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- Title: 560syll
- Type: Notes
- School: Washington
- Course: STAT 560
- Term: Fall
Battle Preliminary Plan CSSS/POLS/STAT 560: Hierarchical Modeling for the Social Sciences Professor: Kevin Quinn, Political Science and CSSS Winter Quarter 2002 Class Room O ce 2:30-4:00 PM Tuesday and Thursday 313 Savery C-14-C Padelford Hall Phone: (206) 221-6981 Email : quinn@stat.washington.edu Preliminaries Overview and Class Goals This class deals with the analysis of clustered data. Examples of clustered data include students nested within classrooms, nested within schools; voters nested within precincts, nested within cities; or repeated measures from survey respondents nested within an individual over time. A great deal of the data analyzed by social scientists are organized according to some sort of clustered or hierarchical structure. Nonetheless, most social scientists have tended to ignore the clustered structure of their data. Thankfully, recent (and some not-so-recent) modeling advances have made it reasonably easy to explicitly model such hierarchically structured data. The goal of this course is to provide students with the knowledge and experience to apply these statistical methods to both standard and novel problems in their discipline. Consequently, most of the emphasis of the class will be on applied problems. Nonetheless, we will spend a fair amount of time during the quarter going through the underlying mathematics of the basic hierarchical model from both a Bayesian and a classical perspective. Prerequisites It is assumed that the students have completed a rst statistics sequence at the level of, for example, SOC 424-426. One book that covers this material is Statistical Methods for the Social Sciences by Alan Agresti and Barbara Finlay. It is also recommended that students have some familiarity with basic calculus (di erentiation and integration), matrix algebra (matrix addition, multiplication, and inverse matrices), and probability (including conditional probability). Class Requirements Final grades will be based on a series of homework assignments (60 % of nal grade), and on a take-home nal exam (40 % of nal grade). Homework will be assigned in class every one to two weeks and will generally be due in class the next week. Depending on the material covered in a given week, the assignment will be either an analytical problem set and/or an exercise dealing with real data and/or computation. I encourage you to work on the home work assignments with each other in small groups. However, I expect each student s write-up of the assignment to be his or her own work. Homework assignments will be graded on a 10 point scale. Homework assignments that are not handed in on time will receive zero points (except in the case of documented emergency). The nal exam will be a take-home, cumulative exam. I will not give incompletes in this course. Computation Fitting hierarchical models / mixed-e ects models is a somewhat tricky matter. In my experience, the best general-purpose package available for tting classical mixed-e ects models is Pinheiro and Bates nlme package available for R and S-PLUS. The nlme package has a very wide range of capabilities and, most importantly, is numerically reliable. For this reason we will be making extensive use of the nlme package in this course. The University has a site license for S-PLUS. You should be able to buy your own copy for about $100. S-PLUS should also be available in most of the computer labs on campus. Professor: Kevin Quinn, Political Science and CSSS Winter Quarter 2002 2 R is a free alternative to S-PLUS. R has very similar functionality to S-PLUS, is very stable, is generally a bit faster than S-PLUS because of the way it manages memory, and is completely open-source. You can download R from http://www.r-project.org/. R should also be available in the CSSCR lab. While I favor R over S-PLUS in almost all situations, tting mixed-e ects models with nlme is one case where S-PLUS is preferred over R. The main reason for this is that the nlme package makes extensive use of the trellis graphics library for exploratory data analysis and model checking. Unfortunately, the R version of nlme does not have any of these graphics capabilities since the trellis libraries have not been fully implemented in R yet. As a result, I recommend that you use S-PLUS for tting mixed-e ects models with nlme. When we begin discussing Bayesian hierarchical modeling towards the end of the course, some students may wish to write