albertbuchard

"""
This example demonstrates that fitting a weighted linear mixed-effects model using lmer(weights = …) 
is algebraically equivalent to pre-multiplying the outcome and all predictors (including intercepts) 
by the square root of the weights and fitting an unweighted model on the transformed data. 
The test validates that this "pre-weight and refit" strategy yields identical fitted values and 
is especially useful when packages like clubSandwich prohibit prior weights in robust variance estimation. 
Includes realistic longitudinal synthetic data with fixed and random effects, dropout, and continuous covariates.
"""
from typing import List

albertbuchard

import numpy as np
import pandas as pd
import cvxpy as cp
from typing import Sequence, Union


def entropy_balance_ipaw(
    df: pd.DataFrame,
    *,

albertbuchard

from typing import Optional

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import warnings

import statsmodels.formula.api as smf
from statsmodels.tools.sm_exceptions import (
    ConvergenceWarning,