leaspy.models.lme

Classes

LMEModel

LMEModel is a benchmark model that fits and personalize a linear mixed-effects model.

Module Contents

class LMEModel(name, **kwargs)

Bases: leaspy.models.generic.GenericModel

LMEModel is a benchmark model that fits and personalize a linear mixed-effects model.

The model specification is the following:

\[y_{ij} = fixed_{intercept} + random_{intercept_i} + (fixed_{slopeAge} + random_{slopeAge_i}) * age_{ij} + \epsilon_{ij}\]

with:

• \(y_{ij}\): value of the feature of the i-th subject at his j-th visit,

• \(age_{ij}\): age of the i-th subject at his j-th visit.

• \(\epsilon_{ij}\): residual Gaussian noise (independent between visits)

Warning

This model must be fitted on one feature only (univariate model).

TODO? should inherit from AbstractModel. TODO? add some covariates in this very simple model.

Parameters:

namestr

The model’s name.

**kwargs

Model hyperparameters:

• with_random_slope_age : bool (default True).

Attributes:

namestr

The model’s name.

is_initializedbool

True if the model is initialized, False otherwise.

with_random_slope_agebool (default True)

Has the LME a random slope for subject’s age? Otherwise it only has a random intercept per subject.

featureslist of str

List of the model features.

Warning

LME has only one feature.

dimensionint

Will always be 1 (univariate).

parametersdict

Contains the model parameters. In particular:

• ages_meanfloat

  Mean of ages (for normalization).

• ages_stdfloat

  Std-dev of ages (for normalization).

• fe_paramsnp.ndarray of float

  Fixed effects.

• cov_renp.ndarray

  Variance-covariance matrix of random-effects.

• cov_re_unscaled_invnp.ndarray

  Inverse of unscaled (= divided by variance of noise) variance-covariance matrix of random-effects. This matrix is used for personalization to new subjects.

• noise_stdfloat

  Std-dev of Gaussian noise.

• bse_fe, bse_renp.ndarray of float

  Standard errors on fixed-effects and random-effects respectively (not used in Leaspy).

Parameters:

name (str)

See also

LMEFitAlgorithm

LMEPersonalizeAlgorithm

dimension = 1

The dimension of the model. If the private attribute is defined, then it takes precedence over the feature length. The associated setters are responsible for their coherence.

compute_individual_trajectory(timepoints, individual_parameters)

Compute scores values at the given time-point(s) given a subject’s individual parameters.

Parameters:

timepointsarray-like of ages (not normalized)

Timepoints to compute individual trajectory at.

individual_parametersdict

Individual parameters:

• random_intercept

• random_slope_age (if with_random_slope_age == True)

Returns:

torch.Tensor of float

The individual trajectories. The shape of the tensor is (n_individuals == 1, n_tpts == len(timepoints), n_features == 1).

Parameters:

individual_parameters (dict)