statsmodels.regression.mixed_linear_model.MixedLM.Estep¶

MixedLM.Estep(fe_params, cov_re, scale)[source]¶

The E-step of the EM algorithm.

This is for ML (not REML), but it seems to be good enough to use for REML starting values.

Parameters:

fe_params : 1d ndarray

The current value of the fixed effect coefficients

cov_re : 2d ndarray

The current value of the covariance matrix of random effects

scale : positive scalar

The current value of the error variance

Returns:

m1x : 1d ndarray

sum_groups $X'*Z*E[gamma | Y]$ , where X and Z are the fixed and random effects covariates, gamma is the random effects, and Y is the observed data

m1y : scalar

sum_groups $Y'*E[gamma | Y]$

m2 : 2d ndarray

sum_groups $E[gamma * gamma' | Y]$

m2xx : 2d ndarray

sum_groups $Z'*Z * E[gamma * gamma' | Y]$