What are Linear Mixed Effects Models in the StatsModels library?

In this recipe, we describe Linear Mixed-Effects Models in the StatsModels library

Recipe Objective - What are Linear Mixed-Effects Models in the StatsModels library?

The linear mixed-effects model is used for regression analysis with dependent data. Such data occurs when working in longitudinal and other study designs where multiple observations are made on each topic. Some specific linear mixed-effects models are 1. Random intercept model in which all answers in a group are additively shifted by group-specific values. 2. Random slopes models in which the response within a group follows a (conditional) mean orbit that is linear with the observed covariates. Gradients (and intercepts in some cases) vary from group to group. 3. Variance components models in which one or more categorical covariate levels are associated with extraction from the distribution. These random terms also determine each observation's conditional mean based on the covariate values.

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Example:

# Importing libraries
import statsmodels.api as sm
import statsmodels.formula.api as smf

# Importing heart dataset from statsmodels in the form of pandas dataframe
data = sm.datasets.heart.load_pandas()

# Storing data
X = data.data

# Fit and summarize mixedLM model with 'survival' as dependent variable and 'censors' as independent variables,
# grouped by 'age'
model = smf.mixedlm('survival ~ censors', X, groups = X['age'])
model = model.fit()

# Model summary
model.summary()

Output - 
Model:	MixedLM	Dependent Variable:	survival
No. Observations:	69	Method:	REML
No. Groups:	61	Scale:	113839.2282
Min. group size:	1	Log-Likelihood:	-501.1812
Max. group size:	2	Converged:	Yes
Mean group size:	1.1		
Coef.	Std.Err.	z	P>|z|	[0.025	0.975]
Intercept	664.570	83.673	7.942	0.000	500.573	828.567
censors	-446.515	101.365	-4.405	0.000	-645.187	-247.843
Group Var	54162.541	236.534		

In this way, we can use Linear Mixed-Effects Models in the statsmodels library.

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