def check_optimize_kwargs(**kwargs):
valid_types = {
"direction": str,
"criterion": typing.Callable,
"params": pd.DataFrame,
"algorithm": (str, typing.Callable),
"criterion_kwargs": dict,
"constraints": list,
"algo_options": dict,
"derivative": (type(None), typing.Callable),
"derivative_kwargs": dict,
"criterion_and_derivative": (type(None), typing.Callable),
"criterion_and_derivative_kwargs": dict,
"numdiff_options": dict,
"logging": (bool, Path),
"log_options": dict,
"error_handling": str,
"error_penalty": dict,
"cache_size": (int, float),
"scaling": bool,
"scaling_options": dict,
"multistart": bool,
"multistart_options": dict,
}
for arg in kwargs:
if not isinstance(kwargs[arg], valid_types[arg]):
raise TypeError(
f"Argument '{arg}' is {kwargs[arg]} which is not {valid_types[arg]}."
)
if kwargs["direction"] not in ["minimize", "maximize"]:
raise ValueError("diretion must be 'minimize' or 'maximize'")
parcols = kwargs["params"].columns
if "value" not in parcols:
raise ValueError("The params DataFrame must contain a 'value' column.")
if "lower" in parcols and "lower_bounds" not in parcols:
msg = "There is a column 'lower' in params. Did you mean 'lower_bounds'?"
warnings.warn(msg)
if "upper" in parcols and "upper_bounds" not in parcols:
msg = "There is a column 'upper' in in params. Did you mean 'upper_bounds'?"
warnings.warn(msg)
if kwargs["error_handling"] not in ["raise", "continue"]:
raise ValueError("error_handling must be 'raise' or 'continue'")
check_numdiff_options(kwargs["numdiff_options"], "optimization")
def check_optimize_kwargs(**kwargs):
valid_types = {
"direction": str,
"criterion": typing.Callable,
"algorithm": (str, typing.Callable),
"criterion_kwargs": dict,
"constraints": (list, dict),
"algo_options": dict,
"derivative": (type(None), typing.Callable, dict),
"derivative_kwargs": dict,
"criterion_and_derivative": (type(None), typing.Callable),
"criterion_and_derivative_kwargs": dict,
"numdiff_options": dict,
"logging": (bool, Path),
"log_options": dict,
"error_handling": str,
"error_penalty": dict,
"cache_size": (int, float),
"scaling": bool,
"scaling_options": dict,
"multistart": bool,
"multistart_options": dict,
}
for arg in kwargs:
if arg in valid_types:
if not isinstance(kwargs[arg], valid_types[arg]):
raise TypeError(
f"Argument '{arg}' must be {valid_types[arg]} not {kwargs[arg]}."
)
if kwargs["direction"] not in ["minimize", "maximize"]:
raise ValueError("diretion must be 'minimize' or 'maximize'")
if kwargs["error_handling"] not in ["raise", "continue"]:
raise ValueError("error_handling must be 'raise' or 'continue'")
check_numdiff_options(kwargs["numdiff_options"], "optimization")
def estimate_ml(
loglike,
params,
optimize_options,
*,
lower_bounds=None,
upper_bounds=None,
constraints=None,
logging=False,
log_options=None,
loglike_kwargs=None,
numdiff_options=None,
jacobian=None,
jacobian_kwargs=None,
hessian=None,
hessian_kwargs=None,
design_info=None,
):
"""Do a maximum likelihood (ml) estimation.
This is a high level interface of our lower level functions for maximization,
numerical differentiation and inference. It does the full workflow for maximum
likelihood estimation with just one function call.
While we have good defaults, you can still configure each aspect of each step
via the optional arguments of this function. If you find it easier to do the
maximization separately, you can do so and just provide the optimal parameters as
``params`` and set ``optimize_options=False``
Args:
loglike (callable): Likelihood function that takes a params (and potentially
other keyword arguments) and returns a dictionary that has at least the
entries "value" (a scalar float) and "contributions" (a 1d numpy array or
pytree) with the log likelihood contribution per individual.
params (pytree): A pytree containing the estimated or start parameters of the
likelihood 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 are
passed explicilty to ``estimate_ml``. 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.
