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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:

def add(self, fixed=None, random=None, priors=None, family='gaussian',
            link=None, categorical=None, append=True):
        '''Adds one or more terms to the model via an R-like formula syntax.

        Args:
            fixed (str): Optional formula specification of fixed effects.
            random (list): Optional list-based specification of random effects.
            priors (dict): Optional specification of priors for one or more
                terms. A dict where the keys are the names of terms in the
                model, and the values are either instances of class Prior or
                ints, floats, or strings that specify the width of the priors
                on a standardized scale.
            family (str, Family): A specification of the model family
                (analogous to the family object in R). Either a string, or an
                instance of class priors.Family. If a string is passed, a
                family with the corresponding name must be defined in the
                defaults loaded at Model initialization. Valid pre-defined
                families are 'gaussian', 'bernoulli', 'poisson', and 't'.
            link (str): The model link function to use. Can be either a string
                (must be one of the options defined in the current backend;
                typically this will include at least 'identity', 'logit',
                'inverse', and 'log'), or a callable that takes a 1D ndarray
                or theano tensor as the sole argument and returns one with
                the same shape.
            categorical (str, list): The names of any variables to treat as
                categorical. Can be either a single variable name, or a list
                of names. If categorical is None, the data type of the columns
                in the DataFrame will be used to infer handling. In cases where
                numeric columns are to be treated as categoricals (e.g., random
                factors coded as numerical IDs), explicitly passing variable
                names via this argument is recommended.
            append (bool): If True, terms are appended to the existing model
                rather than replacing any existing terms. This allows
                formula-based specification of the model in stages.
        '''

        data = self.data

        # Primitive values (floats, strs) can be overwritten with Prior objects
        # so we need to make sure to copy first to avoid bad things happening
        # if user is re-using same prior dict in multiple models.
        if priors is None:
            priors = {}
        else:
            priors = deepcopy(priors)

        if not append:
            self.reset()

        # Explicitly convert columns to category if desired--though this
        # can also be done within the formula using C().
        if categorical is not None:
            data = data.copy()
            cats = listify(categorical)
            data[cats] = data[cats].apply(lambda x: x.astype('category'))

        # Custom patsy.missing.NAAction class. Similar to patsy drop/raise
        # defaults, but changes the raised message and logs any dropped rows
        NA_handler = Custom_NA(dropna=self.dropna)

        # screen fixed terms
        if fixed is not None:
            if '~' in fixed:
                clean_fix = re.sub(r'\[.+\]', '', fixed)
                dmatrices(clean_fix, data=data, NA_action=NA_handler)
            else:
                dmatrix(fixed, data=data, NA_action=NA_handler)

        # screen random terms
        if random is not None:
            for term in listify(random):
                for side in term.split('|'):
                    dmatrix(side, data=data, NA_action=NA_handler)

        # update the running list of complete cases
        if len(NA_handler.completes):
            self.completes.append(NA_handler.completes)

        # save arguments to pass to _add()
        args = dict(zip(
            ['fixed', 'random', 'priors', 'family', 'link', 'categorical'],
            [fixed, random, priors, family, link, categorical]))
        self.added_terms.append(args)

        self.built = False