# Complex Surveys: A Guide to Analysis Using R

# Complex Surveys: A Guide to Analysis Using R

ISBN: 978-0-470-28430-8 March 2010 296 Pages

## Description

**A complete guide to carrying out complex survey analysis using R**

As survey analysis continues to serve as a core component of sociological research, researchers are increasingly relying upon data gathered from complex surveys to carry out traditional analyses. *Complex Surveys* is a practical guide to the analysis of this kind of data using R, the freely available and downloadable statistical programming language. As creator of the specific survey package for R, the author provides the ultimate presentation of how to successfully use the software for analyzing data from complex surveys while also utilizing the most current data from health and social sciences studies to demonstrate the application of survey research methods in these fields.

The book begins with coverage of basic tools and topics within survey analysis such as simple and stratified sampling, cluster sampling, linear regression, and categorical data regression. Subsequent chapters delve into more technical aspects of complex survey analysis, including post-stratification, two-phase sampling, missing data, and causal inference. Throughout the book, an emphasis is placed on graphics, regression modeling, and two-phase designs. In addition, the author supplies a unique discussion of epidemiological two-phase designs as well as probability-weighting for causal inference. All of the book's examples and figures are generated using R, and a related Web site provides the R code that allows readers to reproduce the presented content. Each chapter concludes with exercises that vary in level of complexity, and detailed appendices outline additional mathematical and computational descriptions to assist readers with comparing results from various software systems.

*Complex Surveys* is an excellent book for courses on sampling and complex surveys at the upper-undergraduate and graduate levels. It is also a practical reference guide for applied statisticians and practitioners in the social and health sciences who use statistics in their everyday work.

## Table of contents

Preface.

Acronyms.

**1 Basic Tools.**

1.1 Goals of Inference.

1.1.1 Population or Process?

1.1.2 Probability Samples.

1.1.3 Sampling Weights.

1.1.4 Design Effects.

1.2 An Introduction to the Data.

1.2.1 Real Surveys.

1.2.2 Populations.

1.3 Obtaining the Software.

1.3.1 Obtaining R.

1.3.2 Obtaining the Survey Package.

1.4 Using R.

1.4.1 Reading Plain Text Data.

1.4.2 Reading Data from Other Packages.

1.4.3 Simple Computation.

Exercises.

**2 Simple and Stratified Sampling.**

2.1 Analyzing Simple Random Samples.

2.1.1 Confidence Intervals.

2.1.2 Describing the Sample to R.

2.2 Stratified Sampling.

2.3 Replicate Weights.

2.3.1 Specifying Replicate Weights to R.

2.3.2 Creating Replicate Weights in R.

2.4 Other Population Summaries.

2.4.1 Quantiles.

2.4.2 Contingency Tables.

2.5 Estimates in Subpopulations.

2.6 Design of Stratified Samples.

Exercises.

**3 Cluster Sampling.**

3.1 Introduction.

3.1.1 Why Clusters: The NHANES II Design.

3.1.2 Single-Stage and Multistage Designs.

3.2 Describing Multistage Designs to R.

3.2.1 Strata with Only One PSU.

3.2.2 How Good is the Single-State Approximation?

3.2.3 Replicate Weights for Multistage Samples.

3.3 Sampling by Size.

3.3.1 Loss of Information from Sampling Clusters.

3.4 Repeated Measurements.

Exercises.

**4 Graphics.**

4.1 Why is Survey Data Different?

4.2 Plotting a Table.

4.3 One Continuous Variable.

4.3.1 Graphs Based on the Distribution Function.

4.3.2 Graphs Based on the Density.

4.4 Two Continuous Variables.

4.4.1 Scatterplots.

4.4.2 Aggregation and Smoothing.

4.4.3 Scatterplot Smoothers.

4.5 Conditioning Plots.

4.6 Maps.

4.6.1 Design and Estimation Issues.

4.6.2 Drawing Maps in R.

Exercises.

**5 Ratios and Linear Regression.**

5.1 Ratio Estimation.

5.1.1 Estimating Ratios.

5.1.2 Ratios for Subpopulation Estimates.

5.1.3 Ratio Estimators of Totals.

5.2 Linear Regression.

5.2.1 The Least-Squares Slope as an Estimated Population.

5.2.2 Regression Estimation of Population Totals.

5.2.3 Confounding and Other Criteria for Model Choice.

5.2.4 Linear Models in the Survey Package.

5.3 Is Weighting Needed in Regression Models?

Exercises.

