"""Do a method of simlated moments estimation."""
import functools
import warnings
from collections.abc import Callable
from dataclasses import dataclass, field
from functools import cached_property
from typing import Any, Dict, Union
import numpy as np
import pandas as pd
from pybaum import leaf_names, tree_just_flatten
from estimagic.differentiation.derivatives import first_derivative
from estimagic.estimation.msm_weighting import get_weighting_matrix
from estimagic.exceptions import InvalidFunctionError
from estimagic.inference.msm_covs import cov_optimal, cov_robust
from estimagic.inference.shared import (
FreeParams,
calculate_ci,
calculate_estimation_summary,
calculate_free_estimates,
calculate_p_values,
calculate_summary_data_estimation,
get_derivative_case,
transform_covariance,
transform_free_cov_to_cov,
transform_free_values_to_params_tree,
)
from estimagic.optimization.optimize_result import OptimizeResult
from estimagic.optimization.optimize import minimize
from estimagic.parameters.block_trees import block_tree_to_matrix, matrix_to_block_tree
from estimagic.parameters.conversion import Converter, get_converter
from estimagic.parameters.space_conversion import InternalParams
from estimagic.parameters.tree_registry import get_registry
from estimagic.sensitivity.msm_sensitivity import (
calculate_actual_sensitivity_to_noise,
calculate_actual_sensitivity_to_removal,
calculate_fundamental_sensitivity_to_noise,
calculate_fundamental_sensitivity_to_removal,
calculate_sensitivity_to_bias,
calculate_sensitivity_to_weighting,
)
from estimagic.shared.check_option_dicts import (
check_numdiff_options,
check_optimization_options,
)
from estimagic.utilities import get_rng, to_pickle
[docs]def estimate_msm(
simulate_moments,
empirical_moments,
moments_cov,
params,
optimize_options,
*,
lower_bounds=None,
upper_bounds=None,
constraints=None,
logging=False,
log_options=None,
simulate_moments_kwargs=None,
weights="diagonal",
numdiff_options=None,
jacobian=None,
jacobian_kwargs=None,
):
"""Do a method of simulated moments or indirect inference estimation.
This is a high level interface for our lower level functions for minimization,
numerical differentiation, inference and sensitivity analysis. It does the full
workflow for MSM or indirect inference estimation with just one function call.
While we have good defaults, you can still configure each aspect of each steps
vial the optional arguments of this functions. If you find it easier to do the
minimization separately, you can do so and just provide the optimal parameters as
``params`` and set ``optimize_options=False``.
Args:
simulate_moments (callable): Function that takes params and potentially other
keyword arguments and returns a pytree with simulated moments. If the
function returns a dict containing the key ``"simulated_moments"`` we only
use the value corresponding to that key. Other entries are stored in the
log database if you use logging.
empirical_moments (pandas.Series): A pytree with the same structure as the
result of ``simulate_moments``.
moments_cov (pandas.DataFrame): A block-pytree containing the covariance
matrix of the empirical moments. This is typically calculated with
our ``get_moments_cov`` function.
params (pytree): A pytree containing the estimated or start parameters of the
model. If the supplied parameters are estimated parameters, set
optimize_options to False. Pytrees can be a numpy array, a pandas Series, a
DataFrame with "value" column, a float and any kind of (nested) dictionary
or list containing these elements. See :ref:`params` for examples.
optimize_options (dict, str or False): Keyword arguments that govern the
numerical optimization. Valid entries are all arguments of
:func:`~estimagic.optimization.optimize.minimize` except for those that can
be passed explicitly to ``estimate_msm``. If you pass False as
``optimize_options`` you signal that ``params`` are already
the optimal parameters and no numerical optimization is needed. If you pass
a str as optimize_options it is used as the ``algorithm`` option.
lower_bounds (pytree): A pytree with the same structure as params with lower
bounds for the parameters. Can be ``-np.inf`` for parameters with no lower
bound.
upper_bounds (pytree): As lower_bounds. Can be ``np.inf`` for parameters with
no upper bound.
simulate_moments_kwargs (dict): Additional keyword arguments for
``simulate_moments``.
weights (str): One of "diagonal" (default), "identity" or "optimal".
Note that "optimal" refers to the asymptotically optimal weighting matrix
and is often not a good choice due to large finite sample bias.
constraints (list, dict): List with constraint dictionaries or single dict.
