在databricks的博客中，有一个带有statsmodels链接的pandas udf示例

import statsmodels.api as sm

# df has four columns: id, y, x1, x2

group_column = 'id'
y_column = 'y'
x_columns = ['x1', 'x2']
schema = df.select(group_column, *x_columns).schema

@pandas_udf(schema, PandasUDFType.GROUPED_MAP)

# Input/output are both a pandas.DataFrame

def ols(pdf):
    group_key = pdf[group_column].iloc[0]
    y = pdf[y_column]
    X = pdf[x_columns]
      X = sm.add_constant(X)
    model = sm.OLS(y, X).fit()

    return pd.DataFrame([[group_key] + [model.params[i] for i in   x_columns]], columns=[group_column] + x_columns)

beta = df.groupby(group_column).apply(ols)

如何使用statsmodels公式api重新创建相同的代码？更具体地说，我想定义一个pandas udf，以便它的输入

formula: a string that specifies the R-style regression formula
df:      a Pandas DataFrame

例如，

formula='y ~ x1 + x2 + x1:x2 - 1 '

df=pdf

def ols_formula(formula,df):
    import statsmodels.formula.api as smf

    model = smf.ols(formula, df).fit()

    return model