# -*- coding: utf-8 -*-
import numpy as np
[docs]
def fit_error(y, y_predicted, n_parameters=2):
"""**Calculate the fit error for a model**
Also specific and direct access functions can be used, such as :func:`.fit_mse`,
:func:`.fit_rmse` and :func:`.fit_r2`.
Parameters
----------
y : Union[list, np.array, pd.Series]
The response variable (the y axis).
y_predicted : Union[list, np.array, pd.Series]
The fitted data generated by a model.
n_parameters : int
Number of model parameters (for the degrees of freedom used in R2).
Returns
-------
dict
A dictionary containing different indices of fit error.
See Also
--------
fit_mse, fit_rmse, fit_r2
Examples
--------
.. ipython:: python
import neurokit2 as nk
y = np.array([-1.0, -0.5, 0, 0.5, 1])
y_predicted = np.array([0.0, 0, 0, 0, 0])
# Master function
x = nk.fit_error(y, y_predicted)
x
# Direct access
nk.fit_mse(y, y_predicted)
nk.fit_rmse(y, y_predicted)
nk.fit_r2(y, y_predicted, adjusted=False)
nk.fit_r2(y, y_predicted, adjusted=True, n_parameters=2)
"""
# Get information
SSE, n, df = _fit_error_prepare(y, y_predicted, n_parameters)
# Mean squared error
MSE = SSE / n
# Root mean squared error
RMSE = np.sqrt(SSE / n)
# Adjusted r-squared
# For optimization use 1 - adjR2 since we want to minimize the function
SST = np.std(y) * n
# Get R2
if SST == 0:
R2 = 1
else:
R2 = SSE / SST
# R2 adjusted
R2_adjusted = 1 - (1 - (1 - R2)) * (n - 1) / df
return {"SSE": SSE, "MSE": MSE, "RMSE": RMSE, "R2": R2, "R2_adjusted": R2_adjusted}
# =============================================================================
# Direct accessors
# =============================================================================
[docs]
def fit_mse(y, y_predicted):
"""Compute Mean Square Error (MSE)."""
return fit_error(y, y_predicted)["MSE"]
[docs]
def fit_rmse(y, y_predicted):
"""Compute Root Mean Square Error (RMSE)."""
return fit_error(y, y_predicted)["RMSE"]
[docs]
def fit_r2(y, y_predicted, adjusted=True, n_parameters=2):
"""Compute R2."""
if adjusted is True:
return fit_error(y, y_predicted, n_parameters=n_parameters)["R2_adjusted"]
return fit_error(y, y_predicted, n_parameters=n_parameters)["R2"]
# =============================================================================
# Internals
# =============================================================================
def _fit_error_prepare(y, y_predicted, n_parameters=2):
# n, i.e., how many observations (signal length)
n = len(y)
# Sanitize
if n != len(y_predicted):
raise TypeError("NeuroKit error: fit_error(): 'y' and 'y_predicted' are not of the same length.")
# Residual, i.e. the difference between data and model
residual = y - y_predicted
# Degrees of freedom, i.e., number of observations (length of signal) minus number of parameters
df = n - n_parameters
# Calculate sum of squared errors
SSE = np.sum(residual ** 2)
return SSE, n, df
