def _starting_variance_components(self, kind='equal'):
"""
Starting variance components in optimization.
Valid values:
'minque0': Starting values are those from MINQUE with all weights
set equal to 0 except for the residual variance, which is set
to 1. This is the default method used by SAS's PROC MIXED.
'minque1': Starting values are those from MINQUE with all weights
set equal to 1
'ols': Starting values are all 0 except residual, which is
var(y - X*Beta)
'EM': the starting values are the variance components after
100 iterations of expectation-maximization REML (started from all
equal values).
'equal': Chooses all variance components (including residual)
to be equal.
"""
if kind.lower() == 'minque0':
return minque(self, value=0, return_after=1, return_vcs=True)
if kind.lower() == 'minque1':
return minque(self, value=1, return_after=1, return_vcs=True)
if kind.lower() == 'minquemean':
zero = minque(self, value=0, return_after=1, return_vcs=True)
one = minque(self, value=1, return_after=1, return_vcs=True)
return (zero + one) / 2.0
if kind.lower() == 'ols':
vcs_start = np.zeros(len(self.random_effects))
vcs_start[-1] = self._variance_after_fixefs()
return vcs_start
if kind.lower() == 'equal':
v = self._variance_after_fixefs()
n = len(self.random_effects)
vcs_start = [v/float(n)] * n
return vcs_start
if kind.lower() == 'em':
starts = self._starting_variance_components('equal')
vcs_start = expectation_maximization(self,
starts=starts,
return_after=100)
return vcs_start.parameters
else:
raise ValueError('Unknown method: {}'.format(kind))
def maximize(self, method="Average Information", restricted=False,
starts=None, verbose=False):
"""
Finds the optimal values for variance components of the model by
restricted maximum likelihood estimation.
"""
if (isinstance(self.mle, MLEResult) and
self.maximized.method == method):
return
self.fit_model()
if starts is None:
starts = self._starting_variance_components()
likefunc = REML if restricted else ML
llik = likefunc(self, info=method)
llik.set_parameters(starts)
if method.lower().startswith('minque'):
mle = minque(self, value=0, verbose=verbose, starts=starts)
elif method.lower() in {'em', 'emreml', 'expectation-maximization'}:
mle = expectation_maximization(self, llik, verbose=verbose)
elif method.lower() == 'grid':
mle = grid_search(self, llik, nevals=20, oob=False)
else:
mle = newtonlike_maximization(self, llik, verbose=verbose)
self.mle = mle
self.set_variance_components(mle.parameters)
self.fit_model()
# Get the full loglikelihood at the REML maximimum so we
# can use it later
self.mle.full_loglikelihood = full_loglikelihood(self.y, self.V,
self.X, self.beta)