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": 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".
loglike_kwargs (dict): Additional keyword arguments for loglike.
numdiff_options (dict): Keyword arguments for the calculation of numerical
derivatives for the calculation of standard errors. See
:ref:`first_derivative` for details.
jacobian (callable or None): A function that takes ``params`` and potentially
other keyword arguments and returns the jacobian of loglike["contributions"]
with respect to the params. Note that you only need to pass a Jacobian
function if you have a closed form Jacobian. If you pass None, a numerical
Jacobian will be calculated.
jacobian_kwargs (dict): Additional keyword arguments for the Jacobian function.
hessian (callable or None or False): A function that takes ``params`` and
potentially other keyword arguments and returns the Hessian of
loglike["value"] with respect to the params. If you pass None, a numerical
Hessian will be calculated. If you pass ``False``, you signal that no
Hessian should be calculated. Thus, no result that requires the Hessian will
be calculated.
hessian_kwargs (dict): Additional keyword arguments for the Hessian function.
design_info (pandas.DataFrame): DataFrame with one row per observation that
contains some or all of the variables "psu" (primary sampling unit),
"strata" and "fpc" (finite population corrector). See
:ref:`robust_likelihood_inference` for details.
Returns:
LikelihoodResult: A LikelihoodResult object.
"""
# ==================================================================================
# Check and process inputs
# ==================================================================================
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_ml",
algorithm_mandatory=True,
)
jac_case = get_derivative_case(jacobian)
hess_case = get_derivative_case(hessian)
check_numdiff_options(numdiff_options, "estimate_ml")
numdiff_options = {} if numdiff_options in (None,
False) else numdiff_options
loglike_kwargs = {} if loglike_kwargs is None else loglike_kwargs
constraints = [] if constraints is None else constraints
jacobian_kwargs = {} if jacobian_kwargs is None else jacobian_kwargs
hessian_kwargs = {} if hessian_kwargs is None else hessian_kwargs
# ==================================================================================
# Calculate estimates via maximization (if necessary)
# ==================================================================================
if is_optimized:
estimates = params
opt_res = None
else:
opt_res = maximize(
criterion=loglike,
criterion_kwargs=loglike_kwargs,
params=params,
lower_bounds=lower_bounds,
upper_bounds=upper_bounds,
constraints=constraints,
logging=logging,
log_options=log_options,
**optimize_options,
)
estimates = opt_res.params
# ==================================================================================
# Do first function evaluations at estimated parameters
# ==================================================================================
try:
loglike_eval = loglike(estimates, **loglike_kwargs)
except (KeyboardInterrupt, SystemExit):
raise
except Exception as e:
msg = "Error while evaluating loglike 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 closed form jacobian at estimated params."
raise InvalidFunctionError(msg) from e
else:
jacobian_eval = None
if callable(hessian):
try:
hessian_eval = hessian(estimates, **hessian_kwargs)
except (KeyboardInterrupt, SystemExit):
raise
except Exception as e:
msg = "Error while evaluating closed form hessian at estimated params."
