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README.md
In badp: Bayesian Averaging for Dynamic Panels
badp: Bayesian Averaging for Dynamic Panels
badp: Bayesian Averaging for Dynamic Panels 
Overview
The badp package implements Bayesian model averaging (BMA) for
dynamic panels with weakly exogenous regressors, following the
methodology of Moral-Benito (2016). This addresses both:
- Model uncertainty (selecting among many candidate regressors),
- Reverse causality (weak exogeneity, which permits current values
of regressors to correlate with past shocks and other regressors).
The package features:
- Tools to estimate the entire model space (via maximum likelihood)
and calculate Bayesian information criterion (BIC) for each
variant.
- Flexible model priors (binomial, binomial-beta, optional dilution
prior).
- A selectable learning rate for the model weights (
weighting and
eta in bma()), so the sensitivity of a conclusion to the marginal
likelihood approximation can be checked without re-estimating the model
space.
- Comprehensive BMA statistics, including posterior inclusion
probabilities (PIPs), posterior means, and posterior standard
deviations (regular or robust).
- Functions to visualize prior and posterior model probabilities.
- Jointness measures for pairs of regressors, indicating whether
they are complements or substitutes.
- Support for parallel computing to handle large model spaces.
Installation
You can install the released version of badp from
CRAN with:
install.packages("badp")
And the development version from GitHub with:
# install.packages("devtools")
devtools::install_github("badp-project/badp")
Once installed, simply load the package:
library(badp)
Getting Started
Data Preparation
Your data should be in the following format:
- A time column (e.g.,
year),
- An entity column (e.g.,
country),
- A dependent variable column (the variable of interest,
e.g.
gdp),
- Remaining columns as potential regressors.
A convenience function join_lagged_col() can help transform a dataset
that already contains both a variable and its lagged version into the
required format.
You can also use feature_standardization() to perform mean-centering,
demeaning (entity/time effects), or scaling (standardization) as needed.
For example:
library(magrittr)
set.seed(20)
# Features are scaled and demeaned,
# then centralized around the mean within cross-sections (fixed time effects)
data_prepared <- badp::economic_growth %>%
badp::feature_standardization(
excluded_cols = c(country, year, gdp)
) %>%
badp::feature_standardization(
group_by_col = year,
excluded_cols = country,
scale = FALSE
)
Estimating the Model Space
The function optim_model_space() estimates all possible models (each
possible subset of regressors) via maximum likelihood, storing the
results in a list object.
Note: with strongly correlated regressors, both the estimation and the
subsequent statistics step may emit warnings (e.g. NaNs produced, or a
message that some models did not converge). The exact reason is
non-trivial: it is typically connected to degenerate behaviour of the
likelihood function for some of the models, and understanding it for a
particular dataset requires inspecting the data (e.g. correlations between
regressors), the behaviour of the likelihood, and the per-model
diagnostics stored in the convergence element of the result. A good
starting point is to check which models are affected and how much
posterior model probability they carry - if it is negligible, the
warnings can usually be treated as expected behaviour.
For small to moderately sized datasets:
model_space <- badp::optim_model_space(
df = data_prepared,
dep_var_col = gdp,
timestamp_col = year,
entity_col = country,
init_value = function(n) runif(n, -10, 10)
)
For larger datasets, you can leverage multiple cores:
library(parallel)
# Choose an appropriate number of cores, taking into account system-level limits
cores <- as.integer(Sys.getenv("_R_CHECK_LIMIT_CORES_", unset = NA))
if (is.na(cores)) {
cores <- detectCores()
} else {
cores <- min(cores, detectCores())
}
cl <- makeCluster(cores)
model_space <- badp::optim_model_space(
df = data_prepared,
timestamp_col = year,
entity_col = country,
dep_var_col = gdp,
init_value = function(n) runif(n, -10, 10),
cl = cl
)
stopCluster(cl)
A progress bar is displayed to easily track the ongoing computation.
