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This release reworks the user-facing interface in response to the review of the manuscript submitted to the Journal of Statistical Software. Several changes are breaking; they are marked below.
best_models() returns
a list of individual models rather than nine tables already formatted
for display. Each element is an object of the new class
badp_model carrying that model’s regressors, posterior
model probability, coefficients, standard errors, robust standard errors
and p-values as numbers, where these were previously pasted into display
strings and discarded. Individual models are reached by position, and
each has print(), summary() and
coef() methods.estimate and
robust arguments of best_models() were
removed. They selected which table was drawn on auto-print; the choice
now belongs to the print(), summary() and
plot() methods, which take a robust argument
where it applies.coef() on a badp_model gained a
digits argument. The values are returned as estimated by
default; digits rounds them, which is a convenience when
the coefficient table is being displayed rather than computed with.badp_best_models objects gained print(),
summary(), plot() and [ methods.
print() writes an inclusion table to the console, where the
previous method drew to the graphics device and produced no console
output at all. summary() returns its own classed object
with the formatted estimates, and plot() draws either
table.NT - k degrees of freedom. The estimator is maximum
likelihood with standard errors from the observed information, so no
exact small-sample distribution applies and there are no residual
degrees of freedom to count. The likelihood factorizes over entities
rather than over entity-periods, so NT counted observations
the likelihood never treats as independent; N - k is not an
alternative, being negative for the model spaces shipped with the
package, in which the parameter vector is longer than the number of
entities. The column is now labeled Pr(>|z|). The
practical effect is small: the two-sided five percent critical value
moves from 1.968 to 1.960.df_free element
was removed from badp_bma objects, which now hold 18
elements rather than 19. It recorded the degrees of freedom described
above and is no longer used anywhere in the package. Elements after it
shift down one position; access components by name.model_sizes() and model_pmp() gained a
type argument. "line" keeps the existing
display; "histogram" draws the prior and the posterior as
side-by-side bars, as in the companion package rmsBMA. Bars
read well when few models or model sizes are shown – a small
top, or a handful of regressors – while the lines stay
legible when there are many. The argument passes through
plot(), so
plot(results, which = "model_pmp", top = 5, type = "histogram")
works.
Both functions now build their six graphs from a single internal
builder rather than repeating the same ggplot specification
once per prior and once per dilution setting, so the line and bar forms
cannot drift apart.
print() on a badp_bma object no longer
delegates to summary(). It now gives a compact overview:
the size of the model space, the prior and weighting settings, and the
regressors ranked by posterior inclusion probability.
summary() continues to return a classed object and to print
the full tables under both model priors, so it now says strictly more
than print().
model_sizes(), model_pmp(),
coef_hist() and posterior_dens() return
objects of the new class badp_plots with named elements,
and no longer print a plot as a side effect. A bare list of plots is
auto-printed one element at a time, so on an interactive device each
plot replaced the one before it; the new print() method
draws a single figure instead, the combined plot where there is one and
otherwise all of them arranged together. Individual plots are still
reached by name or position.
plot() on a badp_bma object now draws
exactly one graphic for every value of which and returns
invisibly, rather than relying on auto-printing whatever the underlying
helper returned.
bma_table(), pip(),
pmp(), model_size_table(),
regressors(), n_models(),
weighting(), learning_rate() and
convergence(). Every quantity previously reached by
indexing into the object, by name or by position, now has a documented
accessor. They are generics with methods, so they are listed by
methods(class = "badp_bma") and
methods(class = "badp_model_space").best_models(), jointness(),
model_pmp(), model_sizes(),
coef_hist() and posterior_dens() was renamed
from bma_list to x. The object these functions
consume is of class badp_bma, not a list, and the name
contradicted both the accessors (which all take x) and the
argument of this release. Calls that pass the object as the first,
unnamed argument, which is the documented usage everywhere, are
unaffected; calls written as bma_list = must be
updated.print.badp_drawable_grob() and the internal
as_drawable_grob() helper were removed. Nothing in the
package created an object of class badp_drawable_grob, so
the method was registered for a class that never existed at run time.
They were left over from the previous implementation of
best_models(), which returned grobs.plot() on a badp_bma object with
which = "best_models" handed the whole of ...
to best_models(), which selects the models, although the
drawing is done afterwards by plot() on the result. A
plotting argument therefore reached a function that does not have it,
and plot(x, which = "best_models", robust = TRUE) failed
before anything was drawn. The arguments are now split between the two
by name.
optim_model_space_params() required
nested to be supplied explicitly, although
optim_model_space() and
compute_model_space_stats() both default it to
TRUE. It now defaults to TRUE as well, so the
three functions agree and the documented call works as written.
model_pmp() reset top to the number of
regressors when the requested number exceeded the size of the
model space, so asking for more models than exist silently plotted too
few of them. It is now capped at the size of the model space, as
pmp() and best_models() already were. The
message it prints was reworded to match those two, and no longer claims
that top is a count of regressors.
