def test_adaptive_test(self):
random.seed(123)
np.random.seed(123)
theta_estimate = 0
actual_theta = [0, 1]
items = simulate_items(difficulty={
'mean': 0,
'sd': 1
},
discrimination={
'mean': 1,
'sd': .05
},
guessing=None,
item_count=500)
probabilities, response_vector = item_vectors(items=items,
abilities=actual_theta)
temp = []
for row in response_vector.iterrows():
index, data = row
temp.append(data.tolist())
items['correct'] = temp[0]
items_taken = []
response_list = []
items = pd.DataFrame(items)
# simulate exam
for i in range(0, 40):
remaining = items_remaining(items, items_taken)
remaining_items, next_item = select_next_item(
remaining, theta_estimate)
item = remaining_items.loc[next_item]
a = np.array(item['a'])
b = np.array(item['b'])
current_probabilities = _p_2pl(a, theta_estimate, b)
rand_num = random.uniform(0, 1)
if current_probabilities >= rand_num:
response_list.append(1)
else:
response_list.append(0)
items_taken.append(next_item)
new_dataframe = pd.DataFrame(
list(zip(items_taken, response_list)),
columns=['new_index',
'corrects']).set_index('new_index',
drop=True).sort_index()
del new_dataframe.index.name
taken_items = new_dataframe.join(items)
max_prob, theta_estimate = L(np.array(taken_items['correct']),
np.array(taken_items['a']),
np.array(taken_items['b']))
self.assertEqual(theta_estimate, -0.84000000000006736)
def test_CTT_methods(self):
random.seed(123)
np.random.seed(123)
items = simulate_items()
people = simulate_people(100, {'mean': 0, 'sd': 1})
prob_vector, response_vector = item_vectors(items, people)
alphas = calculate_alpha(response_vector)
p_values = get_p_values(response_vector)
discrim, discrim2 = discrimination_index(response_vector)
examinee_scores = examinee_score(response_vector)
self.assertEqual(alphas, 0.894933894194553)
self.assertEqual(p_values.iloc[0, 0], 0.67)
self.assertEqual(discrim[0], 0.4401980052948809)
self.assertEqual(examinee_scores[0], 15)
def test_response_vector(self):
np.random.seed(123)
random.seed(123)
thetas = [0, 1]
items = simulate_items(difficulty={
'mean': 0,
'sd': 1
},
discrimination={
'mean': 1,
'sd': .05
},
guessing=None,
item_count=3)
expected = pd.DataFrame(data={0: [1, 1], 1: [1, 0], 2: [1, 1]})
probabilities, response_vector = item_vectors(items=items,
abilities=thetas)
self.assertEqual(response_vector[0].tolist(), expected[0].tolist())
df1 = df1.reset_index()
df2 = items.drop(df1.index)
df1.drop(['index'], axis=1)
df1 = examinee_score(df1)
df2 = examinee_score(df2)
reliability = pearsonr(df1, df2)
else:
print("error, please select a valid split")
return reliability
def calculate_sem(items, reliability=None):
if reliability == None:
reliability = calculate_alpha(items)
total_scores = examinee_score(items)
std = np.array(total_scores)
std = np.std(std)
return std * math.sqrt(1 - reliability)
items = simulate_items()
people = simulate_people(100, {'mean': 0, 'sd': 1})
prob_vector, response_vector = item_vectors(items, people)
print(calculate_sem(response_vector))
#todo Calculate SEM using IRT item stats
initial_scores = examinee_score(subsequent_data)
subsequent_scores = examinee_score(subsequent_data) + score_difference
print(test1_info, test2_info)
equating_dict = {
'initial_scores': initial_scores,
'mean_equated_scores': subsequent_scores,
'mean_sd_equated_scores': None
}
equating_df = pd.DataFrame(equating_dict)
if sd_equating == True:
sd_division = test1_info['score_sd'] / test2_info['score_sd']
equating_df['mean_sd_equated_scores'] = (
sd_division) * equating_df['initial_scores'] + (
test1_info['average_score'] -
sd_division * test2_info['average_score'])
equating_dict = equating_df.to_dict()
return equating_dict
items1 = simulate_items()
items2 = simulate_items(difficulty={'mean': 1, 'sd': 1})
people = simulate_people(100, {'mean': 0, 'sd': 1})
prob_vector1, response_vector1 = item_vectors(items1, people)
prob_vector2, response_vector2 = item_vectors(items2, people)
examinee_scores1 = examinee_score(response_vector1)
examinee_scores2 = examinee_score(response_vector2)
print(mean_equating(response_vector1, response_vector2, sd_equating=True))