anova_lm

anova_lm() is the function in Python’s statsmodels library that produces an ANOVA table for one or more fitted linear models. ANOVA (Analysis of Variance) is a statistical method used to determine whether there are significant differences between the means of three or more groups. Researchers and analysts can use anova_lm() to evaluate the effects of categorical variables on a continuous outcome and compare nested linear models to assess their relative explanatory power.

Syntax

statsmodels.stats.anova.anova_lm(*args, **kwargs)

• *args: One or more fitted model results (e.g., instances of OLS model results) to perform ANOVA on.
• **kwargs: Optional keyword arguments to customize the ANOVA test, such as:
  • scale: Specifies the scale parameter.
  • test: Type of test (e.g., ‘F’ for F-test).
  • typ: Specifies the type of sum of squares to calculate (e.g., Type I, II, or III).
  • robust: If True, performs a robust ANOVA.

Example

This example demonstrates how to use the anova_lm() function in the statsmodels library to perform analysis of variance on a fitted linear model:

import statsmodels.api as sm
from statsmodels.formula.api import ols
from statsmodels.stats.anova import anova_lm
import pandas as pd

# Load example data
data = sm.datasets.get_rdataset('iris').data

# Rename columns to make them Python-friendly
data.rename(columns=lambda x: x.replace('.', '_'), inplace=True)

# Fit a linear regression model using Ordinary Least Squares (OLS)
model = ols('Sepal_Length ~ Petal_Length + Petal_Width', data=data).fit()

# Perform ANOVA on the fitted model
anova_results = anova_lm(model, typ=2)

# Print the ANOVA table
print(anova_results)

The ANOVA table produced shows the sum of squares, degrees of freedom, F-statistics, and p-values, helping to evaluate the significance of each predictor in the model:

                 sum_sq     df          F        PR(>F)
Petal_Length   9.934196    1.0  61.150938  9.414477e-13
Petal_Width    0.644340    1.0   3.966300  4.827246e-02
Residual      23.880694  147.0        NaN           NaN