raise InvalidFunctionError(msg) from e
else:
hessian_eval = None
# ==================================================================================
# Get the converter for params and function outputs
# ==================================================================================
converter, internal_estimates = get_converter(
params=estimates,
constraints=constraints,
lower_bounds=lower_bounds,
upper_bounds=upper_bounds,
func_eval=loglike_eval,
primary_key="contributions",
scaling=False,
scaling_options=None,
derivative_eval=jacobian_eval,
)
# ==================================================================================
# Calculate internal jacobian
# ==================================================================================
if jac_case == "closed-form":
int_jac = converter.derivative_to_internal(jacobian_eval,
internal_estimates.values)
elif jac_case == "numerical":
def func(x):
p = converter.params_from_internal(x)
loglike_eval = loglike(p, **loglike_kwargs)["contributions"]
out = converter.func_to_internal(loglike_eval)
return out
jac_res = first_derivative(
func=func,
params=internal_estimates.values,
lower_bounds=internal_estimates.lower_bounds,
upper_bounds=internal_estimates.upper_bounds,
**numdiff_options,
)
int_jac = jac_res["derivative"]
else:
int_jac = None
if constraints in [None, []
] and jacobian_eval is None and int_jac is not None:
loglike_contribs = loglike_eval
if isinstance(loglike_contribs,
dict) and "contributions" in loglike_contribs:
loglike_contribs = loglike_contribs["contributions"]
jacobian_eval = matrix_to_block_tree(
int_jac,
outer_tree=loglike_contribs,
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
# ==================================================================================
# Calculate internal Hessian
# ==================================================================================
if hess_case == "skip":
int_hess = None
elif hess_case == "numerical":
def func(x):
p = converter.params_from_internal(x)
loglike_eval = loglike(p, **loglike_kwargs)["value"]
out = converter.func_to_internal(loglike_eval)
return out
hess_res = second_derivative(
func=func,
params=internal_estimates.values,
lower_bounds=internal_estimates.lower_bounds,
upper_bounds=internal_estimates.upper_bounds,
**numdiff_options,
)
int_hess = hess_res["derivative"]
elif hess_case == "closed-form" and constraints:
raise NotImplementedError(
"Closed-form Hessians are not yet compatible with constraints.")
elif hess_case == "closed-form":
int_hess = block_tree_to_matrix(
hessian_eval,
outer_tree=params,
inner_tree=params,
)
else:
raise ValueError()
if constraints in [None, []
] and hessian_eval is None and int_hess is not None:
hessian_eval = matrix_to_block_tree(
int_hess,
outer_tree=params,
inner_tree=params,
)
if hessian_eval is None:
if hess_case == "skip":
_no_hess_reason = "the hessian calculation was explicitly skipped."
else:
_no_hess_reason = (
"no closed form hessian was provided and there are constraints"
)
else:
_no_hess_reason = None
# ==================================================================================
# create a LikelihoodResult object
# ==================================================================================
free_estimates = calculate_free_estimates(estimates, internal_estimates)
res = LikelihoodResult(
_params=estimates,
_converter=converter,
_optimize_result=opt_res,
_jacobian=jacobian_eval,
_no_jacobian_reason=_no_jac_reason,
_hessian=hessian_eval,
_no_hessian_reason=_no_hess_reason,
_internal_jacobian=int_jac,
_internal_hessian=int_hess,
_design_info=design_info,
_internal_estimates=internal_estimates,
_free_estimates=free_estimates,
_has_constraints=constraints not in [None, []],
)
return res
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"]:
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,
_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
check_optimization_options(
optimize_options,
usage="estimate_ml",
algorithm_mandatory=True,
)
jac_case = get_derivative_case(jacobian)
hess_case = get_derivative_case(hessian)
check_is_optimized_and_derivative_case(is_optimized, jac_case)
check_is_optimized_and_derivative_case(is_optimized, hess_case)
cov_cases = _get_cov_cases(jac_case, hess_case, design_info)
check_numdiff_options(numdiff_options, "estimate_ml")
numdiff_options = {} if numdiff_options in (None,
False) else numdiff_options
constraints = [] if constraints is None else constraints
processed_constraints, _ = process_constraints(constraints, params)
# ==================================================================================
# Calculate estimates via maximization (if necessary)
# ==================================================================================
if is_optimized:
estimates = params
else:
opt_res = maximize(
def test_check_and_process_numdiff_options_with_invalid_entries():
with pytest.raises(ValueError):
check_numdiff_options({"func": lambda x: x}, "estimate_msm")