See :ref:`constraints`.
logging (pathlib.Path, str or False): Path to sqlite3 file (which typically has
the file extension ``.db``. If the file does not exist, it will be created.
The dashboard can only be used when logging is used.
log_options (dict): Additional keyword arguments to configure the logging.
- "fast_logging" (bool):
A boolean that determines if "unsafe" settings are used to speed up
write processes to the database. This should only be used for very short
running criterion functions where the main purpose of the log is a
real-time dashboard and it would not be catastrophic to get a corrupted
database in case of a sudden system shutdown. If one evaluation of the
criterion function (and gradient if applicable) takes more than 100 ms,
the logging overhead is negligible.
- "if_table_exists" (str):
One of "extend", "replace", "raise". What to do if the tables we want to
write to already exist. Default "extend".
- "if_database_exists" (str):
One of "extend", "replace", "raise". What to do if the database we want
to write to already exists. Default "extend".
numdiff_options (dict): Keyword arguments for the calculation of numerical
derivatives for the calculation of standard errors. See
:ref:`first_derivative` for details. Note that by default we increase the
step_size by a factor of 2 compared to the rule of thumb for optimal
step sizes. This is because many msm criterion functions are slightly noisy.
jacobian (callable): A function that take ``params`` and
potentially other keyword arguments and returns the jacobian of
simulate_moments with respect to the params.
jacobian_kwargs (dict): Additional keyword arguments for the jacobian function.
Returns:
dict: The estimated parameters, standard errors and sensitivity measures
and covariance matrix of the parameters.
"""
# ==================================================================================
# Check and process inputs
# ==================================================================================
if weights not in ["diagonal", "optimal", "identity"]:
raise NotImplementedError("Custom weighting matrices are not yet implemented.")
is_optimized = optimize_options is False
if not is_optimized:
if isinstance(optimize_options, str):
optimize_options = {"algorithm": optimize_options}
check_optimization_options(
optimize_options,
usage="estimate_msm",
algorithm_mandatory=True,
)
jac_case = get_derivative_case(jacobian)
check_numdiff_options(numdiff_options, "estimate_msm")
numdiff_options = {} if numdiff_options in (None, False) else numdiff_options.copy()
if "scaling_factor" not in numdiff_options:
numdiff_options["scaling_factor"] = 2
weights, internal_weights = get_weighting_matrix(
moments_cov=moments_cov,
method=weights,
empirical_moments=empirical_moments,
return_type="pytree_and_array",
)
internal_moments_cov = block_tree_to_matrix(
moments_cov,
outer_tree=empirical_moments,
inner_tree=empirical_moments,
)
constraints = [] if constraints is None else constraints
jacobian_kwargs = {} if jacobian_kwargs is None else jacobian_kwargs
simulate_moments_kwargs = (
{} if simulate_moments_kwargs is None else simulate_moments_kwargs
)
# ==================================================================================
# Calculate estimates via minimization (if necessary)
# ==================================================================================
if is_optimized:
estimates = params
opt_res = None
else:
funcs = get_msm_optimization_functions(
simulate_moments=simulate_moments,
empirical_moments=empirical_moments,
weights=weights,
simulate_moments_kwargs=simulate_moments_kwargs,
# Always pass None because we do not support closed form jacobians during
# optimization yet. Otherwise we would get a NotImplementedError
jacobian=None,
jacobian_kwargs=jacobian_kwargs,
)
opt_res = minimize(
lower_bounds=lower_bounds,
upper_bounds=upper_bounds,
constraints=constraints,
logging=logging,
log_options=log_options,
params=params,
**funcs, # contains the criterion func and possibly more
**optimize_options,
)
estimates = opt_res.params
# ==================================================================================
# do first function evaluations
# ==================================================================================
try:
sim_mom_eval = simulate_moments(estimates, **simulate_moments_kwargs)
except (KeyboardInterrupt, SystemExit):
raise
except Exception as e:
msg = "Error while evaluating simulate_moments at estimated params."
raise InvalidFunctionError(msg) from e
if callable(jacobian):
try:
jacobian_eval = jacobian(estimates, **jacobian_kwargs)
except (KeyboardInterrupt, SystemExit):
raise
except Exception as e:
msg = "Error while evaluating derivative at estimated params."
