POLS 8505: MEASUREMENT THEORY
Clyde H. Coombs
Born: 22 July 1912
Died: 4 February 1988
Spring Semester AY2014-2015
Department of Political Science
School of Public and International Affairs
University of Georgia
Athens, GA 30602
Classroom: Baldwin 301
Time: 3:35-6:35 Mondays
Instructor:
Keith T. Poole
Office: Baldwin 304D
E-Mail: 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: Springer-Verlag.
- 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, 71:111-130.
- Palfrey, Thomas R. and Keith T. Poole. 1987. "The Relationship Between
Information, Ideology, and Voting Behavior." American Journal of Political Science,
31:511-530.
- Christopher Hare, David A. Armstrong II, Ryan Bakker, Royce Carroll, and Keith T. Poole. 2014.
"Using Bayesian Aldrich-McKelvey 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,
42:954-993.
- 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 Aldrich-McKelvey 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(1932-33):5-55.
- Classical Scaling of Similarities Data
Assignment:
- Armstrong et al., Chapter 4.1
- Borg and Groenen, Chapter 2, 3, 4, 6, 12
- Double-Centering a Matrix of Squared
Distances
double_center_seven_points_eigen.r
-- Simple R Program that Illustrates Double-Centering and Graphs the Eigenvalues of the Double-Centered Matrix (uses
seven_points_example.txt)
double_center_nations_eigen.r
-- Simple R Program that Illustrates Double-Centering Nations Similarities Data and Graphs the Eigenvalues of the
Double-Centered 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, Nedler-Mead, 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
- The Approximation of One Matrix by Another of Lower Rank.
Psychometrika, vol. 1 number 3, September 1936
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 D-NOMINATE scores and current DW-NOMINATE scores
d-nom_dw-nom_senate.txt
-- 7706 by 11 Matrix of D-NOMINATE and DW-NOMINATE scores for the 1^{st} to 100^{th}
Senates
rotate3.r -- Illustrates Orthogonal Procrustes
Rotation using original D-NOMINATE scores and current DW-NOMINATE scores. Linear and General Linear
Models used to Regress D-NOMINATE onto DW-NOMINATE
rotate4.r -- Illustrates a more efficient Orthogonal Procrustes
Rotation using original D-NOMINATE scores and current DW-NOMINATE scores. Linear and General Linear
Models used to Regress D-NOMINATE onto DW-NOMINATE
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
log-normal 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 Log-Normal 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 Log-Normal Model of the Crime Correlations
- Non-Metric Multidimensional Scaling
Assignment:
- Armstrong et al., Chapter 4.2
- Borg and Groenen, Chapters 7, 8, 9, 10, 11, 13
- Notes on Non-Metric Multidimensional Scaling
- Gleason, Terry C. 1967. "A General Model for Non-Metric
Multidimensional Scaling." Working Paper MMPP 67-3, 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, 18:743-776.
- Rabinowitz, George. 1975. "An Introduction to Nonmetric Multidimensional Scaling."
American Journal of Political Science, 19:343-390.
- Weisberg, Herbert F. and and Jerrold G. Rusk. 1970. "Dimensions of Candidate Evaluation."
The American Political Science Review, 64:1167-1185.
- Rusk, Jerrold G. and Herbert F. Weisberg. 1972.
"Perceptions of Presidential Candidates."
Midwest Journal of Political Science, 16(3):388-410.
- Shepard, Roger N. 1987. "Toward a Universal Law of Generalization for
Psychological Science." Science, 237:1317-1323.
- Ennis, Daniel M., Joseph J. Palen, and Kenneth Mullen. 1988. "A Multidimensional
Stochastic Theory of Similarity." Journal of Mathematical Psychology,
32:449-465.
- Nosofsky, Robert M. 1988. "On Exemplar-Based Exemplar Representations: Reply to
Ennis (1988)." Journal of Experimental Psychology: General, 117:412-414.
- 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, Ming-Mei, Peter H. Schonemann, and Jerrold
G. Rusk. 1975. "A Conjugate Gradient Algorithm for the Multidimensional Analysis of Preference Data."
Multivariate Behavioral Research, 10:45-80.
- Rabinowitz, George. 1976. "A Procedure for Ordering Object Pairs Consistent With
The Multidimensional Unfolding Model." Psychometrika, 41(3):349-373.
- Poole, Keith T. 1984. "Least Squares Metric, Unidimensional
Unfolding." Psychometrika, 49:311-323.
- Poole, Keith T. 1990. "Least Squares Metric, Unidimensional
Scaling of Multivariate Linear Models." Psychometrika,
55:123-149.
- Poole, Keith T. and Howard
Rosenthal. 1984. "U.S. Presidential Elections 1968-80: A Spatial Analysis."
American Journal of Political Science, 28(2):282-312.
- Cahoon, Lawrence S., Melvin J. Hinich, and Peter C. Ordeshook. 1976. "A
Multidimensional Statistical Procedure for Spatial Analysis." Manuscript,
Carnegie-Mellon University.
- Unfolding Analysis of Binary Choice Data
- Parametric Methods
Assignment:
- Armstrong et al., Chapter 6.1-6.5
- 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, 98:355-370.
- Martin, Andrew D. and Kevin M. Quinn. 2002. "Dynamic Ideal Point Estimation via
Markov Chain Monte Carlo for the U.S. Supreme Court, 1953-1999." Political
Analysis, 10:134-153.
- Londregan, John B. 2000. "Estimating Legislators' Preferred Points." Political
Analysis, 8:35-36.
- 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):705-767.
- The NOMINATE Model
wnominate_in_R.r --
-- Simple R Program that does W-NOMINATE that illustrates ways to write out the coordinates.
wnominate_hou108.r -- Runs W-NOMINATE on 108th US House;
plots legislator coordinates and specific roll call vote.
wnominate_senate_111_DADT.r -- Runs W-NOMINATE 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
W-NOMINATE 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): 1008-1028.
- Non-Parametric Methods [Optimal Classification (OC)]
Assignment: