Analyzing Spatial Models of Choice and Judgment with R

351 Pages·2014·2.6 MB·English

by  David A Armstrong

Analyzing Spatial Models
of Choice and Judgment
with R
K15094_FM.indd 1 12/19/13 10:30 AM
Chapman & Hall/CRC
Statistics in the Social and Behavioral Sciences Series
Series Editors
Jeff Gill Steven Heeringa
Washington University, USA University of Michigan, USA
Wim van der Linden J. Scott Long
CTB/McGraw-Hill, USA Indiana University, USA
Tom Snijders
Oxford University, UK
University of Groningen, UK
Aims and scope
Large and complex datasets are becoming prevalent in the social and behavioral
sciences and statistical methods are crucial for the analysis and interpretation of such
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students, researchers and practitioners from the above disciplines. The inclusion of real
examples and case studies is therefore essential.
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Published Titles
Analyzing Spatial Models of Choice and Judgment with R
David A. Armstrong II, Ryan Bakker, Royce Carroll, Christopher Hare,
Keith T. Poole, and Howard Rosenthal
Analysis of Multivariate Social Science Data, Second Edition
David J. Bartholomew, Fiona Steele, Irini Moustaki, and Jane I. Galbraith
Latent Markov Models for Longitudinal Data
Francesco Bartolucci, Alessio Farcomeni, and Fulvia Pennoni
Statistical Test Theory for the Behavioral Sciences
Dato N. M. de Gruijter and Leo J. Th. van der Kamp
Multivariable Modeling and Multivariate Analysis for the Behavioral Sciences
Brian S. Everitt
Bayesian Methods: A Social and Behavioral Sciences Approach,
Second Edition
Jeff Gill
Multiple Correspondence Analysis and Related Methods
Michael Greenacre and Jorg Blasius
Applied Survey Data Analysis
Steven G. Heeringa, Brady T. West, and Patricia A. Berglund
Informative Hypotheses: Theory and Practice for Behavioral and
Social Scientists
Herbert Hoijtink
Foundations of Factor Analysis, Second Edition
Stanley A. Mulaik
Linear Causal Modeling with Structural Equations
Stanley A. Mulaik
Handbook of International Large-Scale Assessment: Background, Technical
Issues, and Methods of Data Analysis
Leslie Rutkowski, Matthias von Davier, and David Rutkowski
Generalized Linear Models for Categorical and Continuous Limited
Dependent Variables
Michael Smithson and Edgar C. Merkle
Incomplete Categorical Data Design: Non-Randomized Response Techniques
for Sensitive Questions in Surveys
Guo-Liang Tian and Man-Lai Tang
K15094_FM.indd 3 12/19/13 10:30 AM
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Chapman & Hall/CRC
Statistics in the Social and Behavioral Sciences Series
Analyzing Spatial Models
of Choice and Judgment
with R
David A. Armstrong II
University of Wisconsin-Milwaukee
Ryan Bakker
University of Georgia
Royce Carroll
Rice University
Christopher Hare
University of Georgia
Keith T. Poole
University of Georgia
Howard Rosenthal
New York University
K15094_FM.indd 5 12/19/13 10:30 AM
CRC Press
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Contents
Preface xi
Author Biographies xix
1 Introduction 1
1.1 The Spatial Theory of Voting . . . . . . . . . . . . . . . . . . 2
1.1.1 TheoreticalDevelopmentandApplicationsoftheSpa-
tial Voting Model . . . . . . . . . . . . . . . . . . . . . 5
1.1.2 The Development of Empirical Estimation Methods
for Spatial Models of Voting . . . . . . . . . . . . . . . 7
1.1.3 The Basic Space Theory . . . . . . . . . . . . . . . . . 8
1.2 Summary of Data Types Analyzed by Spatial Voting Models 11
1.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2 The Basics 13
2.1 Data Basics in R . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.1.1 Storage Modes . . . . . . . . . . . . . . . . . . . . . . 14
2.1.2 Missing Values . . . . . . . . . . . . . . . . . . . . . . 16
2.1.3 Recoding Data . . . . . . . . . . . . . . . . . . . . . . 18
2.1.4 Probability Distributions and Random Numbers . . . 19
2.1.5 Loops and Functions . . . . . . . . . . . . . . . . . . . 20
2.1.6 The apply and sweep Functions . . . . . . . . . . . . . 21
2.1.7 Sorting Data . . . . . . . . . . . . . . . . . . . . . . . 22
2.1.8 Creating Scatter Plots and Kernel Density Plots . . . 23
2.2 Reading Data in R . . . . . . . . . . . . . . . . . . . . . . . . 28
2.2.1 Reading Data from Stata into R . . . . . . . . . . . . 28
2.2.2 Reading Data from SPSS into R . . . . . . . . . . . . 29
2.2.3 Reading Text and Spreadsheet Files into R . . . . . . 32
2.3 Writing Data in R . . . . . . . . . . . . . . . . . . . . . . . . 35
2.3.1 Writing Data as a Stata File . . . . . . . . . . . . . . 35
2.3.2 Writing Data as Text and .csv Files . . . . . . . . . . 36
2.3.3 The dput/dget and save/load Functions in R . . . . . 37
2.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
vii
viii
3 Analyzing Issue Scales 39
3.1 Aldrich-McKelvey Scaling . . . . . . . . . . . . . . . . . . . . 40
3.1.1 The basicspace Package in R . . . . . . . . . . . . . . 43
3.1.2 Example 1: 2009 European Election Study (French
