Package 'badp' reference manual

Title:	Bayesian Averaging for Dynamic Panels
Description:	Implements Bayesian model averaging for dynamic panels with weakly exogenous regressors as described in the paper by Moral-Benito (2013, <doi:10.1080/07350015.2013.818003>). The package provides functions to estimate dynamic panel data models and analyze the results of the estimation.
Authors:	Krzysztof Beck [aut], Piotr Cukier [aut], Marcin Dubel [aut, cre], Mariusz Szczepanczyk [aut], Mateusz Wyszynski [aut]
Maintainer:	Marcin Dubel <[email protected]>
License:	MIT + file LICENSE
Version:	0.5.0
Built:	2026-06-13 07:19:08 UTC
Source:	https://github.com/cran/badp

Table with the best models according to one of the posterior criteria

Description

This function ranks the best models according to posterior model probabilities calculated using one of the available model priors: binomial or beta-binomial. It returns three types of tables in three different formats: an inclusion table, where 1 indicates that a regressor is included in the model and 0 indicates that it is excluded; an estimation results table, which displays the best models and their estimation output, including point estimates, standard errors, and significance levels; and an estimation results table with robust standard errors.

Usage

best_models(
  bma_list,
  prior = "binomial",
  best = 5,
  round = 3,
  estimate = TRUE,
  robust = TRUE
)
best_models(
  bma_list,
  prior = "binomial",
  best = 5,
  round = 3,
  estimate = TRUE,
  robust = TRUE
)

Arguments

bma_list

An object of class badp_bma, typically returned by bma.

prior

Character string specifying the model prior used for the ranking. Options are "binomial" (default) or "beta" (binomial-beta). Models are ranked by the posterior model probability computed under the chosen prior.

best

Integer. The number of best models to display (default: 5).

round

Integer indicating the decimal place to which numbers in the tables should be rounded (default: 3).

estimate

A parameter with values TRUE or FALSE indicating which table should be displayed when TRUE - table with the estimation results
FALSE - table with the inclusion of regressors in the best models

robust

A parameter with values TRUE or FALSE indicating which type of standard errors should be displayed when the function finishes calculations. Works only if estimate = TRUE. Works well when best is small.
TRUE - robust standard errors
FALSE - regular standard errors

Value

A list with best_models objects:

matrix with inclusion of the regressors in the best models
matrix with estimation output in the best models with regular standard errors
matrix with estimation output in the best models with robust standard errors
knitr_kable table with inclusion of the regressors in the best models (the best for the display on the console - up to 11 models)
knitr_kable table with estimation output in the best models with regular standard errors (the best for the display on the console - up to 6 models)
knitr_kable table with estimation output in the best models with robust standard errors (the best for the display on the console - up to 6 models)
gTree table with inclusion of the regressors in the best models (displayed as a plot). Use grid::grid.draw() to display.
gTree table with estimation output in the best models with regular standard errors (displayed as a plot). Use grid::grid.draw() to display.
gTree table with estimation output in the best models with robust standard errors (displayed as a plot). Use grid::grid.draw() to display.

Examples


library(magrittr)

data_prepared <- badp::economic_growth[, 1:6] %>%
  badp::feature_standardization(
    excluded_cols = c(country, year, gdp)
  ) %>%
  badp::feature_standardization(
    group_by_col  = year,
    excluded_cols = country,
    scale         = FALSE
  )

bma_results <- bma(
  model_space = badp::small_model_space,
  round       = 3,
  dilution    = 0
)

best_5_models <- best_models(bma_results, prior = "binomial", best = 5, estimate = TRUE)

library(magrittr)

data_prepared <- badp::economic_growth[, 1:6] %>%
  badp::feature_standardization(
    excluded_cols = c(country, year, gdp)
  ) %>%
  badp::feature_standardization(
    group_by_col  = year,
    excluded_cols = country,
    scale         = FALSE
  )

bma_results <- bma(
  model_space = badp::small_model_space,
  round       = 3,
  dilution    = 0
)

best_5_models <- best_models(bma_results, prior = "binomial", best = 5, estimate = TRUE)

Calculation of the bma object

Description

This function calculates BMA statistics based on the provided model space. Other objects for further analysis are also returned.

Usage

bma(model_space, round = 4, EMS = NULL, dilution = 0, omega = 0.5)
bma(model_space, round = 4, EMS = NULL, dilution = 0, omega = 0.5)

Arguments

model_space

An object of class badp_model_space, typically returned by optim_model_space.

round

Integer indicating the decimal place to which numbers in the BMA tables and prior and posterior model sizes should be rounded (default: 4).

EMS

Numeric. Expected model size for binomial and binomial-beta model prior (default: R/2, where R is the number of regressors).

dilution

Integer. Use 0 for no dilution prior (default), or 1 to apply a dilution prior (George 2010).

omega

Numeric. The exponent of the determinant for the dilution prior (George 2010). Only used when dilution = 1. Default: 0.5.

Value

An object of class badp_bma, which is a list containing:

uniform_table: A table containing the results based on the binomial model prior.
random_table: A table containing the results based on the binomial-beta model prior.
reg_names: A vector containing the names of the regressors, used by the functions.
R: The total number of regressors.
num_of_models: The number of models present in the model space.
jointness_data: A table containing model IDs and posterior model probabilities (PMPs) for the jointness function.
best_models_data: A table containing model IDs, PMPs, coefficients, standard deviations, and standardized regression coefficients (stdRs) for the best_models function.
EMS: The expected model size for the binomial and binomial-beta model priors, as specified by the user (default is EMS = R/2).
size_priors: A table of uniform and random model priors distributed over model sizes for the model_sizes function.
PMPs: A table containing the posterior model probabilities for use in the model_sizes function.
model_priors: A table containing the model priors, used by the model_pmp function.
dilution: A parameter indicating whether the priors were diluted, used in the model_sizes function.
alphas: A matrix of coefficients for the lagged dependent variable across all models, used in the coef_hist function.
betas_nonzero: A matrix of nonzero coefficients for the regressors, used in the coef_hist function.
df_free: A table containing the degrees of freedom for the estimated models in the best_models function.
PMS_table: A table containing the prior and posterior expected model sizes for the binomial and binomial-beta model priors.
omega: The dilution parameter used (the exponent of the determinant). Relevant only when dilution = 1.