raise InvalidFunctionError(msg) from e
else:
jacobian_eval = None
# ==================================================================================
# get converter for params and function outputs
# ==================================================================================
def helper(params):
raw = simulate_moments(params, **simulate_moments_kwargs)
if isinstance(raw, dict) and "simulated_moments" in raw:
out = {"contributions": raw["simulated_moments"]}
else:
out = {"contributions": raw}
return out
if isinstance(sim_mom_eval, dict) and "simulated_moments" in sim_mom_eval:
func_eval = {"contributions": sim_mom_eval["simulated_moments"]}
else:
func_eval = {"contributions": sim_mom_eval}
converter, internal_estimates = get_converter(
params=estimates,
constraints=constraints,
lower_bounds=lower_bounds,
upper_bounds=upper_bounds,
func_eval=func_eval,
primary_key="contributions",
scaling=False,
scaling_options=None,
derivative_eval=jacobian_eval,
)
# ==================================================================================
# Calculate internal jacobian
# ==================================================================================
if jac_case == "closed-form":
x = converter.params_to_internal(estimates)
int_jac = converter.derivative_to_internal(jacobian_eval, x)
else:
def func(x):
p = converter.params_from_internal(x)
sim_mom_eval = helper(p)
out = converter.func_to_internal(sim_mom_eval)
return out
int_jac = first_derivative(
func=func,
params=internal_estimates.values,
lower_bounds=internal_estimates.lower_bounds,
upper_bounds=internal_estimates.upper_bounds,
**numdiff_options,
)["derivative"]
# ==================================================================================
# Calculate external jac (if no constraints and not closed form )
# ==================================================================================
if constraints in [None, []] and jacobian_eval is None and int_jac is not None:
jacobian_eval = matrix_to_block_tree(
int_jac,
outer_tree=empirical_moments,
inner_tree=estimates,
)
if jacobian_eval is None:
_no_jac_reason = (
"no closed form jacobian was provided and there are constraints"
)
else:
_no_jac_reason = None
# ==================================================================================
# Create MomentsResult
# ==================================================================================
free_estimates = calculate_free_estimates(estimates, internal_estimates)
res = MomentsResult(
_params=estimates,
_weights=weights,
_converter=converter,
_optimize_result=opt_res,
_internal_weights=internal_weights,
_internal_moments_cov=internal_moments_cov,
_internal_jacobian=int_jac,
_jacobian=jacobian_eval,
_no_jacobian_reason=_no_jac_reason,
_empirical_moments=empirical_moments,
_internal_estimates=internal_estimates,
_free_estimates=free_estimates,
_has_constraints=constraints not in [None, []],
)
return res
def get_msm_optimization_functions(
simulate_moments,
empirical_moments,
weights,
*,
simulate_moments_kwargs=None,
jacobian=None,
jacobian_kwargs=None,
):
"""Construct criterion functions and their derivatives for msm estimation.
Args:
simulate_moments (callable): Function that takes params and potentially other
keyworrd arguments and returns simulated moments as a pandas Series.
Alternatively, the function can return a dict with any number of entries
as long as one of those entries is "simulated_moments".
empirical_moments (pandas.Series): A pandas series with the empirical
equivalents of the simulated moments.
weights (pytree): The weighting matrix as block pytree.
simulate_moments_kwargs (dict): Additional keyword arguments for
``simulate_moments``.
jacobian (callable or pandas.DataFrame): A function that take ``params`` and
potentially other keyword arguments and returns the jacobian of
simulate_moments with respect to the params. Alternatively you can pass
a pandas.DataFrame with the jacobian at the optimal parameters. This is
only possible if you pass ``optimize_options=False``.
jacobian_kwargs (dict): Additional keyword arguments for jacobian.
Returns:
dict: Dictionary containing at least the entry "criterion". If enough inputs
are provided it also contains the entries "derivative" and
"criterion_and_derivative". All values are functions that take params
as only argument.