badp_bma or
badp_model_space object now uses the component name:
bma_list$R rather than bma_list[[4]],
model_space$params rather than
model_space[[1]], and so on across bma(),
best_models(), jointness(),
model_sizes(), model_pmp(),
coef_hist() and posterior_dens() (36 call
sites). Removing df_free from position 15 in this release
was safe only because nothing happened to index past it; that will no
longer be a matter of luck.bma() instead,
which is what callers and the accessors actually depend on.coef_hist() and
posterior_dens() are named after the variables they show,
so the vignette reaches an individual plot with
coef_plots[["gdp_lag"]] rather than
coef_plots[[1]].bma_table() and model_size_table(), and
no longer refers to components of the fitted objects by position (“the
first element of the list”, “19 elements”). It also gained a short
subsection on convergence(), which was previously
undocumented outside the help pages.bma_results[[16]], which after the
removal of df_free no longer points at the model-size
table), and called top3_binom[[6]], which does not exist
now that best_models() returns one object per model. The
README could not have been re-knitted. It now uses the accessors and the
methods.join_lagged_col() is no longer marked
@keywords internal and now appears in the package index. It
was already exported, already listed in the pkgdown reference under data
preparation, and is demonstrated in both vignettes, so hiding it from
help(package = "badp") was inconsistent. Its help page now
also says when the function is needed: only for data that store the
dependent variable twice, in levels and lagged, which is a property of
the source data and not a step every analysis takes.knitr moved from Imports to
Suggests. The package no longer calls it: the
knitr::kable() renderings were one of the three redundant
display formats that best_models() used to return. It is
still required to build the vignette.Replaced the C++ (Rcpp/RcppArmadillo) SEM likelihood
implementation with an R implementation differentiated via
RTMB (automatic differentiation). Optimization now uses
gradients obtained by automatic differentiation instead of finite
differences, and standard errors are computed from the Hessian and
per-entity score vectors of the same tape instead of finite-difference
approximations. Optimized parameters and standard errors therefore
differ from those of earlier versions; likelihood values at given
parameters are unchanged. The difference is small for the parameter
estimates but can be substantial for the robust standard errors, which
depend on the derivatives twice over. The finite-difference
hessian() function was removed. The Rcpp,
RcppArmadillo, rootSolve and
optimbase dependencies were dropped in favor of
RTMB.
init_value (in optim_model_space() and
related functions) now also accepts a generator function of one argument
n returning n starting values
(e.g. function(n) runif(n, 0.1, 1)), enabling randomized
multi-start experiments, or a single number used as the starting value
for every parameter, as before (init_value = 0.5 is
equivalent to function(n) rep(0.5, n)), so code written
against 0.4.0 and 0.5.0 continues to work. Passing 0, a
vector of length greater than one, or anything that is neither a
function nor a single finite number now fails with an informative error,
as does a generator that draws exactly 0 for an included
parameter; zero is rejected either way because it is reserved to mark a
parameter excluded from a given model.
Per-model optimization is more robust to the harder cases automatic differentiation now makes tractable to explore:
restart_tol
(max_restarts and restart_tol arguments of
optim_model_space()); with max_restarts = 0,
optim()’s own convergence flag is used directly.init_value (up to
max_init_attempts times).max_reoptimizations times) instead of being reported as
a failure.optim code, number of restarts, number of initial draws,
and final gradient norm - are stored in the new convergence
element of badp_model_space objects. Non-converged models
trigger a warning in optim_model_space() and
bma() and are reported by
summary()/print(); they are deliberately not
excluded from the analysis.The model space statistics gained a row holding the numerical
rank of J = sum_i s_i s_i', the outer product of the
entity-level scores from which the robust (“sandwich”) standard errors
are built. Because the per-entity scores share a component identical
across entities, and because they sum to zero at the maximum,
J is unchanged by centering them and depends only on the
variation of the scores across entities. Parameters entering the
log-likelihood solely through terms common to every entity contribute
nothing, so J is rank deficient however many entities are
observed. In the bundled model spaces the scores span between 8% and 29%
of the parameter directions.
The robust standard deviations that bma() reports are
unaffected in the sense that they remain well defined: J
vanishes outside the spanned block, so the sandwich restricted to that
block equals the profile sandwich obtained by profiling the remaining
parameters out. What the construction discards is the score covariance
involving those remaining directions, which is set to zero rather than
estimated. The likelihood, the posterior means, the posterior inclusion
probabilities and the Hessian-based standard errors PSD and
PSDcon do not involve J.
summary() of a model space now reports the fraction of
parameter directions spanned.
bma() gained an eta argument taking the
learning rate directly, which overrides weighting.
eta = 1 reproduces "mb2012" and
eta = 1/N reproduces "mb2016", so the
sensitivity of any conclusion to the rate can be examined without
re-estimation.
