#!/usr/bin/env python
# coding: utf-8

# DO NOT EDIT
# Autogenerated from the notebook ordinal_regression.ipynb.
# Edit the notebook and then sync the output with this file.
#
# flake8: noqa
# DO NOT EDIT

# # Ordinal Regression

import numpy as np
import pandas as pd
import scipy.stats as stats

from statsmodels.miscmodels.ordinal_model import OrderedModel

# Loading a stata data file from the UCLA website.This notebook is
# inspired by https://stats.idre.ucla.edu/r/dae/ordinal-logistic-regression/
# which is a R notebook from UCLA.

url = "https://stats.idre.ucla.edu/stat/data/ologit.dta"
data_student = pd.read_stata(url)

data_student.head(5)

data_student.dtypes

data_student['apply'].dtype

# This dataset is about the probability for undergraduate students to
# apply to graduate school given three exogenous variables:
# - their grade point average(`gpa`), a float between 0 and 4.
# - `pared`, a binary that indicates if at least one parent went to
# graduate school.
# - and `public`, a binary that indicates if the current undergraduate
# institution of the student is public or private.
#
# `apply`, the target variable is categorical with ordered categories:
# `unlikely` < `somewhat likely` < `very likely`. It is a `pd.Serie` of
# categorical type, this is preferred over NumPy arrays.

# The model is based on a numerical latent variable $y_{latent}$ that we
# cannot observe but that we can compute thanks to exogenous variables.
# Moreover we can use this $y_{latent}$ to define $y$ that we can observe.
#
# For more details see the the Documentation of OrderedModel,  [the UCLA
# webpage](https://stats.idre.ucla.edu/r/dae/ordinal-logistic-regression/)
# or this
# [book](https://onlinelibrary.wiley.com/doi/book/10.1002/9780470594001).
#

# ### Probit ordinal regression:

mod_prob = OrderedModel(data_student['apply'],
                        data_student[['pared', 'public', 'gpa']],
                        distr='probit')

res_prob = mod_prob.fit(method='bfgs')
res_prob.summary()

# In our model, we have 3 exogenous variables(the $\beta$s if we keep the
# documentation's notations) so we have 3 coefficients that need to be
# estimated.
#
# Those 3 estimations and their standard errors can be retrieved in the
# summary table.
#
# Since there are 3 categories in the target variable(`unlikely`,
# `somewhat likely`, `very likely`), we have two thresholds to estimate.
# As explained in the doc of the method
# `OrderedModel.transform_threshold_params`, the first estimated threshold
# is the actual value and all the other thresholds are in terms of
# cumulative exponentiated increments. Actual thresholds values can be
# computed as follows:

num_of_thresholds = 2
mod_prob.transform_threshold_params(res_prob.params[-num_of_thresholds:])

# ### Logit ordinal regression:

mod_log = OrderedModel(data_student['apply'],
                       data_student[['pared', 'public', 'gpa']],
                       distr='logit')

res_log = mod_log.fit(method='bfgs', disp=False)
res_log.summary()

predicted = res_log.model.predict(res_log.params,
                                  exog=data_student[['pared', 'public',
                                                     'gpa']])
predicted

pred_choice = predicted.argmax(1)
print('Fraction of correct choice predictions')
print((np.asarray(data_student['apply'].values.codes) == pred_choice).mean())

# ### Ordinal regression with a custom cumulative cLogLog distribution:

# In addition to `logit` and `probit` regression, any continuous
# distribution from `SciPy.stats` package can be used for the `distr`
# argument. Alternatively, one can define its own distribution simply
# creating a subclass from `rv_continuous` and implementing a few methods.

# using a SciPy distribution
res_exp = OrderedModel(data_student['apply'],
                       data_student[['pared', 'public', 'gpa']],
                       distr=stats.expon).fit(method='bfgs', disp=False)
res_exp.summary()


# minimal definition of a custom scipy distribution.
class CLogLog(stats.rv_continuous):
    def _ppf(self, q):
        return np.log(-np.log(1 - q))

    def _cdf(self, x):
        return 1 - np.exp(-np.exp(x))


cloglog = CLogLog()

# definition of the model and fitting
res_cloglog = OrderedModel(data_student['apply'],
                           data_student[['pared', 'public', 'gpa']],
                           distr=cloglog).fit(method='bfgs', disp=False)
res_cloglog.summary()

# ### Using formulas - treatment of endog
#
# Pandas' ordered categorical and numeric values are supported as
# dependent variable in formulas. Other types will raise a ValueError.

modf_logit = OrderedModel.from_formula("apply ~ 0 + pared + public + gpa",
                                       data_student,
                                       distr='logit')
resf_logit = modf_logit.fit(method='bfgs')
resf_logit.summary()

# Using numerical codes for the dependent variable is supported but loses
# the names of the category levels. The levels and names correspond to the
# unique values of the dependent variable sorted in alphanumeric order as in
# the case without using formulas.

data_student["apply_codes"] = data_student['apply'].cat.codes * 2 + 5
data_student["apply_codes"].head()

OrderedModel.from_formula("apply_codes ~ 0 + pared + public + gpa",
                          data_student,
                          distr='logit').fit().summary()

resf_logit.predict(data_student.iloc[:5])

# Using string values directly as dependent variable raises a ValueError.

data_student["apply_str"] = np.asarray(data_student["apply"])
data_student["apply_str"].head()

data_student.apply_str = pd.Categorical(data_student.apply_str, ordered=True)
data_student.public = data_student.public.astype(float)
data_student.pared = data_student.pared.astype(float)