Methods

Objects of class badp_bma have the following methods available:

print.badp_bma - Display results
summary.badp_bma - Detailed statistical summary
coef.badp_bma - Extract coefficients
plot.badp_bma - Visualize results

Examples


library(magrittr)

data_prepared <- badp::economic_growth[, 1:6] %>%
  badp::feature_standardization(
    excluded_cols = c(country, year, gdp)
  ) %>%
  badp::feature_standardization(
    group_by_col  = year,
    excluded_cols = country,
    scale         = FALSE
  )

bma_results <- bma(
  model_space = badp::small_model_space,
  round       = 3,
  dilution    = 0
)

library(magrittr)

data_prepared <- badp::economic_growth[, 1:6] %>%
  badp::feature_standardization(
    excluded_cols = c(country, year, gdp)
  ) %>%
  badp::feature_standardization(
    group_by_col  = year,
    excluded_cols = country,
    scale         = FALSE
  )

bma_results <- bma(
  model_space = badp::small_model_space,
  round       = 3,
  dilution    = 0
)

Graphs of the distribution of the coefficients over the model space

Description

This function draws graphs of the distribution (in the form of histogram or kernel density) of the coefficients for all the considered regressors over the part of the model space that includes these regressors (half of the model space).

Usage

coef_hist(
  bma_list,
  weight = NULL,
  bin_method = c("FD", "SC", "vec"),
  bin_widths = NULL,
  use_bin_count = 0,
  bin_counts = NULL,
  use_kernel = 0
)
coef_hist(
  bma_list,
  weight = NULL,
  bin_method = c("FD", "SC", "vec"),
  bin_widths = NULL,
  use_bin_count = 0,
  bin_counts = NULL,
  use_kernel = 0
)

Arguments

bma_list

An object of class badp_bma, typically returned by bma.

weight

Parameter indicating whether the coefficients should be weighted by posterior model probabilities:

NULL - no weighting (default option)
"binomial" - using posterior model probabilities based on binomial model prior
"beta" - using posterior model probabilities based on binomial-beta model prior

bin_method

Character string specifying the method for bin widths (default: "FD"). One of:
"FD" - Freedman-Diaconis method;
"SC" - Scott method;
"vec" - user specified bin widths provided through a vector (parameter: bin_widths).

bin_widths

A vector with bin widths to be used to construct histograms for the regressors. The vector must be of the size equal to total number of regressors plus one for the lagged dependent variable. The vector with bin widths is used only if parameter bin_method = "vec".

use_bin_count

Parameter taking the values (default: use_bin_count = 0):
1 - the histogram will be built based on the number of bins specified by the user through parameter bin_counts. If use_bin_count = 1, the function ignores parameter bin_method.
0 - the histogram will be built in line with parameter bin_method.

bin_counts

A vector with the numbers of bins to be used to construct histograms for the regressors. The vector must be of the size equal to total number of regressors plus one for the lagged dependent variable. The vector with bin counts is used only if parameter use_bin_count = 1.

use_kernel

A parameter taking the values (default: use_kernel = 0):
1 - the function will build graphs using kernel density for the distribution of coefficients (with use_kernel = 1, the function ignores parameters bin_method and use_bin_count)
0 - the function will build regular histogram density for the distribution of coefficients

Value

A list with the graphs of the distribution of coefficients for all the considered regressors and the lagged dependent variable.

Examples


library(magrittr)

data_prepared <- badp::economic_growth[, 1:6] %>%
  badp::feature_standardization(
    excluded_cols = c(country, year, gdp)
  ) %>%
  badp::feature_standardization(
    group_by_col  = year,
    excluded_cols = country,
    scale         = FALSE
  )

bma_results <- bma(
  model_space = badp::small_model_space,
  round       = 3,
  dilution    = 0
)

coef_plots <- coef_hist(bma_results, use_kernel = 1)

library(magrittr)

data_prepared <- badp::economic_growth[, 1:6] %>%
  badp::feature_standardization(
    excluded_cols = c(country, year, gdp)
  ) %>%
  badp::feature_standardization(
    group_by_col  = year,
    excluded_cols = country,
    scale         = FALSE
  )

bma_results <- bma(
  model_space = badp::small_model_space,
  round       = 3,
  dilution    = 0
)

coef_plots <- coef_hist(bma_results, use_kernel = 1)

Extract posterior statistics from Bayesian Model Averaging Results

Description

Coefficient extraction method for objects of class badp_bma.

Usage

## S3 method for class 'badp_bma'
coef(
  object,
  prior = "both",
  conditional = FALSE,
  se = FALSE,
  robustSE = FALSE,
  PIP = TRUE,
  ...
)
## S3 method for class 'badp_bma'
coef(
  object,
  prior = "both",
  conditional = FALSE,
  se = FALSE,
  robustSE = FALSE,
  PIP = TRUE,
  ...
)

Arguments

object

An object of class badp_bma, typically the result of bma.

prior

Character string specifying which prior to use. Options are "both" (default), "binomial", or "beta". With "both" the result reports estimates under the binomial and the binomial-beta priors and is printed via print.badp_bma_coef.

conditional

Logical. If TRUE, returns posterior means (and posterior standard deviations when se = TRUE) conditional on inclusion of the variable in a model - i.e. the columns whose names end in "con" (PMcon, PSDcon, PSDRcon). If FALSE (default), returns the unconditional posterior mean and standard error.

se

Logical. If TRUE, includes a posterior standard deviation column alongside each posterior mean. Defaults to FALSE.

robustSE

Logical. Only meaningful when se = TRUE. If TRUE, uses the robust posterior standard deviation (PSDR / PSDRcon); if FALSE (default), uses the non-robust version (PSD / PSDcon). Ignored with a warning when se = FALSE.

PIP

Logical. If TRUE (default), includes a posterior inclusion probability column for each prior. Set to FALSE to suppress.

...

Additional arguments (currently unused).

Details

This function extracts coefficient estimates from Bayesian Model Averaging results. By default both priors are reported so the user can compare them at a glance; set prior = "binomial" or prior = "beta" to obtain the legacy single-prior return values (useful when feeding coefficients into downstream code).

Value

The shape of the return value depends on prior, conditional, se, robustSE and PIP:

prior = "both": always a badp_bma_coef data frame. Columns are grouped by prior; for each prior the columns binom_PM / beta_PM (or binom_PMcon / beta_PMcon when conditional = TRUE), standard error columns binom_PSD / beta_PSD (or binom_PSDR / beta_PSDR when robustSE = TRUE, or their con variants when conditional = TRUE) when se = TRUE, and binom_PIP / beta_PIP when PIP = TRUE.
prior = "binomial" or "beta": a named numeric vector of estimates when se = FALSE and PIP = FALSE; otherwise a data frame with columns PM (or PMcon when conditional = TRUE), posterior standard deviation column PSD / PSDR (or PSDcon / PSDRcon) when se = TRUE, and PIP when PIP = TRUE.

