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#' Economic Growth Data in the original format
#'
#' Data used in Growth Empirics in Panel Data under Model Uncertainty and Weak
#' Exogeneity (Moral-Benito, 2016, Journal of Applied Econometrics).
#'
#' @format ## `original_economic_growth`
#' A data frame with 292 rows and 13 columns
#' (73 countries and 4 periods + extra one for lagged dependent variable):
#' \describe{
#' \item{year}{Year}
#' \item{country}{Country ID}
#' \item{gdp}{Logarithm of GDP per capita (2000 US dollars at PP)}
#' \item{gdp_lag}{Lagged logarithm of GDP per capita (2000 US dollars at PP)}
#' \item{ish}{Ratio of real domestic investment to GDP}
#' \item{sed}{Stock of years of secondary education in the total population}
#' \item{pgrw}{Average growth rate of population}
#' \item{pop}{Population in millions of people}
#' \item{ipr}{Purchasing-power-parity numbers for investment goods}
#' \item{opem}{Exports plus imports as a share of GDP}
#' \item{gsh}{Ratio of government consumption to GDP}
#' \item{lnlex}{Logarithm of the life expectancy at birth}
#' \item{polity}{Composite index given by the democracy score minus the
#' autocracy score}
#' }
#' @source <http://qed.econ.queensu.ca/jae/datasets/moral-benito001/>
"original_economic_growth"
#' Economic Growth Data
#'
#' Data used in Growth Empirics in Panel Data under Model Uncertainty and Weak
#' Exogeneity (Moral-Benito, 2016, Journal of Applied Econometrics).
#'
#' @format ## `economic_growth`
#' A data frame with 365 rows and 12 columns
#' (73 countries and 4 periods + extra one for lagged dependent variable):
#' \describe{
#' \item{year}{Year}
#' \item{country}{Country ID}
#' \item{gdp}{Logarithm of GDP per capita (2000 US dollars at PP)}
#' \item{ish}{Ratio of real domestic investment to GDP}
#' \item{sed}{Stock of years of secondary education in the total population}
#' \item{pgrw}{Average growth rate of population}
#' \item{pop}{Population in millions of people}
#' \item{ipr}{Purchasing-power-parity numbers for investment goods}
#' \item{opem}{Exports plus imports as a share of GDP}
#' \item{gsh}{Ratio of government consumption to GDP}
#' \item{lnlex}{Logarithm of the life expectancy at birth}
#' \item{polity}{Composite index given by the democracy score minus the
#' autocracy score}
#' }
#' @source <http://qed.econ.queensu.ca/jae/datasets/moral-benito001/>
"economic_growth"
#' Example output of \code{\link{optim_model_space}} (small version)
#'
#' A list created with \code{\link{optim_model_space}} using the
#' \code{\link{economic_growth}} dataset and only three regressors:
#' \code{ish}, \code{sed}, and \code{pgrw}.
#'
#' @format An object of class \code{badp_model_space}:
#' \describe{
#' \item{params}{
#' A numeric matrix with 40 rows and 8 columns (corresponding to
#' \eqn{2^3 = 8} models), containing parameter values for the model space.
#' Each column represents a different model.
#' }
#' \item{stats}{
#' A numeric matrix of statistics computed by
#' \code{\link{compute_model_space_stats}} based on \code{params}, with one
#' column per model. Row 1 holds the maximized log-likelihood. Row 2 holds
#' the marginal likelihood approximation used to weight the models,
#' \code{exp((loglik - (k/2) * log(N * T)) / N)}; note that it is not a BIC.
#' There follow \code{K} rows of standard deviations and \code{K} rows of
#' robust standard deviations, where \code{K} is the number of regressors
#' including the lagged dependent variable. The final three rows hold
#' \code{tr(H^-1 J)}, the dimension of the parameter vector and the
#' numerical rank of \code{J}; see \code{\link{score_rank}}.
#' }
#' \item{reg_names}{
#' A character vector with the names of the regressors.
#' }
#' \item{observations_num}{
#' The total number of observations in the panel (292).
#' }
#' \item{df}{
#' The data frame used in the analysis.
#' }
#' \item{is_nested}{
#' A logical indicating whether the model space uses nested specifications.
#' }
#' }
"small_model_space"
#' Example output of \code{\link{optim_model_space}}
#'
#' A badp_model_space object created with \code{\link{optim_model_space}} using the
#' \code{\link{economic_growth}} dataset.
#'
#' @format An object of class \code{badp_model_space}:
#' \describe{
#' \item{params}{
#' A numeric matrix with 106 rows and 512 columns (corresponding to
#' \eqn{2^9 = 512} models), containing parameter values for the full model
#' space. Each column represents a different model. Entries are \code{NA}
#' for parameters absent from a given model.
#' }
#' \item{stats}{
#' A numeric matrix of statistics computed by
#' \code{\link{compute_model_space_stats}} based on \code{params}, with one
#' column per model. Row 1 holds the maximized log-likelihood. Row 2 holds
#' the marginal likelihood approximation used to weight the models,
#' \code{exp((loglik - (k/2) * log(N * T)) / N)}; note that it is not a BIC.
#' There follow \code{K} rows of standard deviations and \code{K} rows of
#' robust standard deviations, where \code{K} is the number of regressors
#' including the lagged dependent variable. The final three rows hold
#' \code{tr(H^-1 J)}, the dimension of the parameter vector and the
#' numerical rank of \code{J}; see \code{\link{score_rank}}.
#' }
#' \item{reg_names}{
#' A character vector with the names of the variables.
#' }
#' \item{observations_num}{
#' The total number of observations in the panel (292).
#' }
#' \item{df}{
#' The data frame used in the analysis.