"""
flat_weights = block_tree_to_matrix(
weights,
outer_tree=empirical_moments,
inner_tree=empirical_moments,
)
chol_weights = np.linalg.cholesky(flat_weights)
registry = get_registry(extended=True)
flat_emp_mom = tree_just_flatten(empirical_moments, registry=registry)
_simulate_moments = _partial_kwargs(simulate_moments, simulate_moments_kwargs)
_jacobian = _partial_kwargs(jacobian, jacobian_kwargs)
criterion = functools.partial(
_msm_criterion,
simulate_moments=_simulate_moments,
flat_empirical_moments=flat_emp_mom,
chol_weights=chol_weights,
registry=registry,
)
out = {"criterion": criterion}
if _jacobian is not None:
raise NotImplementedError(
"Closed form jacobians are not yet supported in estimate_msm"
)
return out
def _msm_criterion(
params, simulate_moments, flat_empirical_moments, chol_weights, registry
):
"""Calculate msm criterion given parameters and building blocks."""
simulated = simulate_moments(params)
if isinstance(simulated, dict) and "simulated_moments" in simulated:
simulated = simulated["simulated_moments"]
if isinstance(simulated, np.ndarray) and simulated.ndim == 1:
simulated_flat = simulated
else:
simulated_flat = np.array(tree_just_flatten(simulated, registry=registry))
deviations = simulated_flat - flat_empirical_moments
root_contribs = deviations @ chol_weights
value = root_contribs @ root_contribs
out = {
"value": value,
"root_contributions": root_contribs,
}
return out
def _partial_kwargs(func, kwargs):
"""Partial keyword arguments into a function.
In contrast to normal partial this works if kwargs in None. If func is not a
callable it simply returns None.
"""
if isinstance(func, Callable):
if kwargs not in (None, {}):
out = functools.partial(func, **kwargs)
else:
out = func
else:
out = None
return out
[docs]@dataclass
class MomentsResult:
"""Method of moments estimation results object."""
_params: Any
_internal_estimates: InternalParams
_free_estimates: FreeParams
_weights: Any
_converter: Converter
_internal_moments_cov: np.ndarray
_internal_weights: np.ndarray
_internal_jacobian: np.ndarray
_empirical_moments: Any
_has_constraints: bool
_optimize_result: Union[OptimizeResult, None] = None
_jacobian: Any = None
_no_jacobian_reason: Union[str, None] = None
_cache: Dict = field(default_factory=dict)
def _get_free_cov(self, method, n_samples, bounds_handling, seed):
if method not in {"optimal", "robust"}:
msg = f"Invalid method {method}. method must be in {'optimal', 'robust'}"
raise ValueError(msg)
args = (method, n_samples, bounds_handling, seed)
is_cached = args in self._cache
if is_cached:
free_cov = self._cache[args]
else:
free_cov = _calculate_free_cov_msm(
internal_estimates=self._internal_estimates,
internal_jacobian=self._internal_jacobian,
internal_moments_cov=self._internal_moments_cov,
internal_weights=self._internal_weights,
converter=self._converter,
method=method,
n_samples=n_samples,
bounds_handling=bounds_handling,
seed=seed,
)
if seed is not None:
self._cache[args] = free_cov
elif self._converter.has_transforming_constraints:
msg = (
"seed is set to None and constraints are transforming. This leads "
"to randomness in the result. To avoid random behavior, choose a "
"non-None seed."
)
warnings.warn(msg)
return free_cov
@property
def params(self):
return self._params
@property
def optimize_result(self):
return self._optimize_result
@property
def weights(self):
return self._weights
@property
def jacobian(self):
return self._jacobian
@cached_property
def _se(self):
return self.se()
@cached_property
def _cov(self):
return self.cov()
@cached_property
def _summary(self):
return self.summary()
@cached_property
def _ci(self):
return self.ci()
@cached_property
def _p_values(self):
return self.p_values()
[docs] def se(
self,
method="robust",
n_samples=10_000,
bounds_handling="clip",
seed=None,
):
"""Calculate standard errors.
Args:
method (str): One of "robust", "optimal". Despite the name, "optimal" is
not recommended in finite samples and "optimal" standard errors are
only valid if the asymptotically optimal weighting matrix has been
used. It is only supported because it is needed to calculate
sensitivity measures.
n_samples (int): Number of samples used to transform the covariance matrix
of the internal parameter vector into the covariance matrix of the
external parameters. For background information about internal and
external params see :ref:`implementation_of_constraints`. This is only
used if you are using constraints.
bounds_handling (str): One of "clip", "raise", "ignore". Determines how
bounds are handled. If "clip", confidence intervals are clipped at the
bounds. Standard errors are only adjusted if a sampling step is
necessary due to additional constraints. If "raise" and any lower or
upper bound is binding, we raise an Error. If "ignore", boundary
problems are simply ignored.
seed (int): Seed for the random number generator. Only used if there are
transforming constraints.
