Berk R.A. Regression Analysis: A Constructive Critique

Thousands Oaks: Sage Publications, 2004. — 281 p.Regression is often applied to questions for which it is ill equipped to answer. As a formal matter, conventional regression analysis does nothing more than produce from a data set a collection of conditional means and conditional variances. The problem, though, is that researchers typically want more: they want tests, confidence intervals and the ability to make causal claims. However, these capabilities require information external to that data themselves, and too often that information makes implausible demands on how nature is supposed to function. Convenience samples are treated as if they are random samples. Causal status is given to predictors that cannot be manipulated. Disturbance terms are assumed to behave not as nature might produce them, but as required by the model.
Regression Analysis: A Constructive Critique identifies a wide variety of problems with regression analysis as it is commonly used and then provides a number of ways in which practice could be improved. Regression is most useful for data reduction, leading to relatively simple but rich and precise descriptions of patterns in a data set. The emphasis on description provides readers with an insightful rethinking from the ground up of what regression analysis can do, so that readers can better match regression analysis with useful empirical questions and improved policy-related research.Series Editor’s Introduction
PrefacePrologue: Regression Analysis as Problematic

A Grounded Introduction to Regression Analysis
Some Examples of Regression Analysis
Abortion and Subsequent Crime
Mandatory Basic Education for Welfare Recipients
Gender and Academic Salaries
Climate Change and Water Resources in India
Deforestation and Soil Erosion in the Yangtze
River Valley
Epidemics of Hepatitis C
Onward and Upward
What Is Regression Analysis?
A Simple Illustration
Controlling for a Third Variable
Imposing a Smoother
Getting From Data to StoriesSimple Linear RegressionDescribing a Conditional Relationship With a Straight Line
Defining the “Best” Line
Some Useful Formulas
Standardized Slopes
Using Transformations for a Nonlinear Fit
What About the Variance Function?
Summary and ConclusionsStatistical Inference for Simple Linear Regression
The Role of Sampling
Random Sampling
Strategy I: Treating the Data as Population
Strategy II: Treating the Data as If They Were Generated by Random Sampling From a Population
Strategy III: Inventing an Imaginary Population
Strategy IV: Model-Based Sampling—Inventing a Friendly Natural Process Responsible for the Data
A Note on Randomization Inference
Summing Up
Simple Linear Regression Under Random Sampling
Estimating the Population Regression Line
Estimating the Standard Errors
Estimation Under Model-Based Sampling
Some Things That Can Go Wrong
Tests and Confidence Intervals
Statistical Power
Stochastic Predictors
Measurement Error
Can Resampling Techniques Help?
Percentile Confidence Intervals
Hypothesis Testing
Bootstrapping Regression
Possible Benefits From Resampling
Summary and ConclusionsCausal Inference for the Simple Linear ModelSome Definitions: What’s a Causal Effect?
The Neyman-Rubin Model
Thinking About Causal Effects as Response Schedules
What’s an Intervention?
Studying Cause and Effect With Data
Using Nonstatistical Solutions for Making Causal Inferences
Using Statistical Solutions for Making Causal Inferences
Using the Simple Linear Model for Making Causal Inferences
Summary and ConclusionsThe Formalities of Multiple RegressionTerms and Predictors
Some Notation for Multiple Regression
How Multiple Regression “Holds Constant”
Summary and ConclusionsUsing and Interpreting Multiple RegressionAnother Formal Perspective on Holding Constant
When Does Holding Constant Make Sense?
Standardized Regression Coefficients:
Once More With Feeling
Variances of the Coefficient Estimates
Summary and ConclusionsSome Popular Extensions of Multiple RegressionModel Selection and Stepwise Regression
Model Selection by Removing Terms
Tests to Compare Models
Selecting Terms Without Testing
Stepwise Selection Methods
Some Implications
Using Categorical Terms: Analysis of Variance and Analysis of Covariance
An Extended Example
Back to the Variance Function: Weighted Least Squares
Visualizing Lack of Fit
Weighted Least Squares as a Possible Fix
Evaluating the Mean Function
Locally Weighted Regression Smoother
Summary and ConclusionsSome Regression DiagnosticsTransformations of the Response Variable
Box-Cox Procedures
Inverse Fitted Value Response Plots
Leverage and Influence
Influential Cases and Cook’s Distance
Cross-Validation
Misspecification Tests
Instrumental Variables
Tests for Exogeneity
ConclusionsFurther Extensions of Regression Analysis
Regression Models for Longitudinal Data
Multiple Linear Regression for Time Series Data
Regression Analysis With Multiple
Time Series Data
Fixed Effects Models
Random Effects Models
Estimation
Multilevel Models
The Generalized Linear Model
GLM Structure
Normal Models
Poisson Models
Poisson Models for Contingency Tables
Binomial Regression
Multiple Equation Models
Causal Inference Once Again
A Final Observation
Meta-Analysis
ConclusionsWhat to Do
How Did We Get Into This Mess?
Three Cheers for Description
What’s Description?
Advocacy Settings
Descriptive Regressions as Part of a Broad
Research Program
Spotting Provocative Associations
Some Other Benefits of Description
Two Cheers for Statistical Inference
Working With Near-Random Samples
Working With Data From Nature
Working With a Nearly Correct Model
One Cheer for Causal Inference
Special-Purpose Estimators
Propensity Scores
Sensitivity Analysis of the Selection Process
Bounding Treatment Effects
Some Forecasts
Some Final Observations
A Police Story
Regression Analysis as Too Little, Too LateReferences

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