Package {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
)

Arguments

Value

A list with best_models objects:

1. matrix with inclusion of the regressors in the best models
   

2. matrix with estimation output in the best models with regular standard errors
   

3. matrix with estimation output in the best models with robust standard errors
   

4. knitr_kable table with inclusion of the regressors in the best models (the best for the display on the console - up to 11 models)
   

5. 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)
   

6. 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)
   

7. gTree table with inclusion of the regressors in the best models (displayed as a plot). Use grid::grid.draw() to display.
   

8. gTree table with estimation output in the best models with regular standard errors (displayed as a plot). Use grid::grid.draw() to display.

9. 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)

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)

Arguments

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
)

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,
  ...
)

Arguments

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.

See Also

bma, summary.badp_bma, print.badp_bma_coef

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)

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
)

Arguments

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)

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
)

Arguments

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
 )

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

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/

Matrix with exogenous variables for SEM representation

Description

Create matrix which contains exogenous variables used in the Simultaneous Equations Model (SEM) representation. Currently these are: dependent variable from the lowest time stamp and regressors from the second lowest time stamp. The matrix is then used to compute likelihood for SEM analysis.

Usage

exogenous_matrix(df, timestamp_col, entity_col, dep_var_col)

Arguments

Value

Matrix of size N x k+1 where N is the number of entities considered and k is the number of chosen regressors

Examples

set.seed(1)
df <- data.frame(
  entities = rep(1:4, 5),
  times = rep(seq(1960, 2000, 10), each = 4),
  dep_var = stats::rnorm(20), a = stats::rnorm(20), b = stats::rnorm(20)
)
exogenous_matrix(df, times, entities, dep_var)

Extraction of names of the variables

Description

The function extracts the names of the variables from the data set used in the analysis and places them in a vector.

Usage

extract_names(df)

Arguments

Value

A vector with names of the variables.

Examples

 df <- badp::economic_growth

 reg_names <- extract_names(df)

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)

Arguments

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)

Example output of the bma function

Description

A badp_bma object summarising the BMA analysis

Usage

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

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.

Hessian matrix

Description

Creates the hessian matrix for a given likelihood function.

Usage

hessian(lik, theta, ...)

Arguments

Value

Hessian kxk matrix where k is the number of parameters included in the theta matrix

Examples

lik <- function(theta) {
 return(theta[1]^2 + theta[2]^2)
}

hessian(lik, c(1, 1))

Initialize model space matrix

Description

This function builds a representation of the model space, by creating a dataframe where each column represents values of the parameters for a given model. Real value means that the parameter is included in the model. A parameter not present in the model is marked as NA.

Usage

init_model_space_params(
  df,
  timestamp_col,
  entity_col,
  dep_var_col,
  init_value = 1
)

Arguments

Details

Currently the set of features is assumed to be all columns which remain after excluding timestamp_col, entity_col and dep_var_col.

A power set of all possible exclusions of linear dependence on the given feature is created, i.e. if there are 4 features we end up with 2^4 possible models (for each model we independently decide whether to include or not a feature).

Value

matrix of model parameters

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
  )

init_model_space_params(data_prepared, year, country, gdp)

Dataframe with no lagged column

Description

This function allows the user to turn data in the format with lagged values for a chosen column (i.e. there are two columns with the same quantity, but one column is lagged in time) into the format with just one column

Usage

join_lagged_col(
  df,
  col,
  col_lagged,
  timestamp_col,
  entity_col,
  timestep = NULL
)

Arguments

Value

A dataframe with two columns merged, i.e. just one column with the desired quantity is left.

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),
  gdp_lagged = c(NA, 1, 2, 3, 4)
)

join_lagged_col(df, gdp, gdp_lagged, year, country, 1)

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:

1. HCGHM - for Hofmarcher et al. (2018) measure;
   

2. LS - for Ley & Steel (2007) measure;
   

3. DW - for Doppelhofer & Weeks (2009) measure;
   

4. 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
)

Arguments

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)

List of matrices for SEM model

Description

List of matrices for SEM model

Usage

matrices_from_df(
  df,
  timestamp_col,
  entity_col,
  dep_var_col,
  lin_related_regressors = NULL,
  which_matrices = c("Y1", "Y2", "Z", "cur_Y2", "cur_Z", "res_maker_matrix")
)

Arguments

Value

Named list with matrices as its elements

Examples

matrices_from_df(economic_growth, year, country, gdp, c("pop", "sed"),
                 c("Y1", "Y2"))

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

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

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

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)

Arguments

Value

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

1. The results with binomial model prior (based on PMP - posterior model probability)
   

2. The results with binomial-beta model prior (based on PMP - posterior model probability)
   

3. 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)

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)

Arguments

Value

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

1. The results with binomial model prior
   

2. The results with binomial-beta model prior
   

3. 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)

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

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.

