statsmodels.regression.process_regression.ProcessMLE

class statsmodels.regression.process_regression.ProcessMLE(endog, exog, exog_scale, exog_smooth, exog_noise, time, groups, cov=None, **kwargs)

Fit a Gaussian mean/variance regression model

This class fits a one-dimensional Gaussian process model with parametrized mean and covariance structures to grouped data. For each group, there is an independent realization of a latent Gaussian process indexed by an observed real-valued time variable. The data consist of the Gaussian process observed at a finite number of time values.

The process mean and variance can be linked to covariates. The mean structure is linear in the covariates. The covariance structure is non-stationary, and is defined parametrically through ‘scaling’, and ‘smoothing’ parameters. The covariance of the process between two observations in the same group is a function of the distance between the time values of the two observations. The scaling and smoothing parameters can be linked to covariates.

The observed data are modeled as the sum of the Gaussian process realization and (optionally) independent white noise. The standard deviation of the white noise can be linked to covariates.

The data should be provided in ‘long form’, with a group label to indicate which observations belong to the same group. Observations in different groups are always independent.

Parameters:

endogarray_like

The dependent variable.

exogarray_like

The design matrix for the mean structure

exog_scalearray_like

The design matrix for the scaling structure

exog_smootharray_like

The design matrix for the smoothness structure

exog_noisearray_like

The design matrix for the additive white noise. The linear predictor is the log of the white noise standard deviation. If None, there is no additive noise (the process is observed directly).

timearray_like (1-dimensional)

The univariate index values, used to calculate distances between observations in the same group, which determines their correlations.

groupsarray_like (1-dimensional)

The group values.

cova ProcessCovariance instance

Defaults to GaussianCovariance.

**kwargs

Additional keyword arguments passed to the model constructor.

Attributes:

endog_names

Names of endogenous variables

exog_names

Names of exogenous variables

Methods

covariance(time, scale_params, ...)	Returns a Gaussian process covariance matrix
fit([start_params, method, maxiter])	Fit a grouped Gaussian process regression using MLE
from_formula(formula, data[, subset, drop_cols])	Create a Model from a formula and dataframe
hessian(params)	The Hessian matrix of the model
information(params)	Fisher information matrix of model
initialize()	Initialize (possibly re-initialize) a Model instance
loglike(params)	Calculate the log-likelihood function for the model
predict(params[, exog])	Obtain predictions of the mean structure
score(params)	Calculate the score function for the model
unpack(z)	Split the packed parameter vector into blocks

Methods

covariance(time, scale_params, ...)	Returns a Gaussian process covariance matrix
fit([start_params, method, maxiter])	Fit a grouped Gaussian process regression using MLE
from_formula(formula, data[, subset, drop_cols])	Create a Model from a formula and dataframe
hessian(params)	The Hessian matrix of the model
information(params)	Fisher information matrix of model
initialize()	Initialize (possibly re-initialize) a Model instance
loglike(params)	Calculate the log-likelihood function for the model
predict(params[, exog])	Obtain predictions of the mean structure
score(params)	Calculate the score function for the model
unpack(z)	Split the packed parameter vector into blocks

Properties

endog_names	Names of endogenous variables
exog_names	Names of exogenous variables