Measurement Theory UGA

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: [email protected]
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.
Data Sets Used Armstrong et al.

Data Sets Used in Borg and Groenen
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:
- Armstrong et al., Preface, and Chapters 1 and 2
- Poole, Chapters 1 and 2
- Coombs, Chapter 1
- Borg and Groenen, Preface and Chapter 1
- Carroll, J. Douglas and Phipps Arabie. 1980. "Multidimensional Scaling."Annual Review of Psychology. M. R. Rosenzweig and L. W. Porter, eds.
  - Types of Data Used by MDS Methods
  - Basic Notation used in this Course
  - Reading Data From an SPSS file:
    basicspace_AM_Urban_Unrest_1968_SPSS.r -- R program that performs Aldrich-McKelvey Scaling on the 1968 Urban Unrest Seven Point Scale with the Data stored as a SPSS file
    anes1968.POR -- NES1968 SPSS File (See R Program for documentation)
  - Reading Data From an STATA file:
    basicspace_AM_L-C_2004_Stata.r -- R program that performs Aldrich-McKelvey Scaling on the 2004 Liberal-Conservative Seven Point Scale From the NES 2004 Stata file
    anes2004.DTA -- 2004 NES 2004 (See R Program for documentation)
  - Reading Data From a Text File Using SCAN:
    double_center_seven_points.r -- Simple R Program that Illustrates Double-Centering
    
    seven_points_example.txt -- Simple Squared Distance Matrix for Seven Points
  - Reading Data From a Text File Using FWF:
    double_center_seven_points_fwf.r -- Simple R Program that Illustrates Double-Centering
    
    seven_points_example.txt -- Simple Squared Distance Matrix for Seven Points
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)
  
  nations.txt -- 12 Nations Similarities Data from Wish
- 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
  
  nations.txt -- 12 Nations Similarities Data from Wish
  smacof_metric_senate_90.r -- R program that applies Metric MDS to the agreement score matrix for the 90^th U.S. Senate.
  
  Agreement Scores data as an RDA file -- 90^th Senate Agreement Scores Matrix
  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
  
  svd_example_2007.r -- Simple R Program that Illustrates Singular Value Decomposition
  
  svd_matrix_2007.txt -- Simple 6 by 4 Matrix for SVD
  svd_example.r -- Illustrates SVD on a dataset of 106^th variables
  
  h106_data_2015.txt -- 432 by 11 Matrix of data for 106^th House
  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
  crime_rates.txt -- Seven by Seven correlation matrix of crime rate data.
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.
  
  plot_eigenvalues.r -- Simple R Program that does a Skree Plot of Eigenvalues from OC Output
  eigenvalues_example.txt -- eigenvalues of double-centered agreement score matrix for 88^th Senate
  Weisberg_and_Rusk_Shepard_Plot.r -- R Program that replicates the Weisberg and Rusk analysis of the 1968 Candidate Feeling Thermometers
  therm68.txt -- 12 Candidate Feeling Thermometers from the 1968 National Election Study
  Weisberg_and_Rusk_Shepard_Plot_2015.r -- R Program that replicates the Weisberg and Rusk analysis of the 1968 Candidate Feeling Thermometers
  nes1968_first_11.dta -- Stata 11 File for the 1968 National Election Study. Data drawn from Stata file.
  Weisberg_and_Rusk_Shepard_Plot_2015A.r -- R Program that replicates the Weisberg and Rusk analysis of the 1968 Candidate Feeling Thermometers. This version has SmacofSym for comparative purposes.
  
