statsmodels.regression.process_regression.ProcessMLE¶
- class statsmodels.regression.process_regression.ProcessMLE(endog, exog, exog_scale, exog_smooth, exog_noise, time, groups, cov=None, **kwargs)[source]¶
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 lined 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.
- cov
a
ProcessCovariance
instance
Defaults to GaussianCovariance.
- 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])hessian
(params)The Hessian matrix of the model.
information
(params)Fisher information matrix of model.
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
Names of endogenous variables.
Names of exogenous variables.