Module) . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.1.3 Example 2: 1968 American National Election Study
Urban Unrest and Vietnam War Scales. . . . . . . . . 49
3.1.4 EstimatingBootstrappedStandardErrorsforAldrich-
McKelvey Scaling . . . . . . . . . . . . . . . . . . . . . 55
3.1.5 Bayesian Aldrich-McKelvey Scaling . . . . . . . . . . . 56
3.1.6 Comparing Aldrich-McKelvey Standard Errors . . . . 61
3.2 Basic Space Scaling: The blackbox Function . . . . . . . . . . 66
3.2.1 Example 1: 2000 Convention Delegate Study . . . . . 67
3.2.2 Example 2: 2010 Swedish Parliamentary Candidate
Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
3.2.3 Estimating Bootstrapped Standard Errors for Black
Box Scaling . . . . . . . . . . . . . . . . . . . . . . . . 79
3.3 Basic Space Scaling: The blackbox transpose Function . . . . 83
3.3.1 Example1: 2000and2006ComparativeStudyofElec-
toral Systems (Mexican Modules) . . . . . . . . . . . . 83
3.3.2 Estimating Bootstrapped Standard Errors for Black
Box Transpose Scaling . . . . . . . . . . . . . . . . . . 87
3.3.3 Using the blackbox transpose Function on Datasets
with Large Numbers of Respondents . . . . . . . . . . 89
3.4 Anchoring Vignettes . . . . . . . . . . . . . . . . . . . . . . . 91
3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
3.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
4 Analyzing Similarities and Dissimilarities Data 103
4.1 Classical Metric Multidimensional Scaling . . . . . . . . . . . 104
4.1.1 Example 1: Nations Similarities Data . . . . . . . . . 107
4.1.2 Metric MDS Using Numerical Optimization . . . . . . 109
4.1.3 Metric MDS Using Majorization (SMACOF) . . . . . 114
4.1.4 The smacof Package in R . . . . . . . . . . . . . . . . 114
4.2 Non-metric Multidimensional Scaling . . . . . . . . . . . . . . 119
4.2.1 Example 1: Nations Similarities Data . . . . . . . . . 120
4.2.2 Example 2: 90th US Senate Agreement Scores . . . . 123
4.3 Bayesian Multidimensional Scaling . . . . . . . . . . . . . . . 128
4.3.1 Example 1: Nations Similarities Data . . . . . . . . . 129
4.4 Individual Differences Multidimensional Scaling . . . . . . . . 132
4.4.1 Example 1: 2009 European Election Study (French
Module) . . . . . . . . . . . . . . . . . . . . . . . . . . 137
4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
4.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
ix
5 Unfolding Analysis of Rating Scale Data 147
5.1 Solving the Thermometers Problem . . . . . . . . . . . . . . . 148
5.2 Metric Unfolding Using the MLSMU6 Procedure . . . . . . . 150
5.2.1 Example 1: 1981 Interest Group Ratings of US Sena-
tors Data . . . . . . . . . . . . . . . . . . . . . . . . . 154
5.3 Metric Unfolding Using Majorization (SMACOF) . . . . . . . 156
5.3.1 Example 1: 2009 European Election Study (Danish
Module) . . . . . . . . . . . . . . . . . . . . . . . . . . 159
5.3.2 Comparing the MLSMU6 and SMACOF Metric Un-
folding Procedures . . . . . . . . . . . . . . . . . . . . 163
5.4 Bayesian Multidimensional Unfolding . . . . . . . . . . . . . . 165
5.4.1 Example 1: 1968 American National Election Study
Feeling Thermometers Data . . . . . . . . . . . . . . . 166
5.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
5.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
6 Unfolding Analysis of Binary Choice Data 183
6.1 The Geometry of Legislative Voting . . . . . . . . . . . . . . 184
6.2 Reading Legislative Roll Call Data into R with the pscl Pack-
age . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
6.3 Parametric Methods - NOMINATE . . . . . . . . . . . . . . . 189
6.3.1 ObtainingUncertaintyEstimateswiththeParametric
Bootstrap . . . . . . . . . . . . . . . . . . . . . . . . . 193
6.3.2 Types of NOMINATE Scores . . . . . . . . . . . . . . 193
6.3.3 Accessing DW-NOMINATE Scores . . . . . . . . . . . 195
6.3.4 The wnominate Package in R . . . . . . . . . . . . . . 196
6.3.5 Example 1: The 108th US House . . . . . . . . . . . . 197
6.3.6 Example 2: The First European Parliament (Using
the Parametric Bootstrap) . . . . . . . . . . . . . . . . 212
6.4 MCMC or α-NOMINATE . . . . . . . . . . . . . . . . . . . . 214
6.4.1 The anominate Package in R . . . . . . . . . . . . . . 217
6.5 Parametric Methods - Bayesian Item Response Theory . . . . 221
6.5.1 The MCMCpack and pscl Packages in R . . . . . . . . 225
6.5.2 Example 1: The 2000 Term of the US Supreme Court
(Unidimensional IRT) . . . . . . . . . . . . . . . . . . 225
6.5.3 Running Multiple Markov Chains in MCMCpack and
pscl . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231
6.5.4 Example2: TheConfirmationVoteofRobertBorkto
the US Supreme Court (Unidimensional IRT) . . . . . 234
6.5.5 Example 3: The 89th US Senate (Multidimensional
IRT) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242
6.6 Nonparametric Methods - Optimal Classification . . . . . . . 249
6.6.1 The oc Package in R . . . . . . . . . . . . . . . . . . . 250
6.6.2 Example1: TheFrenchNationalAssemblyduringthe
Fourth Republic . . . . . . . . . . . . . . . . . . . . . 250