POLS 8505: MEASUREMENT THEORY
Clyde H. Coombs
Born: 22 July 1912
Died: 4 February 1988
Spring Semester AY20142015
Department of Political Science
School of Public and International Affairs
University of Georgia
Athens, GA 30602
Classroom: Baldwin 301
Time: 3:356:35 Mondays
Instructor: Keith T. Poole
Office: Baldwin 304D
EMail: ktpoole@uga.edu
WebSite: Voteview Home Page or Office Hours: 2:00  4:00PM Thursdays or By Appointment
The following texts will be used in this course:
 Armstrong, David, Ryan Bakker, Royce Carroll, Christopher Hare, Keith Poole, and Howard
Rosenthal. 2014. Analyzing Spatial Models of Choice and Judgment with R, New York: CRC Press.
 Poole, Keith T. 2005. Spatial Models of Parliamentary Voting, New York: Cambridge University Press.
 Coombs, Clyde. 1964. A Theory of Data. New York: John Wiley (Selected Chapters).
 Borg, Ingwer and Patrick Groenen. 2005. Modern Multidimensional Scaling: Theory and Applications (2nd Edition). New York: SpringerVerlag.
 An Introduction to R. (Reference Work by R Development Core Team)
 Using R for Data Analysis and Graphics: An Introduction. (Reference Work by J. H. Maindonald on R Graphics)
Requirements
This course is concerned with dimensional analysis, that is, the measurement of latent dimensions in data matrices. A working knowledge
of OLS multiple regression analysis and STATA is required for this course. Students will be required to use two statistical packages
 R and WINBUGS/JAGS. We will also use a variety of "canned" programs that perform various kinds of dimensional
analyses.
Grades will be determined by regularly assigned class problems.
Useful Links  R
PCH Symbols in R
Octal References for Math Symbols that can be used in PlotMath in R
Miscellaneous Useful R Programs
Useful Links  EPSILON
EPSILON HomePage  Lugaru Software Ltd.
Useful Epsilon Commands
Epsilon Keyboard Macro Examples
Epsilon Text File Macro Examples
Useful Links  Old Homeworks
Old Homeworks: 2001  2011
Useful Links  How to Install GNU C/C++ and FORTRAN Compilers for WINDOWS and MAC
Machines
How to Install GNU Compilers
Useful Links  How to Install JAGS on the MAC
How to Install JAGS
Useful Links  JAGS for WINDOWS 64 bit
Sourcefore JAGS 3.4  Runs on 64 bit WINDOWS and 64 bit R
Problem Sets (2015)
Homework 1: Due 20 January 2015 (NOTE THAT THIS IS A TUESDAY!)
Homework 2: Due 26 January 2015
Homework 3: Due 2 February 2015
Homework 4: Due 9 February 2015
Homework 5: Due 16 February 2015
Homework 6: Due 23 February 2015
Homework 7: Due 2 March 2015
Homework 8: Due 16 March 2015
Homework 9: Due 30 March 2015
Homework 10: Due 6 April 2015
Homework 11: Due 13 April 2015
Homework 12: Due 20 April 2015
Homework 13: Due 27 April 2015
Course Outline
 Clyde Coombs' Theory of Data: Similarities and Preferential Choice
Assignment:
 Analyzing Issue Scales
Assignment:
 Armstrong et al., Chapter 3
 Aldrich, John H. and Richard D. McKelvey. 1977. "A Method of Scaling with Applications
to the 1968 and 1972 Presidential Elections."American Political Science Review, 71:111130.
 Palfrey, Thomas R. and Keith T. Poole. 1987. "The Relationship Between Information,
Ideology, and Voting Behavior."American Journal of Political Science, 31:511530.
 Christopher Hare, David A. Armstrong II, Ryan Bakker, Royce Carroll, and Keith T.
Poole. 2014. "Using Bayesian AldrichMcKelvey Scaling to Study Citizens' Ideological Preferences
and Perceptions."American Journal of Political Science, forthcoming.
 Poole, Keith T. 1998. "Recovering a Basic Space From a Set of Issue Scales."American Journal of Political Science, 42:954993.
 Poole, Keith T. 1998. "How to Use the Black Box." A Supplement to "Recovering a Basic Space From a Set of Issue Scales" that shows
in detail how to apply the various programs used in the article.
 Poole, Keith T. 2001. "The Relationship Between the AldrichMcKelvey Scaling Solution
and the Individual Differences Problem." Manuscript, University of Houston.
 Notes on The Basic Space Model
 Likert, Rensis. 1932. "A Technique for the Measurement of Attitudes."Archives of Psychology, 22(193233):555.
 Classical Scaling of Similarities Data
Assignment:
 Armstrong et al., Chapter 4.1
 Borg and Groenen, Chapter 2, 3, 4, 6, 12
 DoubleCentering a Matrix of Squared Distances
double_center_seven_points_eigen.r  Simple R Program that Illustrates DoubleCentering and Graphs the Eigenvalues