Examples


data(full_model_space)
results <- bma(full_model_space)

# Posterior means under both priors with PIP
coef(results)

# With standard errors
coef(results, se = TRUE)

# With robust standard errors
coef(results, se = TRUE, robustSE = TRUE)

# Conditional posterior means and SEs
coef(results, conditional = TRUE, se = TRUE)

# Suppress PIP column
coef(results, PIP = FALSE)

# Single-prior numeric vector (legacy behaviour)
coef(results, prior = "binomial", PIP = FALSE)


data(full_model_space)
results <- bma(full_model_space)

# Posterior means under both priors with PIP
coef(results)

# With standard errors
coef(results, se = TRUE)

# With robust standard errors
coef(results, se = TRUE, robustSE = TRUE)

# Conditional posterior means and SEs
coef(results, conditional = TRUE, se = TRUE)

# Suppress PIP column
coef(results, PIP = FALSE)

# Single-prior numeric vector (legacy behaviour)
coef(results, prior = "binomial", PIP = FALSE)

Approximate standard deviations for the models

Description

Approximate standard deviations are computed for the models in the given model space. Two versions are computed.

Usage

compute_model_space_stats(
  df,
  dep_var_col,
  timestamp_col,
  entity_col,
  params,
  nested = TRUE,
  exact_value = FALSE,
  model_prior = "uniform",
  cl = NULL
)
compute_model_space_stats(
  df,
  dep_var_col,
  timestamp_col,
  entity_col,
  params,
  nested = TRUE,
  exact_value = FALSE,
  model_prior = "uniform",
  cl = NULL
)

Arguments

df

Data frame with data for the SEM analysis.

dep_var_col

Column with the dependent variable

timestamp_col

The name of the column with timestamps

entity_col

Column with entities (e.g. countries)

params

A matrix (with named rows) with each column corresponding to a model. Each column specifies model parameters. Compare with optim_model_space_params

nested

Logical. If TRUE (default), compute approximate standard deviations using the nested-model approach via nested_std_dev_from_params(). If FALSE, use the non-nested approach via non_nested_std_dev_from_params(). The choice affects which approximation routine is used for each model in params.

exact_value

Whether the exact value of the likelihood should be computed (TRUE) or just the proportional part (FALSE). Check sem_likelihood for details.

model_prior

Which model prior to use. For now there are two options: 'uniform' and 'binomial-beta'. Default is 'uniform'.

cl

An optional cluster object. If supplied, the function will use this cluster for parallel processing. If NULL (the default), pbapply::pblapply will run sequentially.

Value

Matrix with columns describing likelihood and standard deviations for each model. The first row is the likelihood for the model (computed using the parameters in the provided model space). The second row is almost 1/2 * BIC_k as in Raftery's Bayesian Model Selection in Social Research eq. 19. Then there are rows with standard deviations for each parameter. After that we have rows with robust standard deviation.

Examples


 library(magrittr)
 data_prepared <- badp::economic_growth[, 1:6] %>%
   badp::feature_standardization(
     excluded_cols = c(country, year, gdp)
   ) %>%
   badp::feature_standardization(
     group_by_col  = year,
     excluded_cols = country,
     scale         = FALSE
   )

 compute_model_space_stats(
   df            = data_prepared,
   dep_var_col   = gdp,
   timestamp_col = year,
   entity_col    = country,
   params        = small_model_space$params
 )


library(magrittr)
 data_prepared <- badp::economic_growth[, 1:6] %>%
   badp::feature_standardization(
     excluded_cols = c(country, year, gdp)
   ) %>%
   badp::feature_standardization(
     group_by_col  = year,
     excluded_cols = country,
     scale         = FALSE
   )

 compute_model_space_stats(
   df            = data_prepared,
   dep_var_col   = gdp,
   timestamp_col = year,
   entity_col    = country,
   params        = small_model_space$params
 )

Economic Growth Data

Description

Data used in Growth Empirics in Panel Data under Model Uncertainty and Weak Exogeneity (Moral-Benito, 2016, Journal of Applied Econometrics).

Usage

economic_growth
economic_growth

Format

`economic_growth`

A data frame with 365 rows and 12 columns (73 countries and 4 periods + extra one for lagged dependent variable):

year: Year
country: Country ID
gdp: Logarithm of GDP per capita (2000 US dollars at PP)
ish: Ratio of real domestic investment to GDP
sed: Stock of years of secondary education in the total population
pgrw: Average growth rate of population
pop: Population in millions of people
ipr: Purchasing-power-parity numbers for investment goods
opem: Exports plus imports as a share of GDP
gsh: Ratio of government consumption to GDP
lnlex: Logarithm of the life expectancy at birth
polity: Composite index given by the democracy score minus the autocracy score

Source

http://qed.econ.queensu.ca/jae/datasets/moral-benito001/

Perform feature standardization

Description

This function performs feature standardization (also known as z-score normalization) by centering the features around their mean and scaling by their standard deviation.

Usage

feature_standardization(df, excluded_cols, group_by_col, scale = TRUE)
feature_standardization(df, excluded_cols, group_by_col, scale = TRUE)

Arguments

df

Data frame with the data.

excluded_cols

Unquoted column names to exclude from standardization. If missing, all columns are standardized.

group_by_col

Unquoted column names to group the data by before applying standardization. If missing, no grouping is performed.

scale

Logical. If TRUE (default) scales by the standard deviation.

Value

A data frame with standardized features.