Performing Bayesian Model Averaging
After preparing the model space, run bma() to obtain posterior model
probabilities, posterior inclusion probabilities (PIPs), and other BMA
statistics under the binomial and binomial-beta model priors:
bma_results <- badp::bma(model_space, round = 3)
# Inspect the BMA summary (binomial prior results first, binomial-beta second)
bma_results[[1]] # BMA stats under binomial prior
#> PIP PM PSD PSDR PMcon PSDcon PSDRcon %(+)
#> gdp_lag NA 1.078 0.110 0.229 1.078 0.110 0.229 100
#> ish 0.710 0.085 0.061 0.090 0.120 0.032 0.085 100
#> sed 0.714 -0.046 0.061 0.111 -0.065 0.064 0.127 0
bma_results[[2]] # BMA stats under binomial-beta prior
#> PIP PM PSD PSDR PMcon PSDcon PSDRcon %(+)
#> gdp_lag NA 1.078 0.110 0.239 1.078 0.110 0.239 100
#> ish 0.765 0.091 0.058 0.090 0.120 0.033 0.085 100
#> sed 0.768 -0.048 0.062 0.114 -0.063 0.064 0.126 0
# Posterior model sizes:
bma_results[[16]]
#> Prior model size Posterior model size
#> Binomial 1 1.424
#> Binomial-beta 1 1.533
Key columns in the BMA output include: - PIP: Posterior inclusion
probability for each regressor. - PM: Posterior mean of each
parameter (averaged over all models). - PSD/PSDR: Posterior standard
deviations (regular/robust) of each parameter - %(+): Percentage of
models (among those that include a given regressor) in which the
parameter estimate is positive.
Visualizing Prior and Posterior Probabilities
model_pmp(): Shows prior vs. posterior model probabilities,
ranking models from best to worst.model_sizes(): Displays how prior vs. posterior probabilities
mass is distributed across different model sizes.
# Plot prior vs. posterior model probabilities
pmp_graphs <- badp::model_pmp(bma_results, top = 3) # Show top 3 models
# Plot probabilities by model size
size_graphs <- badp::model_sizes(bma_results)
Selecting the Best Models
Use best_models() to extract specific information about the top-ranked
models:
# Retrieve the 5 best models according to binomial prior
top3_binom <- badp::best_models(bma_results, prior = "binomial", best = 3)
# Print the inclusion matrix for each of the top 3 models
top3_binom[[1]]
#> 'No. 1' 'No. 2' 'No. 3'
#> gdp_lag 1.000 1.000 1.000
#> ish 1.000 0.000 1.000
#> sed 1.000 1.000 0.000
#> PMP 0.508 0.206 0.202
# Retrieve robust standard errors in a knit-friendly table
top3_binom[[6]]
| | ‘No. 1’ | ‘No. 2’ | ‘No. 3’ |
|:--------|:-------------------:|:-------------------:|:-------------------:|
| gdp_lag | 1.079 (0.275)*** | 1.126 (0.151)*** | 1.027 (0.193)*** |
| ish | 0.119 (0.086) | NA | 0.121 (0.082) |
| sed | -0.06 (0.126) | -0.077 (0.128) | NA |
| PMP | 0.508 | 0.206 | 0.202 |
Jointness Measures
Assess whether two regressors tend to co-occur (complements) or exclude
each other (substitutes) using jointness(). By default, it calculates
the Hofmarcher et al. (2018) measure:
joint_measures <- badp::jointness(bma_results)
head(joint_measures)
#> ish sed
#> ish NA 0.159
#> sed 0.505 NA
You can also specify older measures, such as "LS" (Ley & Steel) or
"DW" (Doppelhofer & Weeks):
joint_measures_ls <- badp::jointness(bma_results, measure = "LS")
Example
Below is a minimal reproducible workflow:
# 1) Data preparation
data_prepared <- badp::economic_growth[, 1:5] %>%
badp::feature_standardization(
excluded_cols = c(country, year, gdp)
) %>%
badp::feature_standardization(
group_by_col = year,
excluded_cols = country,
scale = FALSE
)
# 2) Estimate model space
model_space <- badp::optim_model_space(
df = data_prepared,
dep_var_col = gdp,
timestamp_col = year,
entity_col = country,
init_value = function(n) rep(0.5, n),
)
# 3) Run Bayesian Model Averaging
bma_obj <- badp::bma(
model_space = model_space
)
# 4) Inspect the top 3 models under binomial prior
best_3 <- badp::best_models(
bma_list = bma_obj,
prior = "binomial",
best = 3
)
best_3[[1]] # Inclusion table
#> 'No. 1' 'No. 2' 'No. 3'
#> gdp_lag 1.000 1.000 1.000
#> ish 1.000 0.000 1.000
#> sed 1.000 1.000 0.000
#> PMP 0.508 0.206 0.202
best_3[[2]] # Coefficients & standard errors
#> 'No. 1' 'No. 2' 'No. 3'
#> gdp_lag "1.079 (0.111)***" "1.126 (0.106)***" "1.027 (0.093)***"
#> ish "0.119 (0.033)***" NA "0.121 (0.03)***"
#> sed "-0.06 (0.063)" "-0.077 (0.063)" NA
#> PMP "0.508" "0.206" "0.202"
Troubleshooting
- Cannot install required packages / setup renv environment
Make sure to go through the displayed errors. The problem might be
connected to your OS environment. E.g. you might see an information like
the following:
Configuration failed to find one of freetype2 libpng libtiff-4 libjpeg. Try installing:
* deb: libfreetype6-dev libpng-dev libtiff5-dev libjpeg-dev (Debian, Ubuntu, etc)
* rpm: freetype-devel libpng-devel libtiff-devel libjpeg-devel (Fedora, CentOS, RHEL)
* csw: libfreetype_dev libpng16_dev libtiff_dev libjpeg_dev (Solaris)
In such case you should first try installing the recommended packages.