#' }
#' \item{is_nested}{
#' A logical indicating whether the model space uses nested specifications.
#' }
#' }
"full_model_space"
#' Example output of \code{\link{optim_model_space}} for non-nested models
#'
#' A badp_model_space object created with \code{\link{optim_model_space}} using
#' the \code{\link{economic_growth}} dataset and \code{nested = FALSE}. Compare
#' \code{\link{full_model_space}}, which is the same data under the nested
#' approach.
#'
#' @format An object of class \code{badp_model_space}:
#' \describe{
#' \item{params}{
#' A numeric matrix of parameter values for the model space, one column per
#' model. Entries are \code{NA} for parameters absent from a given model.
#' }
#' \item{stats}{
#' A numeric matrix of statistics computed by
#' \code{\link{compute_model_space_stats}} based on \code{params}, with one
#' column per model. Row 1 holds the maximized log-likelihood. Row 2 holds
#' the marginal likelihood approximation used to weight the models,
#' \code{exp((loglik - (k/2) * log(N * T)) / N)}; note that it is not a BIC.
#' There follow \code{K} rows of standard deviations and \code{K} rows of
#' robust standard deviations, where \code{K} is the number of regressors
#' including the lagged dependent variable. The final three rows hold
#' \code{tr(H^-1 J)}, the dimension of the parameter vector and the
#' numerical rank of \code{J}; see \code{\link{score_rank}}.
#' }
#' \item{reg_names}{
#' A character vector with the names of the variables.
#' }
#' \item{observations_num}{
#' The total number of observations in the panel (292).
#' }
#' \item{df}{
#' The data frame used in the analysis.
#' }
#' \item{is_nested}{
#' A logical indicating whether the model space uses nested specifications.
#' }
#' \item{convergence}{
#' A matrix of per-model convergence diagnostics; see
#' \code{\link{optim_model_space}}.
#' }
#' }
"model_space_nonnested"
#' Example output of the bma function
#'
#' A badp_bma object summarising the BMA analysis
#'
#' @format An object of class \code{badp_bma}
"full_bma_results"
#' Migration data in the original format
#'
#' 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}
#'
#' @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):
#' \describe{
#' \item{Time}{Year}
#' \item{Pair}{Country pair ID}
#' \item{Mig}{Net migration between two countries}
#' \item{Mig_lag}{Lagged net migration between two countries}
#' \item{Earn}{Difference in average real after-tax earnings in PPP}
#' \item{Unemp}{Difference in the unemployment rate}
#' \item{Social}{Difference in average social benefits in PPP}
#' \item{Tax}{Difference in average tax rate}
#' }
#' @source \doi{10.7910/DVN/GTOFJB}
"migration_data"
#' Example output of \code{\link{optim_model_space}} in the case of migration data
#'
#' A badp_model_space object created with \code{\link{optim_model_space}} using the
#' \code{\link{migration_data}} dataset.
#'
#' @format An object of class \code{badp_model_space}:
#' \describe{
#' \item{params}{
#' A numeric matrix with 51 rows and 16 columns, containing parameter
#' values for the full model space. Each column represents a different model.
#' }
#' \item{stats}{
#' A numeric matrix of statistics computed by
#' \code{\link{compute_model_space_stats}} based on \code{params}, with one
#' column per model. Row 1 holds the maximized log-likelihood. Row 2 holds
#' the marginal likelihood approximation used to weight the models,
#' \code{exp((loglik - (k/2) * log(N * T)) / N)}; note that it is not a BIC.
#' There follow \code{K} rows of standard deviations and \code{K} rows of
#' robust standard deviations, where \code{K} is the number of regressors
#' including the lagged dependent variable. The final three rows hold
#' \code{tr(H^-1 J)}, the dimension of the parameter vector and the
#' numerical rank of \code{J}; see \code{\link{score_rank}}.
#' }
#' \item{reg_names}{
#' A character vector with the names of the variables.
#' }
#' \item{observations_num}{
#' The total number of observations in the panel (1012).
#' }
#' \item{df}{
#' The data frame used in the analysis.
#' }
#' \item{is_nested}{
#' A logical indicating whether the model space uses nested specifications.
#' }
#' }
"migration_model_space"
#' Example output of \code{\link{optim_model_space}} in the case of migration data obtained with nonnested approach.
#'
#' A badp_model_space object created with \code{\link{optim_model_space}} using the
#' \code{\link{migration_data}} dataset with nonnested approach.
#'
#' @format An object of class \code{badp_model_space}:
#' \describe{
#' \item{params}{
#' A numeric matrix with 51 rows and 16 columns, containing parameter
#' values for the full model space. Each column represents a different model.
#' }
#' \item{stats}{
#' A numeric matrix of statistics computed by
#' \code{\link{compute_model_space_stats}} based on \code{params}, with one
#' column per model. Row 1 holds the maximized log-likelihood. Row 2 holds
#' the marginal likelihood approximation used to weight the models,
#' \code{exp((loglik - (k/2) * log(N * T)) / N)}; note that it is not a BIC.
#' There follow \code{K} rows of standard deviations and \code{K} rows of
#' robust standard deviations, where \code{K} is the number of regressors
#' including the lagged dependent variable. The final three rows hold
#' \code{tr(H^-1 J)}, the dimension of the parameter vector and the
#' numerical rank of \code{J}; see \code{\link{score_rank}}.
#' }
#' \item{reg_names}{
#' A character vector with the names of the variables.
#' }
#' \item{observations_num}{
#' The total number of observations in the panel (1012).
#' }
#' \item{df}{
#' The data frame used in the analysis.
#' }
#' \item{is_nested}{
#' A logical indicating whether the model space uses nested specifications.
#' }
#' }
"migration_model_space_nonnested"
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