response |
W |
global variance |
tau |
cut-points |
Value
value of log-likelihood at Y, W and tau
Examples
set.seed(1234)
K = 3 # number of response categories
Y = sample(1:K, 10, replace=TRUE) # generate responses
W = 1
tau = c(-1, 1) # set parameter values
llike(Y, W, tau)
Ordinal regression in Stan with R2D2 prior
Description
This function carries out a Bayesian ordinal regression model in Stan using the proposed psuedo-R2D2 prior
Usage
ord_r2d2(
x,
y,
K,
a = 1,
b = 10,
hyper = NULL,
alpha = rep(1, K),
nsims = 1000,
nreps = 5,
no_cores = 10,
progress = FALSE,
...
)
Arguments
x |
covariate matrix |
y |
response variables |
K |
number of response categories |
a |
hyper-parameter of prior for R2 ~ Beta(a,b) |
b |
hyper-parameter of prior for R2 ~ Beta(a,b) |
hyper |
hyper-parameters for W prior |
alpha |
prior hyper-parameters for prior Dirichlet distribution on response probabilities |
nsims |
number of times to simulate data |
nreps |
number of times to run the algorithm (default = 5) |
no_cores |
number of cores to parallelize data-generation process |
progress |
logical. if TRUE, shows the progress bars from the posterior sampling. |
... |
optional hyper-parameters for Stan fitting |
Value
Stan model fit
Examples
# X are covariates, Y are responses, K is number of response categories
# This example will yield low R2 values as the response are independent of the covariates.
set.seed(1234)
n = 100
p = 5
X = matrix(rnorm(n*p), nrow = n, ncol=p)
K = 3
Y = sample(1:K, 100, replace=TRUE)
a = 1
b = 5
# Pre-computed hyperparameters
fit <- ord_r2d2(X, Y, K, hyper=c(0.002, 0.989, 1.013), no_cores=1)
out <- rstan::extract(fit)
# Plot histogram of posterior W
hist(out$W, xlab="W")
Posterior distribution of McFadden's R2
Description
This function finds the posterior distribution of McFadden's R2 given the posterior samples from a Stan model fit
Usage
r2_mc(Y, out)
Arguments
Y |
ordinal response |
out |
posterior samples from R2D2 model fit in Stan |
Value
Posterior samples from McFadden's R2
Examples
# Obtain output from ord_r2d2() model fit
set.seed(1234)
# X are covariates, Y are responses, K is number of response categories
# This example will yield low R2 values as the response are independent of the covariates.
n = 100
p = 5
X = matrix(rnorm(n*p), nrow = n, ncol=p)
K = 3
Y = sample(1:K, 100, replace=TRUE)
a = 1
b = 5
# Pre-computed hyperparameters
fit <- ord_r2d2(X, Y, K, hyper=c(0.002, 0.989, 1.013), no_cores=1)
out <- rstan::extract(fit)
# Plot histogram of posterior R2
hist(r2_mc(Y, out), xlab="R2")