OrderedModel.from_formula("apply_str ~ 0 + pared + public + gpa",
                          data_student,
                          distr='logit')

# ### Using formulas - no constant in model
#
# The parameterization of OrderedModel requires that there is **no**
# constant in the model, neither explicit nor implicit. The constant is
# equivalent to shifting all thresholds and is therefore not separately
# identified.
#
# Patsy's formula specification does not allow a design matrix without
# explicit or implicit constant if there are categorical variables (or maybe
# splines) among explanatory variables. As workaround, statsmodels removes
# an explicit intercept.
#
# Consequently, there are two valid cases to get a design matrix without
# intercept.
#
# - specify a model without explicit and implicit intercept which is
# possible if there are only numerical variables in the model.
# - specify a model with an explicit intercept which statsmodels will
# remove.
#
# Models with an implicit intercept will be overparameterized, the
# parameter estimates will not be fully identified, `cov_params` will not be
# invertible and standard errors might contain nans.
#
# In the following we look at an example with an additional categorical
# variable.
#

nobs = len(data_student)
data_student["dummy"] = (np.arange(nobs) < (nobs / 2)).astype(float)

# **explicit intercept**, that will be removed:
#
# Note "1 +" is here redundant because it is patsy's default.

modfd_logit = OrderedModel.from_formula(
    "apply ~ 1 + pared + public + gpa + C(dummy)", data_student, distr='logit')
resfd_logit = modfd_logit.fit(method='bfgs')
print(resfd_logit.summary())

modfd_logit.k_vars

modfd_logit.k_constant

# **implicit intercept** creates overparameterized model
#
# Specifying "0 +" in the formula drops the explicit intercept. However,
# the categorical encoding is now changed to include an implicit intercept.
# In this example, the created dummy variables `C(dummy)[0.0]` and
# `C(dummy)[1.0]` sum to one.

# ```python
# OrderedModel.from_formula("apply ~ 0 + pared + public + gpa + C(dummy)",
# data_student, distr='logit')
# ```

#
# To see what would happen in the overparameterized case, we can avoid the
# constant check in the model by explicitly specifying whether a constant is
# present or not. We use hasconst=False, even though the model has an
# implicit constant.
#
# The parameters of the two dummy variable columns and the first threshold
# are not separately identified. Estimates for those parameters and
# availability of standard errors are arbitrary and depends on numerical
# details that differ across environments.
#
# Some summary measures like log-likelihood value are not affected by
# this, within convergence tolerance and numerical precision. Prediction
# should also be possible. However, inference is not available, or is not
# valid.

modfd2_logit = OrderedModel.from_formula(
    "apply ~ 0 + pared + public + gpa + C(dummy)",
    data_student,
    distr='logit',
    hasconst=False)
resfd2_logit = modfd2_logit.fit(method='bfgs')
print(resfd2_logit.summary())

resfd2_logit.predict(data_student.iloc[:5])

resf_logit.predict()

# ### Binary Model compared to Logit
#
# If there are only two levels of the dependent ordered categorical
# variable, then the model can also be estimated by a Logit model.
#
# The models are (theoretically) identical in this case except for the
# parameterization of the constant. Logit as most other models requires in
# general an intercept. This corresponds to the threshold parameter in the
# OrderedModel, however, with opposite sign.
#
# The implementation differs and not all of the same results statistic and
# post-estimation features are available. Estimated parameters and other
# results statistic differ mainly based on convergence tolerance of the
# optimization.
#

from statsmodels.discrete.discrete_model import Logit
from statsmodels.tools.tools import add_constant

# We drop the middle category from the data and keep the two extreme
# categories.

mask_drop = data_student['apply'] == "somewhat likely"
data2 = data_student.loc[~mask_drop, :]
# we need to remove the category also from the Categorical Index
data2['apply'].cat.remove_categories("somewhat likely", inplace=True)
data2.head()

mod_log = OrderedModel(data2['apply'],
                       data2[['pared', 'public', 'gpa']],
                       distr='logit')

res_log = mod_log.fit(method='bfgs', disp=False)
res_log.summary()

# The Logit model does not have a constant by default, we have to add it
# to our explanatory variables.
#
# The results are essentially identical between Logit and ordered model up
# to numerical precision mainly resulting from convergence tolerance in the
# estimation.
#
# The only difference is in the sign of the constant, Logit and
# OrdereModel have opposite signs of he constant. This is a consequence of
# the parameterization in terms of cut points in OrderedModel instead of
# including and constant column in the design matrix.

ex = add_constant(data2[['pared', 'public', 'gpa']], prepend=False)
mod_logit = Logit(data2['apply'].cat.codes, ex)

res_logit = mod_logit.fit(method='bfgs', disp=False)

res_logit.summary()

# Robust standard errors are also available in OrderedModel in the same
# way as in discrete.Logit.
# As example we specify HAC covariance type even though we have cross-
# sectional data and autocorrelation is not appropriate.

res_logit_hac = mod_logit.fit(method='bfgs',
                              disp=False,
                              cov_type="hac",
                              cov_kwds={"maxlags": 2})
res_log_hac = mod_log.fit(method='bfgs',
                          disp=False,
                          cov_type="hac",
                          cov_kwds={"maxlags": 2})

res_logit_hac.bse.values - res_log_hac.bse