Examples

df <- data.frame(
  year = c(2000, 2001, 2002, 2003, 2004),
  country = c("A", "A", "B", "B", "C"),
  gdp = c(1, 2, 3, 4, 5),
  ish = c(2, 3, 4, 5, 6),
  sed = c(3, 4, 5, 6, 7)
)

# Standardize every column
df_with_only_numeric_values <- df[, setdiff(names(df), "country")]
feature_standardization(df_with_only_numeric_values)

# Standardize all columns except 'country'
feature_standardization(df, excluded_cols = country)

# Standardize across countries (grouped by 'country')
feature_standardization(df, group_by_col = country)

# Standardize, excluding 'country' and group-wise by 'year'
feature_standardization(df, excluded_cols = country, group_by_col = year)

df <- data.frame(
  year = c(2000, 2001, 2002, 2003, 2004),
  country = c("A", "A", "B", "B", "C"),
  gdp = c(1, 2, 3, 4, 5),
  ish = c(2, 3, 4, 5, 6),
  sed = c(3, 4, 5, 6, 7)
)

# Standardize every column
df_with_only_numeric_values <- df[, setdiff(names(df), "country")]
feature_standardization(df_with_only_numeric_values)

# Standardize all columns except 'country'
feature_standardization(df, excluded_cols = country)

# Standardize across countries (grouped by 'country')
feature_standardization(df, group_by_col = country)

# Standardize, excluding 'country' and group-wise by 'year'
feature_standardization(df, excluded_cols = country, group_by_col = year)

Example output of the bma function

Description

A badp_bma object summarising the BMA analysis

Usage

full_bma_results
full_bma_results

Format

An object of class badp_bma

Example output of `optim_model_space`

Description

A badp_model_space object created with optim_model_space using the economic_growth dataset.

Usage

full_model_space
full_model_space

Format

An object of class badp_model_space:

params: A numeric matrix with 40 rows and 512 columns, containing parameter values for the full model space. Each column represents a different model.
stats: A numeric matrix of statistics computed by compute_model_space_stats based on params. Row 1 contains model likelihoods. Row 2 contains a quantity proportional to 0.5 * BIC (cf. Raftery, Bayesian Model Selection in Social Research, Eq. 19). Rows 3–7 contain standard deviations, and rows 8–12 contain robust standard deviations.
reg_names: A character vector with the names of the variables.
observations_num: The total number of observations in the panel (292).
df: The data frame used in the analysis.
is_nested: A logical indicating whether the model space uses nested specifications.

Calculation of the jointness measures

Description

This function calculates four types of the jointness measures based on the posterior model probabilities calculated using binomial and binomial-beta model prior. The four measures are:

HCGHM - for Hofmarcher et al. (2018) measure;
LS - for Ley & Steel (2007) measure;
DW - for Doppelhofer & Weeks (2009) measure;
PPI - for posterior probability of including both variables.
The measures under binomial model prior will appear in a table above the diagonal, and the measure calculated under binomial-beta model prior below the diagonal.

REFERENCES
Doppelhofer G, Weeks M (2009) Jointness of growth determinants. Journal of Applied Econometrics., 24(2), 209-244. doi: 10.1002/jae.1046
Hofmarcher P, Crespo Cuaresma J, Grün B, Humer S, Moser M (2018) Bivariate jointness measures in Bayesian Model Averaging: Solving the conundrum. Journal of Macroeconomics, 57, 150-165. doi: 10.1016/j.jmacro.2018.05.005
Ley E, Steel M (2007) Jointness in Bayesian variable selection with applications to growth regression. Journal of Macroeconomics, 29(3), 476-493. doi: 10.1016/j.jmacro.2006.12.002

Usage

jointness(
  bma_list,
  measure = c("HCGHM", "LS", "DW", "PPI"),
  rho = 0.5,
  round = 3
)
jointness(
  bma_list,
  measure = c("HCGHM", "LS", "DW", "PPI"),
  rho = 0.5,
  round = 3
)

Arguments

bma_list

An object of class badp_bma, typically returned by bma.

measure

Character string specifying the measure of jointness. One of:
"HCGHM" - Hofmarcher et al. (2018) measure (default);
"LS" - Ley & Steel (2007) measure;
"DW" - Doppelhofer & Weeks (2009) measure;
"PPI" - posterior probability of including both variables.

rho

The parameter "rho" ( $\rho$ ) to be used in HCGHM jointness measure (default rho = 0.5). Works only if HCGHM measure is chosen (Hofmarcher et al. 2018).

round

Parameter indicating the decimal place to which the jointness measures should be rounded (default round = 3).

Value

A table with jointness measures for all the pairs of regressors used in the analysis. The results obtained with the binomial model prior are above the diagonal, while the ones obtained with the binomial-beta prior are below.

Examples


library(magrittr)

data_prepared <- badp::economic_growth[, 1:6] %>%
  badp::feature_standardization(
    excluded_cols = c(country, year, gdp)
  ) %>%
  badp::feature_standardization(
    group_by_col  = year,
    excluded_cols = country,
    scale         = FALSE
  )

bma_results <- bma(
  model_space = badp::small_model_space,
  round       = 3,
  dilution    = 0
)

jointness_table <- jointness(bma_results, measure = "HCGHM", rho = 0.5, round = 3)

library(magrittr)

data_prepared <- badp::economic_growth[, 1:6] %>%
  badp::feature_standardization(
    excluded_cols = c(country, year, gdp)
  ) %>%
  badp::feature_standardization(
    group_by_col  = year,
    excluded_cols = country,
    scale         = FALSE
  )

bma_results <- bma(
  model_space = badp::small_model_space,
  round       = 3,
  dilution    = 0
)

jointness_table <- jointness(bma_results, measure = "HCGHM", rho = 0.5, round = 3)

Migration data in the original format

Description

Data used in the manuscript Afonso, A., Alves, J., & Beck, K. (2025). Drivers of migration flows in the European Union: Earnings or unemployment? International Labour Review, 164(2), 1-23. doi:10.16995/ilr.18845

Usage

migration_data
migration_data

Format

`migration_data`

A data frame with 1012 rows and 8 columns (253 country pairs and 4 periods + one additional observation for the lagged dependent variable):

Time: Year
Pair: Country pair ID
Mig: Net migration between two countries
Mig_lag: Lagged net migration between two countries
Earn: Difference in average real after-tax earnings in PPP
Unemp: Difference in the unemployment rate
Social: Difference in average social benefits in PPP
Tax: Difference in average tax rate

Source

doi:10.7910/DVN/GTOFJB

Example output of `optim_model_space` in the case of migration data

Description

A badp_model_space object created with optim_model_space using the migration_data dataset.

Usage

migration_model_space
migration_model_space

Format

An object of class badp_model_space:

params: A numeric matrix with 51 rows and 16 columns, containing parameter values for the full model space. Each column represents a different model.
stats: A numeric matrix of statistics computed by compute_model_space_stats based on params. Row 1 contains model likelihoods. Row 2 contains a quantity proportional to 0.5 * BIC (cf. Raftery, Bayesian Model Selection in Social Research, Eq. 19). Rows 3–7 contain standard deviations, and rows 8–12 contain robust standard deviations.
reg_names: A character vector with the names of the variables.
observations_num: The total number of observations in the panel (1012).
df: The data frame used in the analysis.
is_nested: A logical indicating whether the model space uses nested specifications.

