number of alternatives number of variables)
and an object upc_sequence as arguments. It uses the classes
Probabilities and Utilities contained in upc_sequence
for the maximum likelihood estimation. This assures that if
bhhh_mnl_estimation is plugged into the estimate() method of
ChoiceModel (Section 7.5.3), the model will be
estimated by using the same code for computing utilities and probabilities as
the run() method. The third argument of the run() method of
this class is of type Resources and must contain an entry
selected_choice which is a 0-1 matrix of size number of observations
number of alternatives. For each agent, it contains a 1 on a position
of the chosen alternative, otherwise 0s. Note that ChoiceModel
prepares and passes this matrix automatically.
estimate_linear_regression performs a parameters estimation via the
least squares method. It gets a data array (of size number of observations
number of variables), an instance of class Regression (not
used in this module) and an object Resources as arguments. The last
argument must contain an entry outcome which is a 1-d array of an outcome
for each observation. This class can be plugged into the
RegressionModel which takes care of all arguments.
The estimation modules return a dictionary, with entries estimators and
standard_errors. These contain arrays of estimated coefficients and their
standard errors, respectively. An entry other_measures is a dictionary
which should contain additional measures of the estimates, i.e. their values
should be arrays of the same size as estimators. The two estimation modules
in opus_core return here one entry, namely the t_statistic. The last entry in
the dictionary returned by the modules, other_info, is a dictionary
containing additional information about the estimation. Its values don't
follow any restriction on type and size. Thus, these can be also single values,
such as likelihood ratio test statistics, degrees of freedom, 
etc.