With properly configured system environment everything should work fine.
References
- Moral-Benito, E. (2016). "Growth Empirics in Panel Data Under Model Uncertainty and Weak Exogeneity." Journal of Applied Econometrics.
- Ley, E. and Steel, M. F. J. (2007). "Jointness in Bayesian Variable Selection with Applications to Growth Regression." Journal of Macroeconomics.
- Doppelhofer, G. and Weeks, M. (2009). "Jointness of Growth Determinants." Journal of Applied Econometrics.
- Hofmarcher, P., Crespo Cuaresma, J., Grün, B., Humer, S., and Moser, M. (2018). "Bivariate jointness measures in Bayesian Model Averaging: Solving the conundrum." Journal of Macroeconomics.
(Additional references related to the methodology can be found in the
package vignette.)
Contributions and Issues
We welcome bug reports, feature requests, and contributions. Feel free
to open an issue or pull request on
GitHub.
License
This package is distributed under the MIT license. See the
LICENSE file for details.
Try the badp package in your browser
Any scripts or data that you put into this service are public.
badp documentation built on Aug. 20, 2026, 9:08 a.m.
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
badp: Bayesian Averaging for Dynamic Panels
badp: Bayesian Averaging for Dynamic Panels
Overview
The badp package implements Bayesian model averaging (BMA) for dynamic panels with weakly exogenous regressors, following the methodology of Moral-Benito (2016). This addresses both:
- Model uncertainty (selecting among many candidate regressors),
- Reverse causality (weak exogeneity, which permits current values of regressors to correlate with past shocks and other regressors).
The package features:
- Tools to estimate the entire model space (via maximum likelihood) and calculate Bayesian information criterion (BIC) for each variant.
- Flexible model priors (binomial, binomial-beta, optional dilution prior).
- A selectable learning rate for the model weights (
weightingandetainbma()), so the sensitivity of a conclusion to the marginal likelihood approximation can be checked without re-estimating the model space. - Comprehensive BMA statistics, including posterior inclusion probabilities (PIPs), posterior means, and posterior standard deviations (regular or robust).
- Functions to visualize prior and posterior model probabilities.
- Jointness measures for pairs of regressors, indicating whether they are complements or substitutes.
- Support for parallel computing to handle large model spaces.
Installation
You can install the released version of badp from CRAN with:
install.packages("badp")
And the development version from GitHub with:
# install.packages("devtools")
devtools::install_github("badp-project/badp")
Once installed, simply load the package:
library(badp)
Getting Started
Data Preparation
Your data should be in the following format:
- A time column (e.g.,
year), - An entity column (e.g.,
country), - A dependent variable column (the variable of interest,
e.g.
gdp), - Remaining columns as potential regressors.
A convenience function join_lagged_col() can help transform a dataset
that already contains both a variable and its lagged version into the
required format.
You can also use feature_standardization() to perform mean-centering,
demeaning (entity/time effects), or scaling (standardization) as needed.