Example output of `optim_model_space` in the case of migration data obtained with nonnested approach.

Description

A badp_model_space object created with optim_model_space using the migration_data dataset with nonnested approach.

Usage

migration_model_space_nonnested
migration_model_space_nonnested

Format

An object of class badp_model_space:

params: A numeric matrix with 51 rows and 16 columns, containing parameter values for the full model space. Each column represents a different model.
stats: A numeric matrix of statistics computed by compute_model_space_stats based on params. Row 1 contains model likelihoods. Row 2 contains a quantity proportional to 0.5 * BIC (cf. Raftery, Bayesian Model Selection in Social Research, Eq. 19). Rows 3–7 contain standard deviations, and rows 8–12 contain robust standard deviations.
reg_names: A character vector with the names of the variables.
observations_num: The total number of observations in the panel (1012).
df: The data frame used in the analysis.
is_nested: A logical indicating whether the model space uses nested specifications.

Graphs of the prior and posterior model probabilities for the best individual models

Description

This function draws four graphs of prior and posterior model probabilities for the best individual models:
a) The results with binomial model prior (based on PMP - posterior model probability)
b) The results with binomial-beta model prior (based on PMP - posterior model probability)
Models on the graph are ordered according to their posterior model probability.

Usage

model_pmp(bma_list, top = NULL)
model_pmp(bma_list, top = NULL)

Arguments

bma_list

bma_list object (the result of the bma function)

top

The number of the best model to be placed on the graphs

Value

A list with three graphs with prior and posterior model probabilities for individual models:

The results with binomial model prior (based on PMP - posterior model probability)
The results with binomial-beta model prior (based on PMP - posterior model probability)
One graph combining the aforementioned graphs

Examples


library(magrittr)

data_prepared <- badp::economic_growth[, 1:6] %>%
  badp::feature_standardization(
    excluded_cols = c(country, year, gdp)
  ) %>%
  badp::feature_standardization(
    group_by_col  = year,
    excluded_cols = country,
    scale         = FALSE
  )

bma_results <- bma(
  model_space = badp::small_model_space,
  round       = 3,
  dilution    = 0
)

model_graphs <- model_pmp(bma_results, top = 16)

library(magrittr)

data_prepared <- badp::economic_growth[, 1:6] %>%
  badp::feature_standardization(
    excluded_cols = c(country, year, gdp)
  ) %>%
  badp::feature_standardization(
    group_by_col  = year,
    excluded_cols = country,
    scale         = FALSE
  )

bma_results <- bma(
  model_space = badp::small_model_space,
  round       = 3,
  dilution    = 0
)

model_graphs <- model_pmp(bma_results, top = 16)

Graphs of the prior and posterior model probabilities of the model sizes

Description

This function draws two graphs of prior and posterior model probabilities:
a) The results with binomial model prior
b) The results with binomial-beta model prior
c) One graph combining all the aforementioned graphs

Usage

model_sizes(bma_list)
model_sizes(bma_list)

Arguments

bma_list

bma_list object (the result of the bma function)

Value

A list with three graphs with prior and posterior model probabilities for model sizes:

The results with binomial model prior
The results with binomial-beta model prior
One graph combining all the aforementioned graphs

Examples


library(magrittr)

data_prepared <- badp::economic_growth[, 1:6] %>%
  badp::feature_standardization(
    excluded_cols = c(country, year, gdp)
  ) %>%
  badp::feature_standardization(
    group_by_col  = year,
    excluded_cols = country,
    scale         = FALSE
  )

bma_results <- bma(
  model_space = badp::small_model_space,
  round       = 3,
  dilution    = 0
)

size_graphs <- model_sizes(bma_results)

library(magrittr)

data_prepared <- badp::economic_growth[, 1:6] %>%
  badp::feature_standardization(
    excluded_cols = c(country, year, gdp)
  ) %>%
  badp::feature_standardization(
    group_by_col  = year,
    excluded_cols = country,
    scale         = FALSE
  )

bma_results <- bma(
  model_space = badp::small_model_space,
  round       = 3,
  dilution    = 0
)

size_graphs <- model_sizes(bma_results)

Example output of `optim_model_space` for non-nested models

Description

A badp_model_space object created with optim_model_space using the economic_growth dataset.

Usage

model_space_nonnested
model_space_nonnested

Format

An object of class badp_model_space:

params: A numeric matrix with 40 rows and 512 columns, containing parameter values for the model space. Each column represents a different model.
stats: A numeric matrix of statistics computed by compute_model_space_stats based on params. Row 1 contains model likelihoods. Row 2 contains a quantity proportional to 0.5 * BIC (cf. Raftery, Bayesian Model Selection in Social Research, Eq. 19). Rows 3–7 contain standard deviations, and rows 8–12 contain robust standard deviations.
reg_names: A character vector with the names of the variables.
observations_num: The total number of observations in the panel (292).
df: The data frame used in the analysis.
is_nested: A logical indicating whether the model space uses nested specifications.

Calculation of the model_space object

Description

This function calculates model space, values of the maximized likelihood function, BICs, and standard deviations of the parameters that will be used in Bayesian model averaging. Moreover, it provides a vector with the names of the variables for bma function and the number of observations.

Usage

optim_model_space(
  df,
  timestamp_col,
  entity_col,
  dep_var_col,
  init_value,
  nested = TRUE,
  exact_value = FALSE,
  cl = NULL,
  control = list(trace = 0, maxit = 10000, fnscale = -1, REPORT = 100, scale = 0.05)
)
optim_model_space(
  df,
  timestamp_col,
  entity_col,
  dep_var_col,
  init_value,
  nested = TRUE,
  exact_value = FALSE,
  cl = NULL,
  control = list(trace = 0, maxit = 10000, fnscale = -1, REPORT = 100, scale = 0.05)
)

Arguments

df

Data frame with data for the analysis.

timestamp_col

The name of the column with time stamps

entity_col

Column with entities (e.g. countries)

dep_var_col

Column with the dependent variable

init_value

The value with which the model space will be initialized. This will be the starting point for the numerical optimization.

nested

exact_value

Whether the exact value of the likelihood should be computed (TRUE) or just the proportional part (FALSE). Check sem_likelihood for details.

cl

An optional cluster object. If supplied, the function will use this cluster for parallel processing. If NULL (the default), pbapply::pblapply will run sequentially.

control

a list of control parameters for the optimization which are passed to optim. Default is list(trace = 0, maxit = 10000, fnscale = -1, REPORT = 100, scale = 0.05), but note that scale is used only for adjusting the parscale element added later in the function code.

