def fixed_effect_3level_model(dataframe):
"""
Multi-level model_2_sci includes intercept, variables as fixed effect.
:param dataframe: a data frame with student ID, school ID, country ID,
science, math, reading, and other five selected variables as
predictors.
:return: the model results
"""
# Fixed effects three-level model
model_2_sci = Lmer(
'log_science ~ IBTEACH + WEALTH '
'+ ESCS + female + Sch_science_resource '
'+ (1 | SchoolID/CountryID)',
data=dataframe)
# model must be fitted in order to get estimate results
model_2_sci.fit(REML=False)
# print summary since auto-generated result doesn't include fixed effects
print(model_2_sci.summary())
model_2_sci.plot_summary()
sns.regplot(x='Sch_science_resource',
y='residuals',
data=model_2_sci.data,
fit_reg=False)
# Inspecting overall fit
sns.regplot(x='fits',
y='log_science',
units='CountryID',
data=model_2_sci.data,
fit_reg=True)
return model_2_sci
def random_intercept_3level_model(dataframe):
"""
Multi-level model_0_sci includes grand-mean intercept and setting outcome
of log science
scores as random.
:param dataframe: a data frame with student ID, school ID, country ID,
science, math, reading, and other five selected variables as
predictors.
:return: the model results
"""
# Random Intercept-only three-level model
model_0_sci = Lmer('log_science ~ 1 | SchoolID/CountryID', data=dataframe)
# model must be fitted in order to get estimate results
model_0_sci.fit(REML=False)
# print summary since auto-generated result doesn't include fixed effects
print(model_0_sci.summary())
# plot summary
model_0_sci.plot_summary()
# Inspecting overall fit
sns.regplot(x='fits',
y='log_science',
units='CountryID',
data=model_0_sci.data,
fit_reg=True)
return model_0_sci
def random_effect_2level_model(dataframe):
"""
Multi-level model_1_sci includes intercept, variable as fixed and the
interaction term
random on country level.
:param dataframe: a data frame with student ID, school ID, country ID,
science, math, reading, and other five selected variables as
predictors.
:return: the model results
"""
# Random intercept and slope two-level model:
model_1_sci = Lmer('Science ~ female + (female*ESCS | CountryID)',
data=dataframe)
# model must be fitted in order to get estimate results
model_1_sci.fit(REML=False)
# print summary since auto-generated result doesn't include fixed effects
print(model_1_sci.summary())
model_1_sci.plot_summary()
# Visualizing random effect of a predictor
model_1_sci.plot('female', plot_ci=True, ylabel='Predicted log_science')
sns.regplot(x='female',
y='residuals',
data=model_1_sci.data,
fit_reg=False)
# Inspecting overall fit
sns.regplot(x='fits',
y='log_science',
units='CountryID',
data=model_1_sci.data,
fit_reg=True)
return model_1_sci
def mixeff_multinteraction2level_model(dataframe):
"""
Multi-level model_5_sci includes intercept, multiple interactions and
fixed effects,
and setting ESCS as random on country level.
:param dataframe: a data frame with student ID, school ID, country ID,
science, math, reading, and other five selected variables as
predictors.
:return: the model results
"""
# one random effect and multiple interactions between gender and factors
model_5_sci = Lmer(
'log_science ~ IBTEACH + WEALTH + ESCS + female + '
'Sch_science_resource '
'+ female*ESCS '
'+ female*WEALTH + female*IBTEACH + (ESCS | CountryID)',
data=dataframe)
# model must be fitted in order to get estimate results
model_5_sci.fit(REML=False)
# print summary since auto-generated result doesn't include fixed effects
print(model_5_sci.summary())
model_5_sci.plot_summary()
# Visualizing random effect of a predictor
model_5_sci.plot('ESCS', plot_ci=True, ylabel='Predicted log_science')
sns.regplot(x='ESCS', y='residuals', data=model_5_sci.data, fit_reg=False)
# Inspecting overall fit
sns.regplot(x='fits',
y='log_science',
units='CountryID',
data=model_5_sci.data,
fit_reg=True)
return model_5_sci
