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249 | def luce_choice_ratio(
name="Luce-Choice-Ratio",
resolution=8,
maximum_similarity=10,
focus=0.8,
):
"""
Luce-Choice-Ratio
Args:
name: name of the experiment
added_noise: standard deviation of normally distributed noise added to y-values
resolution: number of allowed values for stimulus DVs
maximum_similarity: upperbound for DVs
focus: parameter measuring participant focus
random_state: integer used to seed the random number generator
Shepard-Luce Choice Rule according to:
- Equation (4) in Logan, G. D., & Gordon, R. D. (2001).
- and in Executive control of visual attention in dual-task situations.
Psychological review, 108(2), 393.
- Equation (5) in Luce, R. D. (1963). Detection and recognition.
Examples:
We can instantiate a Shepard-Cue Choice Experiment. We use a seed to get replicable results:
>>> l_s_experiment = luce_choice_ratio()
We can look at the name of the experiment:
>>> l_s_experiment.name
'Luce-Choice-Ratio'
To call the ground truth, we can use an attribute of the experiment:
>>> l_s_experiment.ground_truth(np.array([[1,2,3,4]]))
similarity_category_A1 ... choose_A1
0 1 ... 0.210526
<BLANKLINE>
[1 rows x 5 columns]
We can also run an experiment:
>>> l_s_experiment.run(np.array([[1,2,3,4]]), random_state=42)
similarity_category_A1 ... choose_A1
0 1 ... 0.211328
<BLANKLINE>
[1 rows x 5 columns]
To plot the experiment use:
>>> l_s_experiment.plotter()
>>> plt.show() # doctest: +SKIP
"""
minimum_similarity = 1 / maximum_similarity
params = dict(
name=name,
maximum_similarity=maximum_similarity,
minimum_similarity=minimum_similarity,
resolution=resolution,
focus=focus,
)
similarity_category_A1 = IV(
name="similarity_category_A1",
allowed_values=np.linspace(minimum_similarity, maximum_similarity, resolution),
value_range=(minimum_similarity, maximum_similarity),
units="similarity",
variable_label="Similarity with Category A1",
type=ValueType.REAL,
)
similarity_category_A2 = IV(
name="similarity_category_A2",
allowed_values=np.linspace(minimum_similarity, maximum_similarity, resolution),
value_range=(minimum_similarity, maximum_similarity),
units="similarity",
variable_label="Similarity with Category A2",
type=ValueType.REAL,
)
similarity_category_B1 = IV(
name="similarity_category_B1",
allowed_values=np.linspace(minimum_similarity, maximum_similarity, resolution),
value_range=(minimum_similarity, maximum_similarity),
units="similarity",
variable_label="Similarity with Category B1",
type=ValueType.REAL,
)
similarity_category_B2 = IV(
name="similarity_category_B2",
allowed_values=np.linspace(minimum_similarity, maximum_similarity, resolution),
value_range=(minimum_similarity, maximum_similarity),
units="similarity",
variable_label="Similarity with Category B2",
type=ValueType.REAL,
)
choose_A1 = DV(
name="choose_A1",
value_range=(0, 1),
units="probability",
variable_label="Probability of Choosing A1",
type=ValueType.PROBABILITY,
)
variables = VariableCollection(
independent_variables=[
similarity_category_A1,
similarity_category_A2,
similarity_category_B1,
similarity_category_B2,
],
dependent_variables=[choose_A1],
)
def run(
conditions: Union[pd.DataFrame, np.ndarray, np.recarray],
focus_: float = focus,
added_noise=0.01,
random_state: Optional[int] = None,
):
rng = np.random.default_rng(random_state)
X = np.array(conditions)
Y = np.zeros((X.shape[0], 1))
for idx, x in enumerate(X):
similarity_A1 = x[0]
similarity_A2 = x[1]
similarity_B1 = x[2]
similarity_B2 = x[3]
y = (similarity_A1 * focus + rng.normal(0, added_noise)) / (
similarity_A1 * focus
+ similarity_A2 * focus
+ similarity_B1 * (1 - focus_)
+ similarity_B2 * (1 - focus_)
)
# probability can't be negative or larger than 1 (the noise can make it so)
if y <= 0:
y = 0.0001
elif y >= 1:
y = 0.9999
Y[idx] = y
experiment_data = pd.DataFrame(conditions)
experiment_data.columns = [v.name for v in variables.independent_variables]
experiment_data[choose_A1.name] = Y
return experiment_data
ground_truth = partial(run, added_noise=0.0)
def domain():
similarity_A1 = variables.independent_variables[0].allowed_values
similarity_A2 = variables.independent_variables[1].allowed_values
similarity_B1 = variables.independent_variables[2].allowed_values
similarity_B2 = variables.independent_variables[3].allowed_values
X = np.array(
np.meshgrid(
similarity_A1,
similarity_A2,
similarity_B1,
similarity_B2,
)
).T.reshape(-1, 4)
# remove all conditions from X where the focus is 0 and the similarity of A1 is 0
# or the similarity of A2 is 0
X = X[~((X[:, 0] == 0) & (X[:, 1] == 0) & (X[:, 2] == 0) & (X[:, 3] == 0))]
return X
def plotter(
model=None,
):
import matplotlib.colors as mcolors
import matplotlib.pyplot as plt
similarity_A1 = np.linspace(
variables.independent_variables[0].value_range[0],
variables.independent_variables[0].value_range[1],
100,
)
similarity_A2 = 0.5 # 1 - similarity_A1
similarity_B1_list = [0.5, 0.75, 1]
similarity_B2 = 0
colors = mcolors.TABLEAU_COLORS
col_keys = list(colors.keys())
for idx, similarity_B1 in enumerate(similarity_B1_list):
# similarity_B2 = 1 - similarity_B1
X = np.zeros((len(similarity_A1), 4))
X[:, 0] = similarity_A1
X[:, 1] = similarity_A2
X[:, 2] = similarity_B1
X[:, 3] = similarity_B2
y = ground_truth(X)
plt.plot(
similarity_A1.reshape((len(similarity_A1), 1)),
y,
label=f"Similarity to B1 = {similarity_B1} (Original)",
c=colors[col_keys[idx]],
)
if model is not None:
y = model.predict(X)
plt.plot(
similarity_A1,
y,
label=f"Similarity to B1 = {similarity_B1} (Recovered)",
c=colors[col_keys[idx]],
linestyle="--",
)
x_limit = [np.min(similarity_A1), np.max(similarity_A1)]
y_limit = [0, 1]
x_label = "Similarity to Category A1"
y_label = "Probability of Selecting Category A1"
plt.xlim(x_limit)
plt.ylim(y_limit)
plt.xlabel(x_label, fontsize="large")
plt.ylabel(y_label, fontsize="large")
plt.legend(loc=4, fontsize="medium")
plt.title("Shepard-Luce Choice Ratio", fontsize="x-large")
collection = SyntheticExperimentCollection(
name=name,
description=luce_choice_ratio.__doc__,
variables=variables,
run=run,
ground_truth=ground_truth,
domain=domain,
plotter=plotter,
params=params,
factory_function=luce_choice_ratio,
)
return collection
|