Linear Mixed Model¶
In [1]:
Copied!
# Uncomment the following line when running on Google Colab
# !pip install "autora"
# Uncomment the following line when running on Google Colab
# !pip install "autora"
The linear mixed model experiment has to be initialized with a specific formula and effects.
In [2]:
Copied!
import numpy as np
from autora.experiment_runner.synthetic.abstract.lmm import lmm_experiment
# Formula
formula = 'rt ~ 1 + x1'
# Initialize effects:
fixed_effects = {'Intercept': 0., 'x1': 2.}
s = lmm_experiment(formula=formula, fixed_effects=fixed_effects)
import numpy as np
from autora.experiment_runner.synthetic.abstract.lmm import lmm_experiment
# Formula
formula = 'rt ~ 1 + x1'
# Initialize effects:
fixed_effects = {'Intercept': 0., 'x1': 2.}
s = lmm_experiment(formula=formula, fixed_effects=fixed_effects)
Check the docstring to get information about the model
In [3]:
Copied!
help(lmm_experiment)
help(lmm_experiment)
Help on function lmm_experiment in module autora.experiment_runner.synthetic.abstract.lmm:
lmm_experiment(formula: str, fixed_effects: Optional[dict] = None, random_effects: Optional[dict] = None, X: Optional[Sequence[autora.variable.IV]] = None, random_state: Optional[int] = None, name: str = 'Linear Mixed Model Experiment')
A linear mixed model synthetic experiments.
Parameters:
name: name of the experiment
formula: formula of the linear mixed model (similar to lmer package in R)
fixed_effects: dictionary describing the fixed effects (Intercept and slopes)
random_effects: nested dictionary describing the random effects of slopes and intercept.
These are standard deviasions in a normal distribution with a mean of zero.
X: Independent variable descriptions. Used to add allowed values
... or use the describe function:
In [4]:
Copied!
from autora.experiment_runner.synthetic.utilities import describe
print(describe(s))
from autora.experiment_runner.synthetic.utilities import describe
print(describe(s))
A linear mixed model synthetic experiments.
Parameters:
name: name of the experiment
formula: formula of the linear mixed model (similar to lmer package in R)
fixed_effects: dictionary describing the fixed effects (Intercept and slopes)
random_effects: nested dictionary describing the random effects of slopes and intercept.
These are standard deviasions in a normal distribution with a mean of zero.
X: Independent variable descriptions. Used to add allowed values
The synthetic experiement s has properties like the name of the experiment:
In [5]:
Copied!
s.name
s.name
Out[5]:
'Linear Mixed Model Experiment'
... a valid variables description:
In [6]:
Copied!
s.variables
s.variables
Out[6]:
VariableCollection(independent_variables=[IV(name='x1', value_range=None, allowed_values=None, units='', type=<ValueType.REAL: 'real'>, variable_label='Independent Variable', rescale=1, is_covariate=False)], dependent_variables=[DV(name='rt', value_range=None, allowed_values=None, units='', type=<ValueType.REAL: 'real'>, variable_label='Dependent Variable', rescale=1, is_covariate=False)], covariates=[])
... this variable description depends on the formula:
In [7]:
Copied!
formula = 'probability ~ 1 + intensity'
# Initialize effects:
fixed_effects = {'Intercept': 0., 'intensity': 2.}
s = lmm_experiment(formula=formula, fixed_effects=fixed_effects)
s.variables
formula = 'probability ~ 1 + intensity'
# Initialize effects:
fixed_effects = {'Intercept': 0., 'intensity': 2.}
s = lmm_experiment(formula=formula, fixed_effects=fixed_effects)
s.variables
Out[7]:
VariableCollection(independent_variables=[IV(name='intensity', value_range=None, allowed_values=None, units='', type=<ValueType.REAL: 'real'>, variable_label='Independent Variable', rescale=1, is_covariate=False)], dependent_variables=[DV(name='probability', value_range=None, allowed_values=None, units='', type=<ValueType.REAL: 'real'>, variable_label='Dependent Variable', rescale=1, is_covariate=False)], covariates=[])
Since we did set the variables via a formula, there is no domain:
In [8]:
Copied!
s.domain()
s.domain()
--------------------------------------------------------------------------- AttributeError Traceback (most recent call last) Cell In[8], line 1 ----> 1 s.domain() File ~/Documents/GitHub/AutoRA/autora-synthetic/src/autora/experiment_runner/synthetic/abstract/lmm.py:300, in lmm_experiment.<locals>.domain() 298 def domain(): 299 """A function which returns all possible independent variable values as a 2D array.""" --> 300 x = variables.independent_variables[0].allowed_values.reshape(-1, 1) 301 return x AttributeError: 'NoneType' object has no attribute 'reshape'
We can set the variables manually in the init function:
In [9]:
Copied!
from autora.variable import IV
formula = 'rt ~ 1 + x1'
# Initialize effects:
fixed_effects = {'Intercept': 0., 'x1': 2.}
independent_variables = [IV(name='x1', allowed_values=np.linspace(0, 10, 11), value_range=(0, 100))]
#
s = lmm_experiment(formula=formula, fixed_effects=fixed_effects, X=independent_variables)
from autora.variable import IV
formula = 'rt ~ 1 + x1'
# Initialize effects:
fixed_effects = {'Intercept': 0., 'x1': 2.}
independent_variables = [IV(name='x1', allowed_values=np.linspace(0, 10, 11), value_range=(0, 100))]
#
s = lmm_experiment(formula=formula, fixed_effects=fixed_effects, X=independent_variables)
... the given variable names have to match the formula:
In [10]:
Copied!