For example:
library(magrittr)
set.seed(20)
# Features are scaled and demeaned,
# then centralized around the mean within cross-sections (fixed time effects)
data_prepared <- badp::economic_growth %>%
badp::feature_standardization(
excluded_cols = c(country, year, gdp)
) %>%
badp::feature_standardization(
group_by_col = year,
excluded_cols = country,
scale = FALSE
)
Estimating the Model Space
The function optim_model_space() estimates all possible models (each
possible subset of regressors) via maximum likelihood, storing the
results in a list object.
Note: with strongly correlated regressors, both the estimation and the
subsequent statistics step may emit warnings (e.g. NaNs produced, or a
message that some models did not converge). The exact reason is
non-trivial: it is typically connected to degenerate behaviour of the
likelihood function for some of the models, and understanding it for a
particular dataset requires inspecting the data (e.g. correlations between
regressors), the behaviour of the likelihood, and the per-model
diagnostics stored in the convergence element of the result. A good
starting point is to check which models are affected and how much
posterior model probability they carry - if it is negligible, the
warnings can usually be treated as expected behaviour.
For small to moderately sized datasets:
model_space <- badp::optim_model_space(
df = data_prepared,
dep_var_col = gdp,
timestamp_col = year,
entity_col = country,
init_value = function(n) runif(n, -10, 10)
)
For larger datasets, you can leverage multiple cores:
library(parallel)
# Choose an appropriate number of cores, taking into account system-level limits
cores <- as.integer(Sys.getenv("_R_CHECK_LIMIT_CORES_", unset = NA))
if (is.na(cores)) {
cores <- detectCores()
} else {
cores <- min(cores, detectCores())
}
cl <- makeCluster(cores)
model_space <- badp::optim_model_space(
df = data_prepared,
timestamp_col = year,
entity_col = country,
dep_var_col = gdp,
init_value = function(n) runif(n, -10, 10),
cl = cl
)
stopCluster(cl)
A progress bar is displayed to easily track the ongoing computation.
Performing Bayesian Model Averaging
After preparing the model space, run bma() to obtain posterior model
probabilities, posterior inclusion probabilities (PIPs), and other BMA
statistics under the binomial and binomial-beta model priors:
bma_results <- badp::bma(model_space, round = 3)
# Inspect the BMA summary (binomial prior results first, binomial-beta second)
bma_results[[1]] # BMA stats under binomial prior
#> PIP PM PSD PSDR PMcon PSDcon PSDRcon %(+)
#> gdp_lag NA 1.078 0.110 0.229 1.078 0.110 0.229 100
#> ish 0.710 0.085 0.061 0.090 0.120 0.032 0.085 100
#> sed 0.714 -0.046 0.061 0.111 -0.065 0.064 0.127 0
bma_results[[2]] # BMA stats under binomial-beta prior
#> PIP PM PSD PSDR PMcon PSDcon PSDRcon %(+)
#> gdp_lag NA 1.078 0.110 0.239 1.078 0.110 0.239 100
#> ish 0.765 0.091 0.058 0.090 0.120 0.033 0.085 100
#> sed 0.768 -0.048 0.062 0.114 -0.063 0.064 0.126 0
# Posterior model sizes:
bma_results[[16]]
#> Prior model size Posterior model size
#> Binomial 1 1.424
#> Binomial-beta 1 1.533
Key columns in the BMA output include: - PIP: Posterior inclusion probability for each regressor. - PM: Posterior mean of each parameter (averaged over all models). - PSD/PSDR: Posterior standard deviations (regular/robust) of each parameter - %(+): Percentage of models (among those that include a given regressor) in which the parameter estimate is positive.
Visualizing Prior and Posterior Probabilities
model_pmp(): Shows prior vs. posterior model probabilities, ranking models from best to worst.model_sizes(): Displays how prior vs. posterior probabilities mass is distributed across different model sizes.
