Multilevel Analysis for Applied Research It's Just Regression!

by Bickel, Robert

• ISBN13: 9781593851910
• ISBN10: 159385191X
• Format: Paperback
• Copyright: 2007-03-20
• Publisher: The Guilford Press

Summary

This book provides a uniquely accessible introduction to multilevel modeling, a powerful tool for analyzing relationships between an individual-level dependent variable, such as student reading achievement, and individual-level and contextual explanatory factors, such as gender and neighborhood quality. Helping readers build on the statistical techniques they already know, Robert Bickel emphasizes the parallels with more familiar regression models, shows how to do multilevel modeling using SPSS, and demonstrates how to interpret the results. He discusses the strengths and limitations of multilevel analysis and explains specific circumstances in which it offers (or does not offer) methodological advantages over more traditional techniques. Over 300 dataset examples from research on educational achievement, income attainment, voting behavior, and other timely issues are presented in numbered procedural steps.

Author Biography

Robert Bickel, PhD, is Professor of Advanced Educational Studies at Marshall University in Huntington, West Virginia, where he teaches research methods, applied statistics, and the sociology of education. His publications have dealt with a broad range of issues, including high school completion, teen pregnancy, crime on school property, correlates of school size, neighborhood effects on school achievement, and the consequences of the No Child Left Behind Act of 2001 for poor rural schools. Before joining the faculty at Marshall University, Dr. Bickel spent 15 years as a program evaluator and policy analyst, working in a variety of state and local agencies.

Table of Contents

Broadening the Scope of Regression Analysis

Chapter Introduction

Why Use Multilevel Regression Analysis?

Limitations of Available Instructional Material

Multilevel Regression Analysis in Suggestive Historical Context

It's Just Regression under Specific Circumstances

Jumping the Gun to a Multilevel Illustration

Summing Up

Useful Resources

The Meaning of Nesting

Chapter Introduction

Nesting Illustrated: School Achievement and Neighborhood Quality

Nesting Illustrated: Comparing Public and Private Schools

Cautionary Comment on Residuals in Multilevel Analysis

Nesting and Correlated Residuals

Nesting and Effective Sample Size

Summing Up

Useful Resources

Contextual Variables

Chapter Introduction

Contextual Variables and Analytical Opportunities

Contextual Variables and Independent Observations

Contextual Variables and Independent Observations: A Nine-Category Dummy Variable

Contextual Variables, Intraclass Correlation, and Misspecification

Contextual Variables and Varying Parameter Estimates

Contextual Variables and Covariance Structure

Contextual Variables and Degrees of Freedom

Summing Up

Useful Resources

From OLS to Random Coefficient to Multilevel Regression

Chapter Introduction

Simple Regression Equation

Simple Regression with an Individual-Level Variable

Multiple Regression: Adding a Contextual Variable

Nesting (Again!) with a Contextual Variable

Is There a Problem with Degrees of Freedom?

Is There a Problem with Dependent Observations?

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The Conceptual Basis of ML Estimators

Desirable Properties of REML Estimators

Applying REML Estimators with Random Coefficient Regression Models

Fixed Components and Random Components

Interpreting Random Coefficients: Developing a Cautionary Comment

Subscript Conventions

Percentage of Variance Explained for Random Coefficient and Multilevel Models

Grand-Mean Centering

Grand-Mean Centering, Group-Mean Centering, and Raw Scores Compared

Summing Up

Useful Resources

Developing the Multilevel Regression Model

Chapter Introduction

From Random Coefficient Regression to Multilevel Regression

Equations for a Random Intercept and Random Slope

Subscript Conventions for Two-Level Models: Gamma Coefficients

The Full Equation

AnImpliedCross-Level Interaction Term

Estimating a Multilevel Model: The Full Equation

A Multilevel Model with a Random Slope and Fixed Slopes at Level One

Complexity and Confusion: Too Many Random Components

Interpreting Multilevel Regression Equations

Comparing Interpretations of Alternative Specifications

What Happened to the Error Term?

Summing Up

Useful Resources

Giving OLS Regression Its Due

Chapter Introduction

An Extended Exercise with County-Level Data

Tentative Specification of an OLS Regression Model

Preliminary Regression Results

Surprise Results and Possible Violation of OLS Assumptions

Curvilinear Relationships:YBUSH byXBLACK,XHISPANIC,XNATIVE

Quadratic Functional Form

A Respecified OLS Regression Model

Interpreting Quadratic Relationships

Nonadditivity and Interaction Terms

Further Respecification of the Regression Model

Clarifying OLS Interaction Effects

Results for the Respecified OLS Regression Equation for County-Level Data

Summing Up

Useful Resources

Does Multilevel Regression Have Anything to Contribute?

Chapt

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