from autora.variable import IV
formula_ = 'rt ~ 1 + x1'
# Initialize effects:
fixed_effects_ = {'Intercept': 0., 'x1': 2.}
independent_variables_ = [IV(name='x', allowed_values=np.linspace(0, 10, 11), value_range=(0, 100))]
#
s_ = lmm_experiment(formula=formula, fixed_effects=fixed_effects, X=independent_variables)
from autora.variable import IV
formula_ = 'rt ~ 1 + x1'
# Initialize effects:
fixed_effects_ = {'Intercept': 0., 'x1': 2.}
independent_variables_ = [IV(name='x', allowed_values=np.linspace(0, 10, 11), value_range=(0, 100))]
#
s_ = lmm_experiment(formula=formula, fixed_effects=fixed_effects, X=independent_variables)
... now we can generate the full domain of the data
In [11]:
Copied!
x = s.domain()
x
x = s.domain()
x
Out[11]:
array([[ 0.],
[ 1.],
[ 2.],
[ 3.],
[ 4.],
[ 5.],
[ 6.],
[ 7.],
[ 8.],
[ 9.],
[10.]])
... the experiment_runner which can be called to generate experimental results:
In [12]:
Copied!
experiment_data = s.run(x)
experiment_data
experiment_data = s.run(x)
experiment_data
Out[12]:
| x1 | rt | |
|---|---|---|
| 0 | 0.0 | 0.006061 |
| 1 | 1.0 | 1.988994 |
| 2 | 2.0 | 4.007712 |
| 3 | 3.0 | 5.980667 |
| 4 | 4.0 | 7.997771 |
| 5 | 5.0 | 9.997181 |
| 6 | 6.0 | 12.018475 |
| 7 | 7.0 | 13.990661 |
| 8 | 8.0 | 16.001257 |
| 9 | 9.0 | 17.998309 |
| 10 | 10.0 | 19.989205 |
... we could also run without noise:
In [22]:
Copied!
s.run(x, added_noise=0)
s.run(x, added_noise=0)
Out[22]:
| x1 | rt | |
|---|---|---|
| 0 | 0.0 | 0.0 |
| 1 | 1.0 | 2.0 |
| 2 | 2.0 | 4.0 |
| 3 | 3.0 | 6.0 |
| 4 | 4.0 | 8.0 |
| 5 | 5.0 | 10.0 |
| 6 | 6.0 | 12.0 |
| 7 | 7.0 | 14.0 |
| 8 | 8.0 | 16.0 |
| 9 | 9.0 | 18.0 |
| 10 | 10.0 | 20.0 |
... a function to plot the ground truth (no noise):
In [23]:
Copied!
s.plotter()
s.plotter()
... against a fitted model if it exists:
In [24]:
Copied!
from sklearn.linear_model import LinearRegression
ivs = [iv.name for iv in s.variables.independent_variables]
dvs = [dv.name for dv in s.variables.dependent_variables]
X = experiment_data[ivs]
y = experiment_data[dvs]
model = LinearRegression().fit(X, y)
s.plotter(model)
from sklearn.linear_model import LinearRegression
ivs = [iv.name for iv in s.variables.independent_variables]
dvs = [dv.name for dv in s.variables.dependent_variables]
X = experiment_data[ivs]
y = experiment_data[dvs]
model = LinearRegression().fit(X, y)
s.plotter(model)
We can wrap this functions to use with the state logic of AutoRA: First, we create the state with the variables:
In [25]:
Copied!
from autora.state import StandardState, on_state, experiment_runner_on_state, estimator_on_state
from autora.experimentalist.grid import grid_pool
from autora.experimentalist.random import random_sample
# We can get the variables from the runner
variables = s.variables
# With the variables, we initialize a StandardState
state = StandardState(variables)
from autora.state import StandardState, on_state, experiment_runner_on_state, estimator_on_state
from autora.experimentalist.grid import grid_pool
from autora.experimentalist.random import random_sample
# We can get the variables from the runner
variables = s.variables
# With the variables, we initialize a StandardState
state = StandardState(variables)
Wrap the experimentalists in on_state function to use them on state:
In [26]:
Copied!
# Wrap the functions to use on state
# Experimentalists:
pool_on_state = on_state(grid_pool, output=['conditions'])
sample_on_state = on_state(random_sample, output=['conditions'])
state = pool_on_state(state)
state = sample_on_state(state, num_samples=2)
print(state.conditions)
# Wrap the functions to use on state
# Experimentalists:
pool_on_state = on_state(grid_pool, output=['conditions'])
sample_on_state = on_state(random_sample, output=['conditions'])
state = pool_on_state(state)
state = sample_on_state(state, num_samples=2)
print(state.conditions)
x1 4 4.0 1 1.0
Wrap the runner with the experiment_runner_on_state wrapper to use it on state:
In [27]:
Copied!
# Runner:
run_on_state = experiment_runner_on_state(s.run)
state = run_on_state(state)
state.experiment_data
# Runner:
run_on_state = experiment_runner_on_state(s.run)
state = run_on_state(state)
state.experiment_data
Out[27]:
| x1 | rt | |
|---|---|---|
| 4 | 4.0 | 8.014508 |
| 1 | 1.0 | 2.019479 |
Wrap the regressor with the estimator_on_state wrapper:
In [28]:
Copied!
theorist = LinearRegression()
theorist_on_state = estimator_on_state(theorist)
state = theorist_on_state(state)
# Access the last model:
model = state.models[-1]
print(f"rt = "
f"{model.coef_[0][0]:.2f}*S0 "
f"{model.intercept_[0]:+.2f} ")
theorist = LinearRegression()
theorist_on_state = estimator_on_state(theorist)
state = theorist_on_state(state)
# Access the last model:
model = state.models[-1]
print(f"rt = "
f"{model.coef_[0][0]:.2f}*S0 "
f"{model.intercept_[0]:+.2f} ")
rt = 2.00*S0 +0.02