python pass pandas dataframe, parameters, and functions to scipy.optimize.minimize

I am trying to use SciPy's scipy.optimize.minimize function to minimize a function I have created. However, the function I am trying to optimize over is itself constructed from other functions which perform calculations based on a pandas DataFrame.

I understand that SciPy's minimize function can input multiple arguments via a tuple (e.g., Structure of inputs to scipy minimize function). However, I do not know how to pass in a function which relies on a pandas DataFrame.

I have created a reproducible example below.

import pandas as pd
import numpy as np
from scipy.stats import norm
from scipy.optimize import minimize


####################     Data     ####################
# Initialize dataframe. 
data = pd.DataFrame({'id_i': ['AA', 'BB', 'CC', 'XX', 'DD'], 
                     'id_j': ['ZZ', 'YY', 'XX', 'BB', 'AA'], 
                     'y': [0.30, 0.60, 0.70, 0.45, 0.65], 
                     'num': [1000, 2000, 1500, 1200, 1700], 
                     'bar': [-4.0, -6.5, 1.0, -3.0, -5.5], 
                     'mu': [-4.261140, -5.929608, 1.546283, -1.810941, -3.186412]})

data['foo_1'] = data['bar'] - 11 * norm.ppf(1/1.9)
data['foo_2'] = data['bar'] - 11 * norm.ppf(1 - (1/1.9))

# Store list of ids.
id_list = sorted(pd.unique(pd.concat([data['id_i'], data['id_j']], axis=0)))


####################     Functions     ####################
# Function 1: Intermediate calculation to calculate predicted values.
def calculate_y_pred(row, delta_params, sigma_param, id_list):

    # Extract the relevant values from delta_params.
    delta_i = delta_params[id_list.index(row['id_i'])]
    delta_j = delta_params[id_list.index(row['id_j'])]

    # Calculate adjusted version of mu. 
    mu_adj = row['mu'] - delta_i + delta_j

    # Calculate predicted value of y.
    y_pred = norm.cdf(row['foo_1'], loc=mu_adj, scale=sigma_param) / \
                (norm.cdf(row['foo_1'], loc=mu_adj, scale=sigma_param) + 
                    (1 - norm.cdf(row['foo_2'], loc=mu_adj, scale=sigma_param)))

    return y_pred

# Function to calculate the log-likelihood (for a row of DataFrame data).
def loglik_row(row, delta_params, sigma_param, id_list):

    # Calculate the log-likelihood for this row.
    y_pred = calculate_y_pred(row, delta_params, sigma_param, id_list)
    y_obs = row['y']
    n = row['num']
    loglik_row = np.log(norm.pdf(((y_obs - y_pred) * np.sqrt(n)) / np.sqrt(y_pred * (1-y_pred))) / 
                            np.sqrt(y_pred * (1-y_pred) / n))

    return loglik_row

# Function to calculate the sum of the negative log-likelihood. 
# This function is called via SciPy's minimize function.
def loglik_total(data, id_list, params):

    # Extract parameters.
    delta_params = list(params[0:len(id_list)])
    sigma_param = init_params[-1]

    # Calculate the negative log-likelihood for every row in data and sum the values.
    loglik_total = -np.sum( data.apply(lambda row: loglik_row(row, delta_params, sigma_param, id_list), axis=1) )

    return loglik_total


####################     Optimize     ####################
# Provide initial parameter guesses. 
delta_params = [0 for id in id_list]
sigma_param = 11
init_params = tuple(delta_params + [sigma_param])

# Maximize the log likelihood (minimize the negative log likelihood). 
minimize(fun=loglik_total, x0=init_params, 
            args=(data, id_list), method='nelder-mead')

This results in the following error: AttributeError: 'numpy.ndarray' object has no attribute 'apply' (the entire error output is below). I believe this error is because minimize is treating X as a numpy array, whereas I would like to pass it as a pandas DataFrame.

AttributeError: 'numpy.ndarray' object has no attribute 'apply'
AttributeErrorTraceback (most recent call last)
<ipython-input-93-9a5866bd626e> in <module>()
      1 minimize(fun=loglik_total, x0=init_params, 
----> 2             args=(data, id_list), method='nelder-mead')
/Users/adam/anaconda/lib/python2.7/site-packages/scipy/optimize/_minimize.pyc in minimize(fun, x0, args, method, jac, hess, hessp, bounds, constraints, tol, callback, options)
    436                       callback=callback, **options)
    437     elif meth == 'nelder-mead':
--> 438         return _minimize_neldermead(fun, x0, args, callback, **options)
    439     elif meth == 'powell':
    440         return _minimize_powell(fun, x0, args, callback, **options)
/Users/adam/anaconda/lib/python2.7/site-packages/scipy/optimize/optimize.pyc in _minimize_neldermead(func, x0, args, callback, maxiter, maxfev, disp, return_all, initial_simplex, xatol, fatol, **unknown_options)
    515 
    516     for k in range(N + 1):
--> 517         fsim[k] = func(sim[k])
    518 
    519     ind = numpy.argsort(fsim)
/Users/adam/anaconda/lib/python2.7/site-packages/scipy/optimize/optimize.pyc in function_wrapper(*wrapper_args)
    290     def function_wrapper(*wrapper_args):
    291         ncalls[0] += 1
--> 292         return function(*(wrapper_args + args))
    293 
    294     return ncalls, function_wrapper
<ipython-input-69-546e169fc54e> in loglik_total(data, id_list, params)
      6 
      7     # Calculate the negative log-likelihood for every row in data and sum the values.
----> 8     loglik_total = -np.sum( data.apply(lambda row: loglik_row(row, delta_params, sigma_param, id_list), axis=1) )
      9 
     10     return loglik_total
AttributeError: 'numpy.ndarray' object has no attribute 'apply'

What would be the proper way to handle the DataFrame data and call my function loglik_total within SciPy's minimize function? Any suggestions are welcome and would be appreciated.

Possible Solution: Note, I have considered that I could edit my functions to treat data as a numpy array rather than a pandas DataFrame. However, I would like to avoid this if possible for a couple reasons: 1) in loglik_total, I use pandas' apply function to apply the loglik_row function to every row of data; 2) it is convenient to refer to columns of data by their column names rather than numerical indices.