**6 Categorical Data Regression.**

6.1 Logistic Regression.

6.1.1 Relative Risk Regression.

6.2 Ordinal Regression.

6.2.1 Other Cumulative Link Models.

6.3 Loglinear Models.

6.3.1 Choosing Models.

6.3.2 Linear Association Models.

Exercises.

**7 Post-Stratification, Raking and Calibration.**

7.1 Introduction.

7.2 Post-Stratification.

7.3 Raking.

7.4 Generalized Raking, GREG Estimation, and Calibration.

7.4.1 Calibration in R.

7.5 Basu’s Elephants.

7.6 Selecting Auxiliary Variables for Non-Response.

7.6.1 Direct Standardization.

7.6.2 Standard Error Estimation.

Exercises.

**8 Two-Phase Sampling.**

8.1 Multistage and Multiphase Sampling.

8.2 Sampling for Stratification.

8.3 The Case-Control Design.

8.3.1 Simulations: Efficiency of the Design-Based Estimator.

8.3.2 Frequency Matching.

8.4 Sampling from Existing Cohorts.

8.4.1 Logistic Regression.

8.4.2 Two-Phase Case-Control Designs in R.

8.4.3 Survival Analysis.

8.4.4 Case-Cohort Designs in R.

8.5 Using Auxiliary Information from Phase One.

8.5.1 Population Calibration for Regression Models.

8.5.2 Two-Phase Designs.

8.5.3 Some History of the Two-Phase Calibration Estimator.

Exercises.

**9 Missing Data.**

9.1 Item Non-Response.

9.2 Two-Phase Estimation for Missing Data.

9.2.1 Calibration for Item Non-Response.

9.2.2 Models for Response Probability.

9.2.3 Effect on Precision.

9.2.4 Doubly-Robust Estimators.

9.3 Imputation of Missing Data.

9.3.1 Describing Multiple Imputations to R.

9.3.2 Example: NHANES III Imputations.

Exercises.

**10 Causal Inference.**

10.1 IPTW Estimators.

10.1.1 Randomized Trials and Calibration.

10.1.2 Estimated Weights for IPTW.

10.1.3 Double Robustness.

10.2 Marginal Structural Models.

**Appendix A: Analytic Details.**

A.1 Asymptotics.

A.1.1 Embedding in an Infinite Sequence.

A.1.2 Asymptotic Unbiasedness.

A.1.3 Asymptotic Normality and Consistency.

A.2 Variances by Linearization.

A.2.1 Subpopulation Inference.

A.3 Tests in Contingency Tables.

A.4 Multiple Imputation.

A.5 Calibration and Influence Functions.

A.6 Calibration in Randomized Trials and ANCOVA.

**Appendix B: Basic R.**

B.1 Reading Data.

B.1.1 Plain Text Data.

B.2 Data Manipulation.

B.2.1 Merging.

B.2.2 Factors.

B.3 Randomness.

B.4 Methods and Objects.

B.5 Writing Functions.

B.5.1 Repetition.

B.5.2 Strings.

**Appendix C: Computational Details.**

C.1 Linearization.

C.1.1 Generalized Linear Models and Expected Information.

C.2 Replicate Weights.

C.2.1 Choice of Estimators.

C.2.2 Hadamard Matrices.

C.3 Scatterplot Smoothers.

C.4 Quantiles.

C.5 Bug Reports and Feature Requests.

**Appendix D: Database-Backed Design Objects.**

D.1 Large Data.

D.2 Setting Up Database Interfaces.

D.2.1 ODBC.

D.2.2 DBI.

**Appendix E: Extending the Survey Package.**

E.1 A Case Study: Negative Binomial Regression.

E.2 Using a Poisson Model.

E.3 Replicate Weights.

E.4 Linearization.

References.

Author Index.

Topic Index.

## Extra

## Features

- Actual analysis code, in R, is presented throughout the book
- Realistically large, but not technologically inaccessible, data sets are showcased and special cases are avoided
- Formulas are developed or given only when illuminating (ex., the Horvitz-Thompson variance estimator, but not the variance of a ratio estimator)
- Coverage of regression modeling in epidemiological two-phase designs is unique, as is probability-weighting for causal inference
- A related Web site houses additional data sets, figures, and code for reproducing the book's examples