Title:	Bayesian Distributed Lag Model Fitting for Binary and Count Response Data
Version:	1.0.0
Maintainer:	Daniel Dempsey <daniel.dempsey0@gmail.com>
Description:	Tools for fitting Bayesian Distributed Lag Models (DLMs) to longitudinal response data that is a count or binary. Count data is fit using negative binomial regression and binary is fit using quantile regression. The contribution of the lags are fit via b-splines. In addition, infers the predictor inclusion uncertainty. Multimomial models are not supported. Based on Dempsey and Wyse (2025) <doi:10.48550/arXiv.2403.03646>.
License:	GPL-3
Encoding:	UTF-8
Imports:	statmod, BayesLogit, dlnm, splines, dplyr, ggplot2, ggridges, reshape2
RoxygenNote:	7.3.2
URL:	https://github.com/DanDempsey/DiscreteDLM
BugReports:	https://github.com/DanDempsey/DiscreteDLM/issues
NeedsCompilation:	yes
Packaged:	2025-02-06 01:49:36 UTC; bluff
Author:	Daniel Dempsey [aut, cre], Jason Wyse [ctb], Christian E. Galarza [ctb] (Author of the ald package, which this package derives some code from (see the COPYRIGHT file in the inst folder).), Victor H. Lachos [ctb] (Author of the ald package, which this package derives some code from (see the COPYRIGHT file in the inst folder).)
Repository:	CRAN
Date/Publication:	2025-02-06 19:40:10 UTC

The Asymmetric Laplacian Distribution

Description

Density, distribution function, quantile function and random generation for the Asymmetric Laplacian Distribution (ALD). Also contains random number generation for a truncated ALD. Our code here is heavily derived from the "ald" package by Galarza and Lachos (2021), adapted to vectorize the mu parameter.

Usage

dALD(x, mu = 0, sigma = 1, p = 0.5)
pALD(q, mu = 0, sigma = 1, p = 0.5)
qALD(prob, mu = 0, sigma = 1, p = 0.5)
rALD(n, mu = 0, sigma = 1, p = 0.5)
rTALD(n, upper_tail, mu = 0, sigma = 1, p = 0.5)

Arguments

Details

These functions are based on the three parameter ALD:

f(x|\mu, \sigma, p) = \frac{p(1-p)}{\sigma}exp\left(-\rho_p(\frac{x-\mu}{\sigma})\right)

where

\rho_p(z) = z(p - I_{z<0})

These functions differ than the ones provided in the ald package by vectorising the mu parameter. In addition we have implemented a function to sample from the truncated ALD (rTALD), which is needed for Bayesian quantile regression. Note that truncation is fixed at zero; the user only decides whether the negative or positive axis is discarded.

Value

Each function returns a vector. dALD, pALD and qALD returns the PDF, CDF and inverse CDF of the ALD respectively. rALD returns a random sample from the ALD distribution, and rTALD returns a random sample from the ALD truncated at 0.

Author(s)

Daniel Dempsey (daniel.dempsey0@gmail.com). Original code from the ald package were written by Christian E. Galarza and Victor H. Lachos.

Examples

set.seed( 100 )

### Vectorised input
random_ALD <- rALD( 1000, mu = runif(1000, -100, 100) )
plot( random_ALD )

### Truncated version
trunc_random_ALD <- rTALD( 1000, TRUE, mu = 2, sigma = 3, p = 0.75 )
plot( dALD(sort(trunc_random_ALD), mu = 2, sigma = 3, p = 0.75) )

Fitting Discrete Distributed Lag Models with Variable Selection via MCMC

Description

DiscreteDLM contains functionality for fitting and visualising Bayesian Distributed Lag Models (DLMs) when the response variable is either count or binary. More specifically, this package contains an implementation of Bayesian quantile binary regression (for binary response data) and negative-binomial regression (for count response data). Additionally, these functions implement variable uncertainty inference for each predictor. Multinomial regression is not implemented.

While these functions can be applied to any standard regression problem, the package was set up with DLMs in mind; the functions therein allow for an easy-to-use pipeline to go from defining the DLM, fitting the DLM, and visualising the results.