Value

An object of class badp_model_space, which is a list with the following elements:

params - table with parameters of all estimated models
stats - table with the value of maximized likelihood function, BIC, and standard errors for all estimated models
reg_names - vector with the names of the variables
observations_num - number of observations
df - data frame used in estimation
is_nested - logical indicating whether nested approach was used

Methods

Objects of class badp_model_space have the following methods available:

print.badp_model_space - Display model space information

Examples


library(magrittr)

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
  )

optim_model_space(
  df            = data_prepared,
  dep_var_col   = gdp,
  timestamp_col = year,
  entity_col    = country,
  init_value    = 0.5
)

library(magrittr)

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
  )

optim_model_space(
  df            = data_prepared,
  dep_var_col   = gdp,
  timestamp_col = year,
  entity_col    = country,
  init_value    = 0.5
)

Finds MLE parameters for each model in the given model space

Description

Given a dataset and an initial value for parameters, initializes a model space with parameters equal to the initial value for each model. Then for each model performs a numerical optimization and finds parameters which maximize the likelihood.

Usage

optim_model_space_params(
  df,
  timestamp_col,
  entity_col,
  dep_var_col,
  init_value,
  nested,
  exact_value = FALSE,
  cl = NULL,
  control = list(trace = 0, maxit = 10000, fnscale = -1, REPORT = 100, scale = 0.05)
)
optim_model_space_params(
  df,
  timestamp_col,
  entity_col,
  dep_var_col,
  init_value,
  nested,
  exact_value = FALSE,
  cl = NULL,
  control = list(trace = 0, maxit = 10000, fnscale = -1, REPORT = 100, scale = 0.05)
)

Arguments

df

Data frame with data for the analysis.

timestamp_col

The name of the column with time stamps.

entity_col

Column with entities (e.g. countries).

dep_var_col

Column with the dependent variable.

init_value

The value with which the model space will be initialized. This will be the starting point for the numerical optimization.

nested

exact_value

Whether the exact value of the likelihood should be computed (TRUE) or just the proportional part (FALSE). Check sem_likelihood for details.

cl

An optional cluster object. If supplied, the function will use this cluster for parallel processing. If NULL (the default), pbapply::pblapply will run sequentially.

control

a list of control parameters for the optimization which are passed to optim. Default is list(trace = 0, maxit = 10000, fnscale = -1, REPORT = 100, scale = 0.05).

Value

List (or matrix) of parameters describing analyzed models.

Economic Growth Data in the original format

Description

Data used in Growth Empirics in Panel Data under Model Uncertainty and Weak Exogeneity (Moral-Benito, 2016, Journal of Applied Econometrics).

Usage

original_economic_growth
original_economic_growth

Format

`original_economic_growth`

A data frame with 292 rows and 13 columns (73 countries and 4 periods + extra one for lagged dependent variable):

year: Year
country: Country ID
gdp: Logarithm of GDP per capita (2000 US dollars at PP)
gdp_lag: Lagged logarithm of GDP per capita (2000 US dollars at PP)
ish: Ratio of real domestic investment to GDP
sed: Stock of years of secondary education in the total population
pgrw: Average growth rate of population
pop: Population in millions of people
ipr: Purchasing-power-parity numbers for investment goods
opem: Exports plus imports as a share of GDP
gsh: Ratio of government consumption to GDP
lnlex: Logarithm of the life expectancy at birth
polity: Composite index given by the democracy score minus the autocracy score

Source

http://qed.econ.queensu.ca/jae/datasets/moral-benito001/

Plot Bayesian Model Averaging Results

Description

Plot method for objects of class badp_bma.

Usage

## S3 method for class 'badp_bma'
plot(x, which = "model_sizes", ...)
## S3 method for class 'badp_bma'
plot(x, which = "model_sizes", ...)

Arguments

x

An object of class badp_bma, typically the result of bma.

which

Character string specifying which plot to create. Options are:

"model_sizes" - Model size distributions (default)
"best_models" - Best models
"jointness" - Jointness analysis
"coef_hist" - Coefficient histograms
"posterior_dens" - Posterior densities
"model_pmp" - Model posterior probabilities

...

Additional arguments passed to the underlying plot function.

Details

This function dispatches to the appropriate visualization function based on the which parameter. The default plot shows model size distributions, which provides a comprehensive overview of the prior and posterior distributions over model sizes.

Value

The object returned by the selected visualization helper. Depending on which, this may be a single plot object or a list containing plots and/or tables; some helpers may also print output as a side effect.

Examples


data(full_model_space)
results <- bma(full_model_space)

# Default plot (model sizes)
plot(results)

# Other plot types
plot(results, which = "best_models")
plot(results, which = "jointness")


data(full_model_space)
results <- bma(full_model_space)

# Default plot (model sizes)
plot(results)

# Other plot types
plot(results, which = "best_models")
plot(results, which = "jointness")

Graphs of the posterior densities of the coefficients

Description

This function draws graphs of the posterior densities of all the coefficients of interest.

Usage

posterior_dens(bma_list, prior = "binomial", SE = "standard")
posterior_dens(bma_list, prior = "binomial", SE = "standard")

Arguments

bma_list

bma object (the result of the bma function)

prior

Parameter indicating which model prior should be used for calculations:

"binomial" - using binomial model prior (default option)
"beta" - using binomial-beta model prior

SE

Parameter indicating which standard errors should be used in calculation of posterior standard deviation:

"standard" - regular standard errors (default option)
"robust" - robust standard errors

Value

A list with the graphs of the posterior densities of coefficients for all the considered regressors.