Returns:
Any: A pytree with the same structure as params containing standard errors
for the parameter estimates.
"""
free_cov = self._get_free_cov(
method=method,
n_samples=n_samples,
bounds_handling=bounds_handling,
seed=seed,
)
free_se = np.sqrt(np.diagonal(free_cov))
se = transform_free_values_to_params_tree(
values=free_se,
free_params=self._free_estimates,
params=self._params,
)
return se
[docs] def cov(
self,
method="robust",
n_samples=10_000,
bounds_handling="clip",
return_type="pytree",
seed=None,
):
"""Calculate the variance-covariance matrix of the estimated parameters.
Args:
method (str): One of "robust", "optimal". Despite the name, "optimal" is
not recommended in finite samples and "optimal" standard errors are
only valid if the asymptotically optimal weighting matrix has been
used. It is only supported because it is needed to calculate
sensitivity measures.
n_samples (int): Number of samples used to transform the covariance matrix
of the internal parameter vector into the covariance matrix of the
external parameters. For background information about internal and
external params see :ref:`implementation_of_constraints`. This is only
used if you are using constraints.
bounds_handling (str): One of "clip", "raise", "ignore". Determines how
bounds are handled. If "clip", confidence intervals are clipped at the
bounds. Standard errors are only adjusted if a sampling step is
necessary due to additional constraints. If "raise" and any lower or
upper bound is binding, we raise an Error. If "ignore", boundary
problems are simply ignored.
return_type (str): One of "pytree", "array" or "dataframe". Default pytree.
If "array", a 2d numpy array with the covariance is returned. If
"dataframe", a pandas DataFrame with parameter names in the
index and columns are returned.
seed (int): Seed for the random number generator. Only used if there are
transforming constraints.
Returns:
Any: The covariance matrix of the estimated parameters as block-pytree or
numpy array.
"""
free_cov = self._get_free_cov(
method=method,
n_samples=n_samples,
bounds_handling=bounds_handling,
seed=seed,
)
cov = transform_free_cov_to_cov(
free_cov=free_cov,
free_params=self._free_estimates,
params=self._params,
return_type=return_type,
)
return cov
[docs] def summary(
self,
method="robust",
n_samples=10_000,
ci_level=0.95,
bounds_handling="clip",
seed=None,
):
"""Create a summary of estimation results.
Args:
method (str): One of "robust", "optimal". Despite the name, "optimal" is
not recommended in finite samples and "optimal" standard errors are
only valid if the asymptotically optimal weighting matrix has been
used. It is only supported because it is needed to calculate
sensitivity measures.
ci_level (float): Confidence level for the calculation of confidence
intervals. The default is 0.95.
n_samples (int): Number of samples used to transform the covariance matrix
of the internal parameter vector into the covariance matrix of the
external parameters. For background information about internal and
external params see :ref:`implementation_of_constraints`. This is only
used if you are using constraints.
bounds_handling (str): One of "clip", "raise", "ignore". Determines how
bounds are handled. If "clip", confidence intervals are clipped at the
bounds. Standard errors are only adjusted if a sampling step is
necessary due to additional constraints. If "raise" and any lower or
upper bound is binding, we raise an Error. If "ignore", boundary
problems are simply ignored.
seed (int): Seed for the random number generator. Only used if there are
transforming constraints.
Returns:
Any: The estimation summary as pytree of DataFrames.
"""
summary_data = calculate_summary_data_estimation(
self,
free_estimates=self._free_estimates,
method=method,
ci_level=ci_level,
n_samples=n_samples,
bounds_handling=bounds_handling,
seed=seed,
)
summary = calculate_estimation_summary(
summary_data=summary_data,
names=self._free_estimates.all_names,
free_names=self._free_estimates.free_names,
)
return summary
[docs] def ci(
self,
method="robust",
n_samples=10_000,
ci_level=0.95,
bounds_handling="clip",
seed=None,
):
"""Calculate confidence intervals.