Details

Author(s)

Daniel Dempsey <daniel.dempsey0@gmail.com>, with contributions and supervision by Jason Wyse <wyseja@tcd.ie>

References

Daniel Dempsey and Jason Wyse. 2025. "Bayesian Variable Selection in Distributed Lag Models: A Focus on Binary Quantile and Count Data Regressions." https://doi.org/10.48550/arXiv.2403.03646.

See Also

dataframe_DLM,NB_MCMC,QB_MCMC

Negative Binomial Regression via MCMC

Description

Fits a negative binomial regression model using Gibbs sampling and performs Bayesian variable selection.

Usage

NB_MCMC(
  formula,
  data = NULL,
  nsamp = 1000,
  nburn = 1000,
  thin = 1,
  standardize = TRUE,
  prior_beta_mu = 0,
  prior_beta_sigma = 100,
  prior_gamma_p = 0.5,
  prior_xi_shape = 2,
  prior_xi_scale = 1/50,
  init_beta = 0,
  init_gamma = FALSE,
  init_xi = 1,
  verbose = TRUE
)

Arguments

Details

This function fits a negative binomial regression model via MCMC. Latent variable representation allows for Gibbs sampling of the parameters; see Pillow and Scott (2012) and Zhou et. al. (2012). The algorithm also includes predictor inclusion uncertainty inference (inferred via a Metroplis step) adapted from Holmes and Held (2006).

The parameters of interest for this model are the regression slopes (beta), the binary predictor inclusion indicator (gamma) and the negative binomial stopping parameter (xi). For further details, see Dempsey and Wyse (2024).

Note that when setting initial values and priors for gamma, the intercept must be included and therefore its initial value and prior are forced to be equal to 1. If an intercept is not used, then the first variable is forced to be included instead.

Value

An "MCMC_DLM" object; a list containing the MCMC-derived posterior sample, as well as the data that were used.

Author(s)

Daniel Dempsey (daniel.dempsey0@gmail.com)

References

Chris C. Holmes and Leonhard Held. 2006. "Bayesian auxiliary variable models for binary and multinomial regression." Bayesian Analysis 1(1): 145-168.

Daniel Dempsey and Jason Wyse. 2025. "Bayesian Variable Selection in Distributed Lag Models: A Focus on Binary Quantile and Count Data Regressions." https://doi.org/10.48550/arXiv.2403.03646

Jonathan Pillow and James Scott. 2012. "Fully Bayesian inference for neural models with negative-binomial spiking." Advances in neural information processing systems 25.

Mingyuan Zhou, Lingbo Li, David Dunson and Lawrence Carin. 2012. "Lognormal and gamma mixed negative binomial regression." Proceedings of the... International Conference on Machine Learning. International Conference on Machine Learning. Vol. 2012. NIH Public Access.

See Also

QB_MCMC, dataframe_DLM, plot.MCMC_DLM

Examples

### Set up data
X <- dplyr::select( dlnm::chicagoNMMAPS, c('cvd', 'dow', 'temp', 'dptp', 'o3') )
X <- na.omit( X )
arglag <- list( fun = 'bs', df = 4 )
DLM_dat <- dataframe_DLM( X, lag = 40, dynamic_vars =  c('temp', 'dptp', 'o3'), arglag = arglag )

### Fit model
# NOTE: Only using 100 total iterations for illustration purposes!
myfit <- NB_MCMC( cvd ~ ., data = DLM_dat, nsamp = 50, nburn = 50 )
summary( myfit )

Binary Quantile Regression via MCMC

Description

Fits a quantile regression model to a binary response dataset using Gibbs sampling and performs Bayesian variable selection.

Usage

QB_MCMC(
  formula,
  data = NULL,
  quantile = 0.5,
  nsamp = 1000,
  nburn = 1000,
  thin = 1,
  standardize = TRUE,
  prior_beta_mu = 0,
  prior_beta_sigma = 100,
  prior_gamma_p = 0.5,
  init_beta = 0,
  init_gamma = FALSE,
  verbose = TRUE
)

Arguments

Details

This function fits a quantile binary regression model via MCMC. Latent variable representation allows for Gibbs sampling of the parameters; see Benoit and Van den Poel (2017). The algorithm also includes predictor inclusion uncertainty inference (inferred via a Metroplis step) adapted from Holmes and Held (2006).