Examples


library(magrittr)

data_prepared <- badp::economic_growth[, 1:6] %>%
  badp::feature_standardization(
    excluded_cols = c(country, year, gdp)
  ) %>%
  badp::feature_standardization(
    group_by_col  = year,
    excluded_cols = country,
    scale         = FALSE
  )

bma_results <- bma(
  model_space = badp::small_model_space,
  round       = 3,
  dilution    = 0
)

posterior_graphs <- posterior_dens(bma_results, prior = "binomial", SE = "robust")

library(magrittr)

data_prepared <- badp::economic_growth[, 1:6] %>%
  badp::feature_standardization(
    excluded_cols = c(country, year, gdp)
  ) %>%
  badp::feature_standardization(
    group_by_col  = year,
    excluded_cols = country,
    scale         = FALSE
  )

bma_results <- bma(
  model_space = badp::small_model_space,
  round       = 3,
  dilution    = 0
)

posterior_graphs <- posterior_dens(bma_results, prior = "binomial", SE = "robust")

Print Best Models Tables

Description

Print method for objects of class badp_best_models returned by best_models. Draws the table chosen by the estimate and robust arguments of the original best_models call to the active graphics device.

Usage

## S3 method for class 'badp_best_models'
print(x, ...)
## S3 method for class 'badp_best_models'
print(x, ...)

Arguments

x

An object of class badp_best_models.

...

Additional arguments (currently unused).

Details

Because R only auto-prints expressions evaluated at the top level, calling best_models(bma_list) without assignment triggers this method (and hence the table is drawn), while best <- best_models(bma_list) stays silent.

Value

Invisibly returns the input object x.

Print Bayesian Model Averaging Results

Description

Print method for objects of class badp_bma.

Usage

## S3 method for class 'badp_bma'
print(x, ...)
## S3 method for class 'badp_bma'
print(x, ...)

Arguments

x

An object of class badp_bma, typically the result of bma.

...

Additional arguments (currently unused).

Details

This method is a thin wrapper that delegates to summary.badp_bma and then prints the resulting summary, so print(x) and print(summary(x)) produce identical output. The output displays BMA statistics for both the binomial and binomial-beta priors to allow direct comparison.

Value

Invisibly returns the input object x.

Examples


data(full_model_space)
results <- bma(full_model_space)
print(results)


data(full_model_space)
results <- bma(full_model_space)
print(results)

Print Coefficient Tables from Bayesian Model Averaging

Description

Print method for objects of class badp_bma_coef produced by coef.badp_bma when prior = "both".

Usage

## S3 method for class 'badp_bma_coef'
print(x, digits = 4, ...)
## S3 method for class 'badp_bma_coef'
print(x, digits = 4, ...)

Arguments

x

An object of class badp_bma_coef.

digits

Integer. Number of significant digits used when printing numeric columns. Defaults to 4.

...

Additional arguments passed to print.data.frame.

Details

When the result contains only point estimates (se = FALSE, PIP = FALSE), the two priors are printed side by side. Otherwise the output is split into two stacked panels - one per prior - each with the requested combination of estimate, std.error and PIP columns. The header reflects whether the estimates are unconditional or conditional on inclusion, and whether standard errors are robust.

Value

Invisibly returns the input object x.

Print a Drawable Best-Models Grob

Description

Print method for the captured gTree objects stored in positions 7-9 of the list returned by best_models. Renders the grob to the active graphics device via grid.draw so that typing e.g. best[[9]] at the console displays the picture instead of a description string.

Usage

## S3 method for class 'badp_drawable_grob'
print(x, newpage = TRUE, ...)
## S3 method for class 'badp_drawable_grob'
print(x, newpage = TRUE, ...)

Arguments

x

A badp_drawable_grob object (a gTree captured by grid.grabExpr).

newpage

Logical; if TRUE (default) a new graphics page is started before drawing.

...

Additional arguments (currently unused).

Value

Invisibly returns the input object x.

Print Model Space Object

Description

Print method for objects of class badp_model_space.

Usage

## S3 method for class 'badp_model_space'
print(x, ...)
## S3 method for class 'badp_model_space'
print(x, ...)

Arguments

x

An object of class badp_model_space, typically the result of optim_model_space.

...

Additional arguments forwarded to summary.badp_model_space.

Details

This method is a thin wrapper that delegates to summary.badp_model_space and then prints the resulting summary, so print(x) and print(summary(x)) produce identical output.

Value

Invisibly returns the input object x.

Examples


data(full_model_space)
print(full_model_space)


data(full_model_space)
print(full_model_space)

Print Summary of Bayesian Model Averaging Results

Description

Print method for summary.badp_bma objects.

Usage

## S3 method for class 'summary.badp_bma'
print(x, ...)
## S3 method for class 'summary.badp_bma'
print(x, ...)

Arguments

x

An object of class summary.badp_bma.

...

Additional arguments (currently unused).

Value

Invisibly returns the input object x.

Print Summary of a Model Space Object

Description

Print method for summary.badp_model_space objects.

Usage

## S3 method for class 'summary.badp_model_space'
print(x, ...)
## S3 method for class 'summary.badp_model_space'
print(x, ...)

Arguments

x

An object of class summary.badp_model_space.

...

Additional arguments (currently unused).

Value

Invisibly returns the input object x.

Likelihood for the SEM model

Description

Likelihood for the SEM model

Usage

sem_likelihood(
  params,
  data,
  timestamp_col,
  entity_col,
  dep_var_col,
  lin_related_regressors = NULL,
  per_entity = FALSE,
  exact_value = TRUE
)
sem_likelihood(
  params,
  data,
  timestamp_col,
  entity_col,
  dep_var_col,
  lin_related_regressors = NULL,
  per_entity = FALSE,
  exact_value = TRUE
)

Arguments

params

Parameters describing the model. Can be either a vector or a list with named parameters. See 'Details'

data

Data for the likelihood computations. Can be either a list of matrices or a dataframe. If the dataframe, additional parameters are required to build the matrices within the function.

timestamp_col

Column which determines time stamps. For now only natural numbers can be used.

entity_col

Column which determines entities (e.g. countries, people)

dep_var_col

Column with dependent variable

lin_related_regressors

Which subset of columns should be used as regressors for the current model. In other words regressors are the total set of regressors and lin_related_regressors are the ones for which linear relation is not set to zero for a given model.

per_entity

Whether to compute overall likelihood or a vector of likelihoods with per entity value

exact_value

Whether the exact value of the likelihood should be computed (TRUE) or just the proportional part (FALSE). Currently TRUE adds: 1. a normalization constant coming from Gaussian distribution, 2. a term disappearing during likelihood simplification in Likelihood-based Estimation of Dynamic Panels with Predetermined Regressors by Moral-Benito (see Appendix A.1). The latter happens when transitioning from equation (47) to equation (48), in step 2: the term trace(HG_22) is dropped, because it can be assumed to be constant from Moral-Benito perspective. To get the exact value of the likelihood we have to take this term into account.

