Lesson 14

Comparing Nonnested Models

Big question

How should students compare models when one is not just a larger version of the other?

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Big question
Concept
Activity
Quiz

Learning objectives

  • Explain comparing nonnested models in plain language.
  • Use prediction interval correctly in an interpretation.
  • Connect the lesson idea to a formula, graph, Python result, or real example.

Simple explanation

Nonnested models cannot be compared with a simple exclusion F test. Students should compare research purpose, variables, sample, fit measures, and out-of-sample logic.

Key terms

Prediction interval
An interval for an individual future outcome, usually wider than an interval for the conditional mean.
Semi-elasticity
A coefficient interpretation involving a level change in one variable and a percent change in another.
Interaction
A product of variables that lets one slope depend on another variable.

Core formula

comparemodelsonlyonthesameyandsamplecompare models only on the same y and sample

Use plain-language interpretation before algebra.

Example

M6_STARTUP_PREDICTION is a synthetic teaching dataset for comparing nonnested models. It is designed to practice nonnested comparison without presenting fabricated real-world empirical findings.

Interactive visual

Choose between two nonnested prediction models and explain which comparison criteria are legitimate.

Original Module 6 visual for Comparing Nonnested Models.

wage_sample.csv

y variable

wage

The dependent variable. It is the outcome students want to explain.

x variable

education

The explanatory variable. It is used to describe changes in wage.

Live Python

Comparing Nonnested Models Python example

Comparing Nonnested Models Python example

Stdout

Run Python to see results here.

Status / stderr

Ready to run Python in your browser.

Line-by-line guide

  1. Line 1Load a Python library needed for data work or regression.
  2. Line 2Load a Python library needed for data work or regression.
  3. Line 4Load the dataset into a pandas DataFrame.
  4. Line 5Add an intercept column to the regression design matrix.
  5. Line 6Add an intercept column to the regression design matrix.
  6. Line 7Display a result so students can inspect the output.
  7. Line 8Display a result so students can inspect the output.
  8. Line 9Display a result so students can inspect the output.

Python walkthrough

  1. 1Load the synthetic teaching dataset from the Module 6 public data folder.
  2. 2Create transformed variables only after checking their meaning and valid support.
  3. 3Fit a regression that matches the lesson's interpretation target.
  4. 4Print coefficient or prediction summaries that students can connect to the formula.
  5. 5Use comments and output labels so no empirical result is presented without context.

Live notebook

Run this lesson as a notebook

Open an editable notebook cell-by-cell, run Python in the browser, and download the `.ipynb` file for later.

Open live notebookDownload .ipynbDownload .py

Related dataset

M6_POLICY_CONTROLS

Estimated time

25 to 40 min

Packages

pandas, numpy, statsmodels, patsy

Expected output

A regression or inference table with coefficients, uncertainty, and short interpretation notes.

Learning goals

  • Load and inspect M6_POLICY_CONTROLS.
  • Run the Python cells connected to Adjusted R-Squared and Model Size.
  • Interpret the output using adjusted R-squared and model comparison.

Common errors

  • File not found: check that M6_POLICY_CONTROLS.csv is installed or use the course data folder.
  • Package import error: use the browser notebook first, then download for local Jupyter if your local packages differ.
  • Column name error: compare your variable names with the dataset variables listed for this notebook.

Dataset path helper

import pandas as pd

df = pd.read_csv("/data/module-6/M6_POLICY_CONTROLS.csv")
df.head()

Interactive activity

NonnestedModelComparator

Compare nonnested models

Check whether model comparison is legitimate before choosing a specification.

M6_STARTUP_PREDICTION

Inputs

Try it yourself

Write one plain-English sentence explaining the main idea from this lesson.

Common mistakes

Check these before you move on.

A regression coefficient describes a pattern unless the assumptions or research design support a causal interpretation.

Quick quiz

What is the main mistake to avoid in Comparing Nonnested Models?

Quick quiz

What is the main mistake to avoid in Comparing Nonnested Models?

Quick quiz

Why is M6_HOUSING_LOGS a reasonable practice dataset here?

Key takeaway

Comparing Nonnested Models helps students make multiple regression more flexible while keeping interpretation precise and honest.

Download dataDownload resultsDownload interpretation