Helper-function - finds parameters minimizing log-likelihood function for the nested version of the SEM setup, using BFGS method

Description

Helper-function - finds parameters minimizing log-likelihood function for the nested version of the SEM setup, using BFGS method

Usage

nested_optimization_wrapper(
  params,
  df,
  timestamp_col,
  entity_col,
  dep_var_col,
  data,
  exact_value,
  control
)

Arguments

Value

List (or matrix) of parameters describing analyzed models.

Helper function - wraps single execution of the log-likelihood & deviation parameters calculations. Used for nested version of SEM likelihood.

Description

Helper function - wraps single execution of the log-likelihood & deviation parameters calculations. Used for nested version of SEM likelihood.

Usage

nested_std_dev_from_params(
  params,
  data,
  df,
  timestamp_col,
  entity_col,
  dep_var_col,
  n_entities,
  n_periods
)

Arguments

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.

Helper-function - finds parameters minimizing log-likelihood function for the non-nested version of the SEM setup, using BFGS method

Description

Helper-function - finds parameters minimizing log-likelihood function for the non-nested version of the SEM setup, using BFGS method

Usage

non_nested_optimization_wrapper(
  params,
  df,
  timestamp_col,
  entity_col,
  dep_var_col,
  exact_value,
  n_all_regressors,
  n_timestamps,
  control
)

Arguments

Value

List (or matrix) of parameters describing analyzed models.

Helper function - wraps single execution of the log-likelihood & deviation parameters calculations. Used for non-nested version of SEM likelihood.

Description

Helper function - wraps single execution of the log-likelihood & deviation parameters calculations. Used for non-nested version of SEM likelihood.

Usage

non_nested_std_dev_from_params(
  params,
  df,
  timestamp_col,
  entity_col,
  dep_var_col,
  n_entities,
  n_periods
)

Arguments

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.

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)
)

Arguments

Value

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

1. params - table with parameters of all estimated models
   

2. stats - table with the value of maximized likelihood function, BIC, and standard errors for all estimated models
   

3. reg_names - vector with the names of the variables
   

4. observations_num - number of observations
   

5. df - data frame used in estimation
   

6. 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
)

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)
)

Arguments

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

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", ...)

Arguments

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.

See Also

bma, model_sizes, best_models, jointness, coef_hist, posterior_dens, model_pmp

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")

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")

Arguments

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")

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, ...)

Arguments

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.

See Also

best_models

Print Bayesian Model Averaging Results

Description

Print method for objects of class badp_bma.

Usage

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

Arguments

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.

See Also

bma, summary.badp_bma, coef.badp_bma

Examples

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, ...)

Arguments

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.

See Also

coef.badp_bma

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, ...)

Arguments

Value

Invisibly returns the input object x.

See Also

best_models, grid.draw

Print Model Space Object

Description

Print method for objects of class badp_model_space.

Usage

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

Arguments

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.

See Also

summary.badp_model_space, optim_model_space, bma

Examples

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, ...)

Arguments

Value

Invisibly returns the input object x.

See Also

summary.badp_bma

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, ...)

Arguments

Value

Invisibly returns the input object x.

See Also

summary.badp_model_space

Helper function to extract names from a vector defining a model

Description

For now it is assumed that we can only exclude linear relationships between regressors and the dependent variable.

Usage

regressor_names_from_params_vector(params)

Arguments

Details

The vector needs to have named rows, i.e. it is assumed it comes from a model space (see init_model_space_params for details).

Value

Names of regressors which are assumed to be linearly connected with dependent variable within the model described by the params vector.

Examples

params <- c(alpha = 1, beta_gdp = 1, beta_gdp_lagged = 1, phi_0 = 1, err_var = 1)
regressor_names_from_params_vector(params)

Residual Maker Matrix

Description

Create residual maker matrix from a given matrix m. See article about projection matrix on the Wikipedia.

