Measurement Theory UGA

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POLS 8505: MEASUREMENT THEORY

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

Fall Semester AY2011-2012
Department of Political Science
School of Public and International Affairs
University of Georgia
Athens, GA 30602

Classroom: Baldwin 302
Time: 3:35-6:35 Wednesdays

Instructor: Keith T. Poole

Office: Baldwin 304D
E-Mail: ktpoole@uga.edu
WebSite: Voteview Home Page or Georgia Voteview Home Page

Office Hours: 2:00 - 4:00PM Thursdays or By Appointment

The following texts will be used in this course:

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 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 learn Epsilon (EMACS), a screen editor, and the open-source statistical package -- R. In the second half of the course we will also use the open-source Bayesian statistical package WINBUGS. 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.

Below are links to my Advanced Multivariate Statistics course web page for the fall of 2001 and and spring of 2003 at the University of Houston and my Prob-Stat II (required MBA course) web pages from AY1997-98 at Carnegie-Mellon University. These should be helpful if you need to refresh your memory about multiple regression.

POLS 6382 Advanced Multivariate Statistics (UH, fall 2001)

Probability and Statistics II Main Page (CMU Spring 1998)

Prob-Stat II 1997-98: First Homework Assignment

Prob-Stat II 1997-98: Answers For First Homework Assignment

Useful Links -- EPSILON

EPSILON HomePage -- Lugaru Software Ltd.

Useful Epsilon Commands

Epsilon Keyboard Macro Examples

Epsilon Text File Macro Examples

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 -- Multidimensional Scaling

How to Use KYST, A Very Flexible Program to do Multidimensional Scaling and Unfolding

Useful Links -- Old Homeworks

Old Homeworks: 2001 - 2008

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 3.1 -- Runs on 64 bit WINDOWS and 64 bit R

Problem Sets (2011)

Homework 1: Due 24 August 2011(WINDOWS)
Homework 1: Due 24 August 2011(iMAC)
Homework 2: Due 31 August 2011(WINDOWS)
Homework 2: Due 31 August 2011(iMAC)
Homework 3: Due 7 September 2011(WINDOWS)
Homework 3: Due 7 September 2011(iMAC)
Homework 4: Due 14 September 2011(WINDOWS)
Homework 4: Due 14 September 2011(iMAC)
Homework 5: Due 21 September 2011(WINDOWS)
Homework 5: Due 21 September 2011(iMAC)
Homework 6: Due 28 September 2011(WINDOWS)
Homework 6: Due 28 September 2011(iMAC)
Homework 7: Due 5 October 2011(WINDOWS)
Homework 7: Due 5 October 2011(iMAC)
Homework 8: Due 12 October 2011(WINDOWS)
Homework 8: Due 12 October 2011(iMAC)
Homework 9: Due 19 October 2011(WINDOWS)
Homework 9: Due 19 October 2011(iMAC)
Homework 10: Due 26 October 2011(WINDOWS)
Homework 10: Due 26 October 2011(iMAC)
Homework 11: Due 2 November 2011(WINDOWS)
Homework 11: Due 2 November 2011(iMAC)
Homework 12: Due 9 November 2011(WINDOWS)
Homework 12: Due 9 November 2011(iMAC)
Homework 13: Due 16 November 2011(WINDOWS)
Homework 13: Due 16 November 2011(iMAC)
Homework 14: Due 30 November 2011(WINDOWS)
Homework 14: Due 30 November 2011(iMAC)

Course Outline

Clyde Coombs' Theory of Data: Similarities and Preferential Choice

Assignment:

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., vol. 31, 1980.

Poole, Chapters 1 and 2

Classical Scaling of Similarities Data

Assignment:

Borg and Groenen, Chapter 2, 3, 4, 6, 12

Double-Centering a Matrix of Squared Distances

double_center_seven_points.r -- Simple R Program that Illustrates Double-Centering

seven_points_example.txt -- Simple Squared Distance Matrix for Seven Points

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_nations2_geometry.r -- R Program that Illustrates Metric Multidimensional Scaling -- Conditional Minimum Algorithm, Nedler-Mead, Simulated Annealing, and BFGS

nations.txt -- 12 Nations Similarities Data from Wish

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_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

Non-Metric Multidimensional Scaling

Assignment:

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.

shepard_plot_nations.r -- R Program that Illustrates the Shepard Plot using KYST Output for Nations Similarities Data

nations_2011.prn -- -- KYST listing of DHATS and DISTs for Nations 1 to 3 Dimensional Solution

shepard_plot.r -- R Program that Illustrates the Shepard Plot using KYST Output

kyst_Weisberg_DIST_DHAT.txt -- KYST listing of DHATS and DISTs for Weisberg and Rusk 2-Dimensional Solution
colors_DIST_DHAT.txt -- KYST listing of DHATS and DISTs for Color Circle 2-Dimensional Solution

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

Morse_two_ways.r -- R Program that performs NonMetric MDS on the Upper and Lower Morse Code Data using isoMDS

morse_confusions_data.txt -- 36 by 36 Morse Code Confusions 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:

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

Unfolding Analysis: Non-Parametric Methods [Optimal Classification (OC)]

Assignment:

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

Unfolding Analysis: Parametric Methods

Analysis of Interval Level Data -- Interest Group Ratings and Thermometer Scores

Assignment:

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.

Analysis of Perceptual Data -- Seven Point Scales

Assignment:

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.

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.

Analysis of Roll Call Data (Discrete Data)

Assignment:

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

The Quadratic Utility Model

Notes on the NOMINATE Model

wnominate_in_R.r -- Simple R Program that does W-NOMINATE

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