The "curvature" weighting, which estimated the
learning rate by the magnitude (“omnibus”) adjustment for misspecified
likelihoods, has been withdrawn before release. The adjustment assumes
J estimates the variance of the score, and J
is rank deficient for this likelihood, so the rate would be calibrated
on the small part of the parameter space the entity-level scores span,
with no way to assess what the remainder contributes. Use
eta to set a rate explicitly instead. The ingredients,
tr(H^-1 J), dim(theta) and
rank(J), remain stored with every fitted model space, so
the rate can still be computed and inspected directly.
bma() gained a weighting argument
selecting the approximation to the marginal likelihood used to weight
the models. Writing A_j = loglik_j - (k_j/2)*log(N*T),
three of the four options are the same construction with different
learning rates eta, log w_j = eta * A_j:
"mb2016" (default, eta = 1/N) is unchanged
behavior, the approximation computed by the implementation accompanying
Moral-Benito (2016), and the option that reproduces the posterior
inclusion probabilities and posterior moments published there;"mb2012" (eta = 1) is the Schwarz
criterion exactly as stated in equations (24)-(30) of Moral-Benito
(2012);"nt" (eta = 1/(N*T)) averages over
entity-periods rather than entities, the scaling that would be
internally consistent with the log(N*T) penalty.The fourth option, "uip", instead alters the penalty,
using exp(loglik - (k/2)*log(N)) with the entity as the
unit of information, as implied by the unit information prior of Kass
and Wasserman (1995) given that the likelihood factorizes over
entities.
Any eta != 1 gives a tempered (power) posterior over
models, which lies outside the approximation that motivates the
criterion. A rate held fixed as the sample grows only rescales the log
weights, so the posterior still concentrates, more slowly for
eta < 1. A rate that shrinks with the sample is
different in kind: under eta = 1/N the log weights converge
to constants and the posterior never concentrates. Conversely
eta = 1 concentrates sharply and can place nearly all
posterior mass on a single model. The choice can therefore change
posterior inclusion probabilities materially, and users are encouraged
to check the sensitivity of their conclusions. Switching between the
options requires no re-estimation, as all are recovered from the same
fitted model space.
The selected weighting and the realized learning rate are
recorded in the new weighting and eta elements
(slots 18 and 19) of badp_bma objects. Existing slots 1-17
are unchanged, so numeric indexing of earlier elements continues to
work.
Model weights are now formed on the log scale and shifted before exponentiation, which prevents overflow when log Bayes factors are large.
coef_hist() labels the y axis “Density” rather than
“Frequency”, matching what the histograms actually show.
sem_sigma_matrix() builds variances with
multiplication rather than ^2, avoiding a NaN
second derivative that automatic differentiation would otherwise produce
when a variance parameter is exactly zero.
sem_C_matrix() validates that phi_1 is
supplied with the same length as beta.
RTMB (>= 1.6) is now required, for
automatic-differentiation support in chol() and
determinant().
The minimum required R version was raised from 3.5 to 4.4, to
match the requirement of Matrix, on which RTMB
depends through TMB. The previous declaration could not be
satisfied in practice.
Regenerated every bundled model space
(small_model_space, full_model_space,
model_space_nonnested, migration_model_space
and migration_model_space_nonnested) and
full_bma_results with the fixed automatic differentiation
pipeline. model_space_nonnested had no generating script;
data-raw/model_space_nonnested.R now provides one.
best_models() now
takes a character prior argument in place of the integer
criterion argument. Use prior = "binomial"
(default) instead of criterion = 1, and
prior = "beta" instead of criterion = 2. This
brings the API in line with summary.badp_bma(), which
already used prior = "binomial" | "beta".dil.Par
parameter to omega for clarity and consistency with
statistical literature.bma() now returns an object of class
badp_bma (previously unclassed list).optim_model_space() now returns an object of class
badp_model_space.badp_bma objects:
print.badp_bma() - Clean, informative console
output.summary.badp_bma() - Detailed statistical summary with
highlighted important variables. Enhanced to display BMA statistics for
both binomial and binomial-beta priors simultaneously.coef.badp_bma() - Extract coefficients with optional
standard errors and PIPs.plot.badp_bma() - Default visualization with dispatch
to existing plot functions.print.badp_model_space() for model space
objects.bma() output: removed spaces,
duplicates, and typos; all names are now valid R identifiers (e.g.,
uniform_table, random_table,
reg_names, dilution,
alphas).results[[3]]) and helper functions
(best_models(), jointness(), etc.) are fully
preserved. Named access is available via the new identifiers (e.g.,
results$reg_names), but code using the previous long
component names must be updated.@keywords internal to
hide helper and implementation functions from user-facing help
documentation.sem_likelihood example: use the bundled
economic_growth dataset instead of small random data that
could produce NA or invalid positive values on some
platforms.ggpubr dependency; plotting functions now use
patchwork for plot arrangement.migration_data dataset with migration flows data
from Afonso, Alves, & Beck (2025).migration_model_space and
migration_model_space_nonnested example model space
objects.feature_standardization function to handle tibble
input correctly.join_lagged_col function.n_ prefix for counts, df_free for
degrees of freedom).devbox-based reproducible development
environment (devbox.json) and a justfile with
shortcuts for common development tasks (just test,
just check, just document, etc.).bdsm to badp
(Bayesian Averaging for Dynamic Panels).df argument from the bma
function; data is no longer required at the BMA stage.posterior_dens function for plotting posterior
densities of coefficients.coef_hist via
the weight parameter (based on posterior model
probabilities).extract_names function.optim_model_space.bma function for improved robustness and
compatibility.These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.