Usage

residual_maker_matrix(m)

Arguments

Value

M x M matrix where M is the number of rows in the m matrix.

Examples

residual_maker_matrix(matrix(c(1,2,3,4), nrow = 2))

Coefficients matrix for SEM representation

Description

Create coefficients matrix for Simultaneous Equations Model (SEM) representation.

Usage

sem_B_matrix(alpha, n_periods, beta = NULL)

Arguments

Value

List with two matrices B11 and B12

Examples

sem_B_matrix(3, 4, 4:6)

Coefficients matrix for initial conditions

Description

Create matrix for Simultaneous Equations Model (SEM) representation with coefficients placed next to initial values of regressors, dependent variable and country-specific time-invariant variables.

Usage

sem_C_matrix(alpha, phi_0, n_periods, beta = NULL, phi_1 = NULL)

Arguments

Value

matrix

Examples

alpha <- 9
phi_0 <- 19
beta <- 11:15
phi_1 <- 21:25
n_periods <- 4
sem_C_matrix(alpha, phi_0, n_periods, beta, phi_1)

Matrix with dependent variable data for SEM representation

Description

Create matrix which contains dependent variable data used in the Simultaneous Equations Model (SEM) representation on the left hand side of the equations. The matrix contains the data for time periods greater than or equal to the second lowest time stamp. The matrix is then used to compute likelihood for SEM analysis.

Usage

sem_dep_var_matrix(df, timestamp_col, entity_col, dep_var_col)

Arguments

Value

Matrix of size N x T where N is the number of entities considered and T is the number of periods greater than or equal to the second lowest time stamp.

Examples

set.seed(1)
df <- data.frame(
  entities = rep(1:4, 5),
  times = rep(seq(1960, 2000, 10), each = 4),
  dep_var = stats::rnorm(20), a = stats::rnorm(20), b = stats::rnorm(20)
)
sem_dep_var_matrix(df, times, entities, dep_var)

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
)

Arguments

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)

Matrix with psi parameters for SEM representation

Description

Matrix with psi parameters for SEM representation

Usage

sem_psi_matrix(psis, n_timestamps, n_features)

Arguments

Value

A matrix with n_timestamps rows and (n_timestamps - 1) * n_features columns. Psis are filled in row by row in a block manner, i.e. blocks of size n_features are placed next to each other

Examples

sem_psi_matrix(1:30, 4, 5)

Matrix with regressors data for SEM representation

Description

Create matrix which contains regressors data used in the Simultaneous Equations Model (SEM) representation on the left hand side of the equations. The matrix contains regressors data for time periods greater than or equal to the second lowest time stamp. The matrix is then used to compute likelihood for SEM analysis.

Usage

sem_regressors_matrix(df, timestamp_col, entity_col, dep_var_col)

Arguments

Value

Matrix of size N x (T-1)*k where N is the number of entities considered, T is the number of periods greater than or equal to the second lowest time stamp and k is the number of chosen regressors. If there are no regressors returns NULL.

Examples

set.seed(1)
df <- data.frame(
  entities = rep(1:4, 5),
  times = rep(seq(1960, 2000, 10), each = 4),
  dep_var = stats::rnorm(20), a = stats::rnorm(20), b = stats::rnorm(20)
)
sem_regressors_matrix(df, times, entities, dep_var)

Covariance matrix for SEM representation

Description

Create covariance matrix for Simultaneous Equations Model (SEM) representation. Only the part necessary to compute concentrated likelihood function is computed (cf. Appendix in the Moral-Benito paper)

Usage

sem_sigma_matrix(err_var, dep_vars, phis = NULL, psis = NULL)

Arguments

Value

List with two matrices Sigma11 and Sigma12

Examples

err_var <- 1
dep_vars <- c(2, 2, 2, 2)
phis <- c(10, 10, 20, 20, 30, 30)
psis <- c(101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112)
sem_sigma_matrix(err_var, dep_vars, phis, psis)

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

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, ...)

Arguments

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

See Also

bma, print.badp_bma, coef.badp_bma

Examples

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, ...)

Arguments

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.

See Also

print.badp_model_space, print.summary.badp_model_space, optim_model_space, bma

Examples

data(full_model_space)
summary(full_model_space)