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:

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 $X'ZE[gamma \| Y]$ , 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 $Z'Z E[gamma * gamma' \| Y]$

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