of the DoubleCentered Matrix (uses seven_points_example.txt)
double_center_nations_eigen.r  Simple R Program that Illustrates DoubleCentering Nations Similarities Data and
Graphs the Eigenvalues of the DoubleCentered Matrix (and shows the negative eigenvalues)
 Eigenvalues and Eigenvectors
 Solving the Metric Similarities Problem
metric_mds_nations_poole_1984.r  R Program that Illustrates Metric MDS Scaling Developed by Poole, Psychometrika, 1984
smacof_metric_senate_90.r  R program that applies Metric MDS to the agreement score matrix for the 90^{th} U.S. Senate.
metric_mds_nations2_geometry.r  R Program that Illustrates Metric Multidimensional Scaling  Conditional Minimum
Algorithm, NedlerMead, Simulated Annealing, and BFGS
similarities_missing_2015.r  R Program that Illustrates How to Create Similarities Matrices and use Double
Centering Even if there is Missing Data
similarities_missing_2015_eigenvalues.r  R Program that Illustrates How to Create Similarities Matrices and use Double
Centering Even if there is Missing Data. This version also graphs the first 20 eigenvalues.
 Singular Value Decomposition
svd_example_2007.r  Simple R Program that Illustrates Singular Value Decomposition
svd_example.r  Illustrates SVD on a dataset of 106^{th} variables
rotate2.r  Illustrates Orthogonal Procrustes Rotation using original DNOMINATE scores and current DWNOMINATE scores
dnom_dwnom_senate.txt  7706 by 11 Matrix of DNOMINATE and DWNOMINATE scores for the 1^{st} to 100^{th} Senates
rotate3.r  Illustrates Orthogonal Procrustes Rotation using original DNOMINATE scores and
current DWNOMINATE scores. Linear and General Linear Models used to Regress DNOMINATE
onto DWNOMINATE
rotate4.r  Illustrates a more efficient Orthogonal Procrustes Rotation using original DNOMINATE
scores and current DWNOMINATE scores. Linear and General Linear Models used to Regress
DNOMINATE onto DWNOMINATE
svd_example_3_2007.r  R Program that Illustrates Point Clouds Singular Vectors
svd_new_example_1_2007.r  R Program that Illustrates Ratios of First Two Singular Values
 The Log Normal Model of Relational Data
Plot_Log_Normal.r  Program that illustrates the lognormal model of distances.
Weisberg_and_Rusk_log_normal.r  R Program that replicates the Weisberg and Rusk analysis of the 1968 Candidate
Feeling Thermometers Only with a LogNormal Model of the Candidate Correlations
nes1968_first_11.dta  Stata 11 File for the 1968 National Election Study. Data drawn from Stata file.
crime_rates_BG_log_normal.r  R Program that analyzes the U.S. crime data on page 4 of Borg and Groenen with
a LogNormal Model of the Crime Correlations
 NonMetric Multidimensional Scaling
Assignment:
 Armstrong et al., Chapter 4.2
 Borg and Groenen, Chapters 7, 8, 9, 10, 11, 13
 Notes on NonMetric Multidimensional Scaling
 Gleason, Terry C. 1967. "A General Model for NonMetric Multidimensional Scaling." Working Paper MMPP 673, University of Michigan Mathematical Psychology Program.
 Weisberg, Herbert F. 1984. "Scaling Objectives and Procedures." In Theory Building and Data Analysis in the Social Sciences. Edited by Herbert Asher, Herbert F. Weisberg, John Kessel, and W. Phillips Shively.
 Weisberg, Herbert F. 1974. "Dimensionland: An Excursion into Spaces."American Journal of Political Science, 18:743776.
 Rabinowitz, George. 1975. "An Introduction to Nonmetric Multidimensional Scaling."American Journal of Political Science, 19:343390.
 Weisberg, Herbert F. and and Jerrold G. Rusk. 1970. "Dimensions of Candidate Evaluation."The American Political Science Review, 64:11671185.
 Rusk, Jerrold G. and Herbert F. Weisberg. 1972. "Perceptions of Presidential Candidates."Midwest Journal of Political Science, 16(3):388410.
 Shepard, Roger N. 1987. "Toward a Universal Law of Generalization for Psychological
Science."Science, 237:13171323.
 Ennis, Daniel M., Joseph J. Palen, and Kenneth Mullen. 1988. "A Multidimensional Stochastic
Theory of Similarity."Journal of Mathematical Psychology, 32:449465.
 Nosofsky, Robert M. 1988. "On ExemplarBased Exemplar Representations: Reply to Ennis
(1988)."Journal of Experimental Psychology: General, 117:412414.
 Bayesian Multidimensional Scaling
 Assignment:
 Unfolding Analysis of Rating Scale Data  Interest Group Ratings and Thermometer
Scores
Assignment:
 Armstrong et al., Chapter 5
 Borg and Groenen, Chapters 14, 15, 16 (14, 15 1997 edition)
 Solving the Thermometer Problem