The parameters of interest for this model are the regression slopes (beta) and the binary predictor inclusion indicator (gamma). For further details, see Dempsey and Wyse (2024).

Note that when setting initial values and priors for gamma, the intercept must be included and therefore its initial value and prior are forced to be equal to 1. If an intercept is not used, then the first variable is forced to be included instead.

Value

An "MCMC_DLM" object; a list containing the MCMC-derived posterior sample, as well as the data that were used.

Author(s)

Daniel Dempsey (daniel.dempsey0@gmail.com)

References

Chris C. Holmes and Leonhard Held. 2006. "Bayesian auxiliary variable models for binary and multinomial regression." Bayesian Analysis 1(1): 145-168.

Daniel Dempsey and Jason Wyse. 2025. "Bayesian Variable Selection in Distributed Lag Models: A Focus on Binary Quantile and Count Data Regressions." https://doi.org/10.48550/arXiv.2403.03646

Dries F. Benoit and Dirk Van den Poel. 2017. "bayesQR: A Bayesian approach to quantile regression." Journal of Statistical Software 76: 1-32.

See Also

NB_MCMC, dataframe_DLM, plot.MCMC_DLM

Examples

### Set up data
set.seed( 100 )
binary_response <- dlnm::chicagoNMMAPS$cvd > 65
predictors <- dplyr::select( dlnm::chicagoNMMAPS, c('dow', 'temp', 'dptp', 'o3') )
X <- cbind( binary_response, predictors )
X <- na.omit( X )
arglag <- list( fun = 'bs', df = 4 )
DLM_dat <- dataframe_DLM( X, lag = 40, dynamic_vars =  c('temp', 'dptp', 'o3'), arglag = arglag )

### Fit model
# NOTE: Only using 100 total iterations for illustration purposes!
myfit <- QB_MCMC( binary_response ~ ., data = DLM_dat, nsamp = 50, nburn = 50 )
summary( myfit )

Creating a DLM-Ready Dataframe

Description

Transforms a dataframe to prepare it for distributed lag modelling.

Usage

dataframe_DLM(X, lag, dynamic_vars = NULL, arglag = list(fun = "bs"), ...)

Arguments

Details

The purpose of this function is to streamline the preperation of the data for distributed lag modelling in the case where every dynamic variable is handled the same way.

If no dynamic variables are given, the input dataframe is returned unaltered with a warning. Otherwise, the function returns a dataframe_DLM object, which is essentially treated like a standard dataframe but contains extra information to simplify the process of distributed lag modelling when using the NB_MCMC or QB_MCMC functions.

Value

The input is returned unchanged if no dynamic variables are given. Otherwise a dataframe_DLM object is returned. See details.

Author(s)

Daniel Dempsey (daniel.dempsey0@gmail.com)

Examples

X <- dplyr::select( dlnm::chicagoNMMAPS, c('cvd', 'dow', 'temp', 'dptp', 'o3') )
X <- na.omit( X )
arglag <- list( fun = 'bs', df = 4 )
DLM_dat <- dataframe_DLM( X, lag = 40, dynamic_vars =  c('temp', 'dptp', 'o3'), arglag = arglag )

Visualises Results from MCMC_DLM Fits

Description

Provides some ggplot visualisations of the posterior from MCMC_DLM objects.

Usage

## S3 method for class 'MCMC_DLM'
plot(x, type = "beta", include_intercept = FALSE, print_output = TRUE, ...)

Arguments

Details

The type of plot generated is determined by the type argument. The options are:

• beta: A ridgeplot of the regression slopes,

• gamma: A bar chart of the mean probability of inclusion,

• xi: A kernel density estimate plot of the negative binomial stopping parameter (of course, this only works for negative binomial regression fits),

• lags: A collection of plots (supplied in a list), each containing a line chart of the lag-response for each dynamic variable.

Value

A ggplot object, except when type = 'lags', in which case it will be a list of ggplot objects. Will display the ggplot visual if print_output = TRUE.

Author(s)

Daniel Dempsey (daniel.dempsey0@gmail.com)