# Plot prior vs. posterior model probabilities
pmp_graphs <- badp::model_pmp(bma_results, top = 3) # Show top 3 models
# Plot probabilities by model size
size_graphs <- badp::model_sizes(bma_results)
Selecting the Best Models
Use best_models() to extract specific information about the top-ranked
models:
# Retrieve the 5 best models according to binomial prior
top3_binom <- badp::best_models(bma_results, prior = "binomial", best = 3)
# Print the inclusion matrix for each of the top 3 models
top3_binom[[1]]
#> 'No. 1' 'No. 2' 'No. 3'
#> gdp_lag 1.000 1.000 1.000
#> ish 1.000 0.000 1.000
#> sed 1.000 1.000 0.000
#> PMP 0.508 0.206 0.202
# Retrieve robust standard errors in a knit-friendly table
top3_binom[[6]]
| | ‘No. 1’ | ‘No. 2’ | ‘No. 3’ | |:--------|:-------------------:|:-------------------:|:-------------------:| | gdp_lag | 1.079 (0.275)*** | 1.126 (0.151)*** | 1.027 (0.193)*** | | ish | 0.119 (0.086) | NA | 0.121 (0.082) | | sed | -0.06 (0.126) | -0.077 (0.128) | NA | | PMP | 0.508 | 0.206 | 0.202 |
Jointness Measures
Assess whether two regressors tend to co-occur (complements) or exclude
each other (substitutes) using jointness(). By default, it calculates
the Hofmarcher et al. (2018) measure:
joint_measures <- badp::jointness(bma_results)
head(joint_measures)
#> ish sed
#> ish NA 0.159
#> sed 0.505 NA
You can also specify older measures, such as "LS" (Ley & Steel) or
"DW" (Doppelhofer & Weeks):
joint_measures_ls <- badp::jointness(bma_results, measure = "LS")
Example
Below is a minimal reproducible workflow:
# 1) Data preparation
data_prepared <- badp::economic_growth[, 1:5] %>%
badp::feature_standardization(
excluded_cols = c(country, year, gdp)
) %>%
badp::feature_standardization(
group_by_col = year,
excluded_cols = country,
scale = FALSE
)
# 2) Estimate model space
model_space <- badp::optim_model_space(
df = data_prepared,
dep_var_col = gdp,
timestamp_col = year,
entity_col = country,
init_value = function(n) rep(0.5, n),
)
# 3) Run Bayesian Model Averaging
bma_obj <- badp::bma(
model_space = model_space
)
# 4) Inspect the top 3 models under binomial prior
best_3 <- badp::best_models(
bma_list = bma_obj,
prior = "binomial",
best = 3
)
best_3[[1]] # Inclusion table
#> 'No. 1' 'No. 2' 'No. 3'
#> gdp_lag 1.000 1.000 1.000
#> ish 1.000 0.000 1.000
#> sed 1.000 1.000 0.000
#> PMP 0.508 0.206 0.202
best_3[[2]] # Coefficients & standard errors
#> 'No. 1' 'No. 2' 'No. 3'
#> gdp_lag "1.079 (0.111)***" "1.126 (0.106)***" "1.027 (0.093)***"
#> ish "0.119 (0.033)***" NA "0.121 (0.03)***"
#> sed "-0.06 (0.063)" "-0.077 (0.063)" NA
#> PMP "0.508" "0.206" "0.202"
Troubleshooting
- Cannot install required packages / setup renv environment
Make sure to go through the displayed errors. The problem might be connected to your OS environment. E.g. you might see an information like the following:
Configuration failed to find one of freetype2 libpng libtiff-4 libjpeg. Try installing:
* deb: libfreetype6-dev libpng-dev libtiff5-dev libjpeg-dev (Debian, Ubuntu, etc)
* rpm: freetype-devel libpng-devel libtiff-devel libjpeg-devel (Fedora, CentOS, RHEL)
* csw: libfreetype_dev libpng16_dev libtiff_dev libjpeg_dev (Solaris)
In such case you should first try installing the recommended packages. With properly configured system environment everything should work fine.
References
- Moral-Benito, E. (2016). "Growth Empirics in Panel Data Under Model Uncertainty and Weak Exogeneity." Journal of Applied Econometrics.
- Ley, E. and Steel, M. F. J. (2007). "Jointness in Bayesian Variable Selection with Applications to Growth Regression." Journal of Macroeconomics.
- Doppelhofer, G. and Weeks, M. (2009). "Jointness of Growth Determinants." Journal of Applied Econometrics.
- Hofmarcher, P., Crespo Cuaresma, J., Grün, B., Humer, S., and Moser, M. (2018). "Bivariate jointness measures in Bayesian Model Averaging: Solving the conundrum." Journal of Macroeconomics.
(Additional references related to the methodology can be found in the package vignette.)
Contributions and Issues
We welcome bug reports, feature requests, and contributions. Feel free to open an issue or pull request on GitHub.
License
This package is distributed under the MIT license. See the LICENSE file for details.
Try the badp package in your browser
Any scripts or data that you put into this service are public.
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
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