 Wang, MingMei, Peter H. Schonemann, and Jerrold G. Rusk. 1975. "A Conjugate Gradient
Algorithm for the Multidimensional Analysis of Preference Data."Multivariate Behavioral Research, 10:4580.
 Rabinowitz, George. 1976. "A Procedure for Ordering Object Pairs Consistent With The
Multidimensional Unfolding Model."Psychometrika, 41(3):349373.
 Poole, Keith T. 1984. "Least Squares Metric, Unidimensional Unfolding."Psychometrika, 49:311323.
 Poole, Keith T. 1990. "Least Squares Metric, Unidimensional Scaling of Multivariate
Linear Models."Psychometrika, 55:123149.
 Poole, Keith T. and Howard Rosenthal. 1984. "U.S. Presidential Elections 196880:
A Spatial Analysis."American Journal of Political Science, 28(2):282312.
 Cahoon, Lawrence S., Melvin J. Hinich, and Peter C. Ordeshook. 1976. "A Multidimensional
Statistical Procedure for Spatial Analysis." Manuscript, CarnegieMellon University.
 Unfolding Analysis of Binary Choice Data

 Parametric Methods
Assignment:

 Armstrong et al., Chapter 6.16.5
 Package MCMCPack  Andrew Martin and Kevin Quinn (PDF)
 MCMCPack (HTML)
 Poole, Chapters 4, 5, 6
 Clinton, Joshua D., Simon D. Jackman, and Douglas Rivers. 2004. "The Statistical Analysis
of Roll Call Data: A Unified Approach." American Political Science Review, 98:355370.
 Martin, Andrew D. and Kevin M. Quinn. 2002. "Dynamic Ideal Point Estimation via Markov
Chain Monte Carlo for the U.S. Supreme Court, 19531999." Political Analysis, 10:134153.
 Londregan, John B. 2000. "Estimating Legislators' Preferred Points." Political Analysis, 8:3536.
 Lewis, Jeffrey B. and Keith T. Poole. 2003. "Measuring Bias and Uncertainty in Ideal
Point Estimates via the Parametric Bootstrap." Working Paper, UCLA and UH, 20 May 2003.
 Neal, Radford M. 2003. "Slice Sampling." Annals of Statistics, 31(3):705767.
 The NOMINATE Model

wnominate_in_R.r   Simple R Program that does WNOMINATE that illustrates ways to write out the
coordinates.
wnominate_hou108.r  Runs WNOMINATE on 108th US House; plots legislator coordinates and specific roll
call vote.wnominate_senate_111_DADT.r  Runs WNOMINATE on the 111^{th} US Senate; plots legislator coordinates on the repeal of "Don't Ask Don't Tell roll
call vote.oc_senate_111_DADT.r  Runs Optimal Classification on the 111^{th} US Senate; plots legislator coordinates on the repeal of "Don't Ask Don't Tell roll
call vote. Illustrates the Difference between WNOMINATE and Optimal Classification.
wnominate_house_113_coombs_mesh.r  R program that runs WNOMINATE, writes the legislator and roll call coordinates
to disk, outputs the summary plot of the results, and makes a plot of the Coombs Mesh
and a histogram of the cutting line angles.
 The Quadratic Utility Model
 The One Parameter IRT (Rasch) Model

 Notes on the NOMINATE Model
 Royce Carroll, Jeffrey B. Lewis, James Lo, Keith T. Poole, and Howard Rosenthal. 2013.
"The Structure of Utility in Spatial Models of Voting." American Journal of Political Science 57(4): 10081028.
 NonParametric Methods [Optimal Classification (OC)]
 Assignment:

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