Args:
method (str): One of "robust", "optimal". Despite the name, "optimal" is
not recommended in finite samples and "optimal" standard errors are
only valid if the asymptotically optimal weighting matrix has been
used. It is only supported because it is needed to calculate
sensitivity measures.
ci_level (float): Confidence level for the calculation of confidence
intervals. The default is 0.95.
n_samples (int): Number of samples used to transform the covariance matrix
of the internal parameter vector into the covariance matrix of the
external parameters. For background information about internal and
external params see :ref:`implementation_of_constraints`. This is only
used if you are using constraints.
bounds_handling (str): One of "clip", "raise", "ignore". Determines how
bounds are handled. If "clip", confidence intervals are clipped at the
bounds. Standard errors are only adjusted if a sampling step is
necessary due to additional constraints. If "raise" and any lower or
upper bound is binding, we raise an Error. If "ignore", boundary
problems are simply ignored.
seed (int): Seed for the random number generator. Only used if there are
transforming constraints.
Returns:
Any: Pytree with the same structure as params containing lower bounds of
confidence intervals.
Any: Pytree with the same structure as params containing upper bounds of
confidence intervals.
"""
free_cov = self._get_free_cov(
method=method,
n_samples=n_samples,
bounds_handling=bounds_handling,
seed=seed,
)
free_lower, free_upper = calculate_ci(
free_values=self._free_estimates.values,
free_standard_errors=np.sqrt(np.diagonal(free_cov)),
ci_level=ci_level,
)
lower, upper = (
transform_free_values_to_params_tree(
values, free_params=self._free_estimates, params=self._params
)
for values in (free_lower, free_upper)
)
return lower, upper
[docs] def p_values(
self,
method="robust",
n_samples=10_000,
bounds_handling="clip",
seed=None,
):
"""Calculate p-values.
Args:
method (str): One of "robust", "optimal". Despite the name, "optimal" is
not recommended in finite samples and "optimal" standard errors are
only valid if the asymptotically optimal weighting matrix has been
used. It is only supported because it is needed to calculate
sensitivity measures.
n_samples (int): Number of samples used to transform the covariance matrix
of the internal parameter vector into the covariance matrix of the
external parameters. For background information about internal and
external params see :ref:`implementation_of_constraints`. This is only
used if you are using constraints.
bounds_handling (str): One of "clip", "raise", "ignore". Determines how
bounds are handled. If "clip", confidence intervals are clipped at the
bounds. Standard errors are only adjusted if a sampling step is
necessary due to additional constraints. If "raise" and any lower or
upper bound is binding, we raise an Error. If "ignore", boundary
problems are simply ignored.
seed (int): Seed for the random number generator. Only used if there are
transforming constraints.
Returns:
Any: Pytree with the same structure as params containing p-values.
Any: Pytree with the same structure as params containing p-values.
"""
free_cov = self._get_free_cov(
method=method,
n_samples=n_samples,
bounds_handling=bounds_handling,
seed=seed,
)
free_p_values = calculate_p_values(
free_values=self._free_estimates.values,
free_standard_errors=np.sqrt(np.diagonal(free_cov)),
)
p_values = transform_free_values_to_params_tree(
free_p_values, free_params=self._free_estimates, params=self._params
)
return p_values
[docs] def sensitivity(
self,
kind="bias",
n_samples=10_000,
bounds_handling="clip",
seed=None,
return_type="pytree",
):
"""Calculate sensitivity measures for moments estimates.
The sensitivity measures are based on the following papers:
Andrews, Gentzkow & Shapiro (2017, Quarterly Journal of Economics)
Honore, Jorgensen & de Paula
(https://onlinelibrary.wiley.com/doi/full/10.1002/jae.2779)
In the papers the different kinds of sensitivity measures are just called
m1, e2, e3, e4, e5 and e6. We try to give them more informative names, but
list the original names for references.
Args:
kind (str): The following kinds are supported:
- "bias":
Origally m1. How strongly would the parameter estimates be biased if
the kth moment was misspecified, i.e not zero in expectation?
- "noise_fundamental":
Originally e2. How much precision would be lost if the kth moment
was subject to a little additional noise if the optimal weighting
matrix was used?
- "noise":
Originally e3. How much precision would be lost if the kth moment
was subjet to a little additional noise?
- "removal":
Originally e4. How much precision would be lost if the kth moment
was excluded from the estimation?
- "removal_fundamental":
Originally e5. How much precision would be lost if the kth moment
was excluded from the estimation if the asymptotically optimal
weighting matrix was used.