  Morse_two_ways_smacof.r -- R Program that performs NonMetric MDS on the Upper and Lower Morse Code Data using isoMDS and SmacofSym for comparative purposes, and Orthogonal Procrustes Rotation using MCMCpack and the hard-coded Procrustes solution shown in Homework Seven.
  morse_confusions_data.txt -- 36 by 36 Morse Code Confusions Matrix
  nmds_color_circle.r -- R Program that performs NonMetric MDS on the famous Color Circle Data.
  colors.txt -- 14 by 14 Color Similarites Matrix
- 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:
- Armstrong et al., Chapter 4.3
- Bakker and Poole, Bayesian Metric Multidimensional Scaling
- Bakker and Poole: Two Levels of Constraints
- Derivation of the Logit Probability Distribution Function
  
  metric_mds_nations_log_normal_2.r -- Program to optimize the Log-Normal Bayesian Model for the Nations data.
  nations.txt -- Nations Similarities data
  JAGS_mds_colors.r -- Uses JAGS to analyze the Posterior Distribution of the Color Circle Data.
  JAGS_mds_model_color.bug -- Model used by JAGS
  colors.txt -- Colors Similarities data
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
- MLSMU6_interest1981.r -- Program to Perform Metric Unfolding using Poole's MLSMU6 Algorithm.
  interest1981.RDA -- 1981 Interest Groups Ratings data
  nes_thermometers_smacof_MLSMU6.r -- Program to Perform Metric Unfolding using smacofRect and MLSMU6 on the 1968 Candidate Feeling Thermometers.
  nes1968_first_11.dta -- The 1968 National Election Study
  bayesianunfolding_ANES1968thermometers_pc64bit.r -- Program to Perform Bakker-Poole Bayesian Metric Multidimensional Unfolding (64 bit).
  ANES1968.Rda: 1968 American National Election Study Feeling Thermometers
  .dll File (PC: 64 bit)
  
  oc_ANES2008_thermometers.r: Runs Optimal Classification on the 2008 American National Election study feeling thermometers.
  candidatetherms2008.Rda -- 2008 Candidate Thermometer data read by program.
  presvote2008.Rda -- Respondent's reported vote in 2008 (read by program
- 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
1. Parametric Methods
  
  Assignment:
2. - 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.
3. The NOMINATE Model
4. wnominate_in_R.r -- -- Simple R Program that does W-NOMINATE that illustrates ways to write out the coordinates.
  sen88kh.ord -- 88^th House (1963-64) Roll Call Data
  wnominate_hou108.r -- Runs W-NOMINATE on 108th US House; plots legislator coordinates and specific roll call vote.
  hou108kh.ord -- 108^th House (2003-04) Roll Call Data
  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.
  sen111kh.ord -- 111^th House (2009-10) Roll Call Data
  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.
  hou113kh.ord -- 113^th House (2013-14) Roll Call Data
5. The Quadratic Utility Model
6. The One Parameter IRT (Rasch) Model
7. bayesirt_SupCourt2000.r: Runs Bayesian IRT on the 2000 Term of the US Supreme Court using the "MCMCirt1d" function in the MCMCpack package.
  
  bayesirt_SupCourt2000_pscl.r: Runs Bayesian IRT on the 2000 Term of the US Supreme Court using the "ideal" function in the pscl package.
  
  bayesirt_multidimensional_sen89_pscl.r: Runs multidimensional Bayesian IRT on the 89^th US Senate using the "ideal" function in the pscl package.
  sen89kh.ord -- 89^th Senate Roll Call data.
8. Notes on the NOMINATE Model
9. 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.
  
  anominate_sen111_onedim.r -- Program to run alpha-NOMINATE in one dimension:
  sen111kh.ord -- 111^th Senate Roll Call data.
10. Non-Parametric Methods [Optimal Classification (OC)]
11. Assignment:
- Armstrong et al., Chapter 6.6-6.7
- Poole, Chapter 3
- Poole, Notes on the Geometry of Logit and Probit
- Poole, Notes on the Geometry of Perfect One Dimensional Voting
- Poole, Notes on the Janice and Edith Algorithms
- Poole, Notes on the Geometry of Perfect Two Dimensional Voting
  
  coombs_mesh.r -- R Program that does Complete Coombs Mesh
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POLS 8505: MEASUREMENT THEORY

Clyde H. Coombs Born: 22 July 1912 Died: 4 February 1988

Clyde H. Coombs
Born: 22 July 1912
Died: 4 February 1988