Details

The params argument is a list that should contain the following components:

alpha scalar value which determines linear dependence on lagged dependent variable

phi_0 scalar value which determines linear dependence on the value of dependent variable at the lowest time stamp

err_var scalar value which determines classical error component (Sigma11 matrix, sigma_epsilon^2)

dep_vars double vector of length equal to the number of time stamps (i.e. time stamps greater than or equal to the second lowest time stamp)

beta double vector which determines the linear dependence on regressors different than the lagged dependent variable; The vector should have length equal to the number of regressors.

phi_1 double vector which determines the linear dependence on initial values of regressors different than the lagged dependent variable; The vector should have length equal to the number of regressors.

phis double vector which together with psis determines upper right and bottom left part of the covariance matrix; The vector should have length equal to the number of regressors times number of time stamps minus 1, i.e. n_regressors * (n_periods - 1)

psis double vector which together with psis determines upper right and bottom left part of the covariance matrix; The vector should have length equal to the number of regressors times number of time stamps minus 1 times number of time stamps divided by 2, i.e. n_regressors * (n_periods - 1) * n_periods / 2

Value

The value of the likelihood for SEM model (or a part of interest of the likelihood)

Examples

data(economic_growth)
eg <- feature_standardization(economic_growth, excluded_cols = c(year, country))
sem_likelihood(0.5, eg, year, country, gdp)
data(economic_growth)
eg <- feature_standardization(economic_growth, excluded_cols = c(year, country))
sem_likelihood(0.5, eg, year, country, gdp)

Example output of `optim_model_space` (small version)

Description

A list created with optim_model_space using the economic_growth dataset and only three regressors: ish, sed, and pgrw.

Usage

small_model_space
small_model_space

Format

An object of class badp_model_space:

params: A numeric matrix with 40 rows and 8 columns (corresponding to $2^3 = 8$ models), containing parameter values for the model space. Each column represents a different model.
stats: A numeric matrix of statistics computed by compute_model_space_stats based on params. Row 1 contains model likelihoods. Row 2 contains a quantity proportional to 0.5 * BIC (cf. Raftery, Bayesian Model Selection in Social Research, Eq. 19). Rows 3–7 contain standard deviations, and rows 8–12 contain robust standard deviations.
reg_names: A character vector with the names of the regressors.
observations_num: The total number of observations in the panel (292).
df: The data frame used in the analysis.
is_nested: A logical indicating whether the model space uses nested specifications.

Summarize Bayesian Model Averaging Results

Description

Summary method for objects of class badp_bma.

Usage

## S3 method for class 'badp_bma'
summary(object, ...)
## S3 method for class 'badp_bma'
summary(object, ...)

Arguments

object

An object of class badp_bma, typically the result of bma.

...

Additional arguments (currently unused).

Details

This function creates a comprehensive summary object that includes model space information, BMA statistics for both priors, and highlights variables with high posterior inclusion probabilities. The summary always displays results for both the binomial and binomial-beta priors to allow direct comparison.

Value

An object of class summary.badp_bma containing:

model_space_size - Total number of models in the model space
num_regressors - Number of regressors (excluding lagged dependent variable)
expected_model_size - Expected model size
dilution_applied - Logical indicating if dilution prior was used
omega - Numeric value of the dilution parameter (omega); only relevant when dilution_applied is TRUE
results_binomial - Coefficient table for binomial prior
results_beta - Coefficient table for binomial-beta prior
model_sizes - Prior and posterior model sizes table
reg_names - Variable names

Examples


data(full_model_space)
results <- bma(full_model_space)
summary(results)


data(full_model_space)
results <- bma(full_model_space)
summary(results)

Summarize a Model Space Object

Description

Summary method for objects of class badp_model_space. Replaces the default summary() output (which just lists the structure of the underlying list) with a structured object describing the dimensions of the model space, its variables, and a brief look at the per-model log-likelihoods stored in object$stats.

Usage

## S3 method for class 'badp_model_space'
summary(object, ...)
## S3 method for class 'badp_model_space'
summary(object, ...)

Arguments

object

An object of class badp_model_space, typically the result of optim_model_space.

...

Additional arguments (currently unused).

Value

An object of class summary.badp_model_space containing:

num_models - Number of models in the model space ( $2^R$ ).
num_regressors - Number of regressors excluding the lagged dependent variable ( $R$ ).
num_params - Number of parameters in the full parameter vector (rows of object$params).
observations_num - Number of observations used.
is_nested - Logical, whether the model space is nested.
reg_names - All variable names (lagged dependent first).
dep_var_name - The (lagged) dependent variable name.
regressor_names - The regressor names.
data_dim - Dimensions of the source data frame, or NULL if not stored.
likelihoods - Per-model log-likelihood values (row 1 of object$stats), or NULL if not available.

Examples


data(full_model_space)
summary(full_model_space)


data(full_model_space)
summary(full_model_space)

Package 'badp'

Help Index

Table with the best models according to one of the posterior criteria

Description

Usage

Arguments

Value

Examples

Calculation of the bma object

Description

Usage

Arguments

Value

Methods

Examples

Graphs of the distribution of the coefficients over the model space

Description

Usage

Arguments

Value

Examples

Extract posterior statistics from Bayesian Model Averaging Results

Description

Usage

Arguments

Details

Value

See Also

Examples

Approximate standard deviations for the models

Description

Usage

Arguments

Value

Examples

Economic Growth Data

Description

Usage

Format

economic_growth

Source

Perform feature standardization

Description

Usage

Arguments

Value

Examples

Example output of the bma function

Description

Usage

Format

Example output of optim_model_space

Description

Usage

Format

Calculation of the jointness measures

Description

Usage

Arguments

Value

Examples

Migration data in the original format

Description

Usage

Format

migration_data

Source

Example output of optim_model_space in the case of migration data

Description

Usage

Format

Example output of optim_model_space in the case of migration data obtained with nonnested approach.

Description

Usage

Format

Graphs of the prior and posterior model probabilities for the best individual models

Description

Usage

Arguments

Value

`economic_growth`

Example output of `optim_model_space`

`migration_data`

Example output of `optim_model_space` in the case of migration data

Example output of `optim_model_space` in the case of migration data obtained with nonnested approach.

Example output of `optim_model_space` for non-nested models

`original_economic_growth`