- "weighting":
Originally e6. How would the precision change if the weight of the
kth moment is increased a little?
n_samples (int): Number of samples used to transform the covariance matrix
of the internal parameter vector into the covariance matrix of the
external parameters. For background information about internal and
external params see :ref:`implementation_of_constraints`. This is only
used if you are using constraints.
bounds_handling (str): One of "clip", "raise", "ignore". Determines how
bounds are handled. If "clip", confidence intervals are clipped at the
bounds. Standard errors are only adjusted if a sampling step is
necessary due to additional constraints. If "raise" and any lower or
upper bound is binding, we raise an Error. If "ignore", boundary
problems are simply ignored.
seed (int): Seed for the random number generator. Only used if there are
transforming constraints.
return_type (str): One of "array", "dataframe" or "pytree". Default pytree.
If your params or moments have a very nested format, return_type
"dataframe" might be the better choice.
Returns:
Any: The sensitivity measure as a pytree, numpy array or DataFrame.
In 2d formats, the sensitivity measures have one row per estimated
parameter and one column per moment.
"""
if self._has_constraints:
raise NotImplementedError(
"Sensitivity measures with constraints are not yet implemented."
)
jac = self._internal_jacobian
weights = self._internal_weights
moments_cov = self._internal_moments_cov
params_cov = self._get_free_cov(
method="robust",
n_samples=n_samples,
bounds_handling=bounds_handling,
seed=seed,
)
weights_opt = get_weighting_matrix(
moments_cov=moments_cov,
method="optimal",
empirical_moments=self._empirical_moments,
)
params_cov_opt = cov_optimal(jac, weights_opt)
if kind == "bias":
raw = calculate_sensitivity_to_bias(jac=jac, weights=weights)
elif kind == "noise_fundamental":
raw = calculate_fundamental_sensitivity_to_noise(
jac=jac,
weights=weights_opt,
moments_cov=moments_cov,
params_cov_opt=params_cov_opt,
)
elif kind == "noise":
m1 = calculate_sensitivity_to_bias(jac=jac, weights=weights)
raw = calculate_actual_sensitivity_to_noise(
sensitivity_to_bias=m1,
weights=weights,
moments_cov=moments_cov,
params_cov=params_cov,
)
elif kind == "removal":
raw = calculate_actual_sensitivity_to_removal(
jac=jac,
weights=weights,
moments_cov=moments_cov,
params_cov=params_cov,
)
elif kind == "removal_fundamental":
raw = calculate_fundamental_sensitivity_to_removal(
jac=jac,
moments_cov=moments_cov,
params_cov_opt=params_cov_opt,
)
elif kind == "weighting":
raw = calculate_sensitivity_to_weighting(
jac=jac,
weights=weights,
moments_cov=moments_cov,
params_cov=params_cov,
)
else:
raise ValueError(f"Invalid kind: {kind}")
if return_type == "array":
out = raw
elif return_type == "pytree":
out = matrix_to_block_tree(
raw,
outer_tree=self._params,
inner_tree=self._empirical_moments,
)
elif return_type == "dataframe":
registry = get_registry(extended=True)
row_names = self._internal_estimates.names
col_names = leaf_names(self._empirical_moments, registry=registry)
out = pd.DataFrame(
data=raw,
index=row_names,
columns=col_names,
)
else:
msg = (
f"Invalid return type: {return_type}. Valid are 'pytree', 'array' "
"and 'dataframe'"
)
raise ValueError(msg)
return out
[docs] def to_pickle(self, path):
"""Save the MomentsResult object to pickle.
Args:
path (str, pathlib.Path): A str or pathlib.path ending in .pkl or .pickle.
"""
to_pickle(self, path=path)
def _calculate_free_cov_msm(
internal_estimates,
internal_jacobian,
internal_moments_cov,
internal_weights,
converter,
method,
n_samples,
bounds_handling,
seed,
):
if method == "optimal":
internal_cov = cov_optimal(internal_jacobian, internal_weights)
else:
internal_cov = cov_robust(
internal_jacobian, internal_weights, internal_moments_cov
)
rng = get_rng(seed)
free_cov = transform_covariance(
internal_params=internal_estimates,
internal_cov=internal_cov,
converter=converter,
n_samples=n_samples,
rng=rng,
bounds_handling=bounds_handling,
)
return free_cov