their own code to t various models via Markov chain Monte Carlo algorithms. Such students will invariably want to use a compiled programming language (such as C++ or Fortran) or a fast matrix language (such as Ox). For those wishing to use C++ for statistical computation, the Scythe project (http://scythe.wustl.edu) provides an easy to use open-source matrix library, random number generators, and optimization module. While not as fast as optimized C++ code, Ox (http://www.nuff.ox.ac.uk/Users/Doornik/index.html) is reasonably fast and easy to use. O ce Hours and Availability My o ce hours will be by appointment this quarter. To set up a meeting time please email me at quinn@stat.washington.edu or call me at my o ce: 221-6981. If you have questions about the course material, computational issues, or other course-related issues please do not hesitate to set up an appointment. I will also try to answer questions by email whenever possible. My email address is quinn@stat.washington.edu. If the topic of the question is relevant to the class as a whole and others can learn from the question and response, I will forward the question and my answer to the rest of the class. If you would like identifying information stripped out of your email or you do not want your question forwarded please say so explicitly in your message. Course Website The course website is located at the following URL: http://www.stat.washington.edu/quinn/classes/560/560.html. This site will provide homework assignments, datasets, and supplementary materials. Reasonable Accommodation Statement The University of Washington is committed to providing access, equal opportunity and reasonable accommodation in its services, programs, activities, education and employment for individuals with disabilities. For information or to request disability accommodation contact: Disabled Student Services at (206) 543-8924/V, (206) 543-8925/TTY, (206)616-8379 (FAX), or e-mail at: uwdss@u.washington.edu. Required Books The following books are required. Pinheiro, Jose C., and Douglas M. Bates. 2000. Mixed E ects Models in S and S-PLUS. New York: Springer. Snijders, Tom, and Roel Bosker. 1999. Multilevel Analysis. London: Sage. Gelman, Andrew, John B. Carlin, Hal S. Stern, and Donald B. Rubin. 1995. Bayesian Data Analysis. London: Chapman and Hall. addition, In I will distribute copies of additional readings in class the week before the reading assignment is due. 3 Optional Books The following books are optional but may prove useful. McCulloch, Charles E, and Shayle R. Searle. 2001. Generalized, Linear, and Mixed Models. New York: Wiley. Venables W.N., and B.D. Ripley. 1999. Modern Applied Statistics with S-PLUS. 3rd Edition. New York: Springer. Preliminary Schedule The following is a preliminary schedule of course topics. It is a rough guide to what we will be covering and may well undergo some changes over the quarter. In addition to the readings listed below I will occasionally hand out articles that feature interesting applications of hierarchical models but that do not t neatly into the course schedule. In addition, I encourage you to attend the CSSS seminar series this quarter as there are several talks that feature interesting applications involving hierarchical models. The CSSS seminar is held in Savery 209 from 12:30-2:00pm every Wednesday. Part I Clustered Data 1 Introduction: What is Clustered Data and How Should it be Analyzed? Required Reading Snijders and Bosker, Chapters 1-3 Optional Reading Draper, David. 1999. Inference and Hierarchical Modeling in the Social Sciences. University of Bath Working Paper. http://www.bath.ac.uk/ masdd/Papers/ihmss.ps. McCulloch and Searle, Chapter 1 Gelman et al., pp. 366-375 2 Summarizing and Exploring Clustered Data Required Reading Pinheiro and Bates, Chapter 3 Part II Likelihood Inference for Mixed E ects Models 3 Refresher: Likelihood Inference for the Basic Linear Model 4 Required Reading Pinheiro and Bates, pp. 134-146 Optional Reading McCulloch and Searle, Chapter 4 4 The One-Level Random E ects Model Required Reading Snijders and Bosker, Chapter 4 Pinheiro and Bates, pp. 1-12, 30-40, 58-60, 133-157 5 The One-Level Random Coe cients Model Required Reading Snijders and Bosker, Chapter 5 Pinheiro and Bates, pp. 58-60, 133-157 Optional Reading Laird, N.M., and J.H. Ware. 1982. Random E ects Models for Longitudinal Data. Biometrics. 38:963974. 6 Likelihood Theory and Estimation for Mixed E ects Models Required Reading Pinheiro and Bates, Chapter 2 Optional Reading McCulloch and Searle, Chapter 6 7 Assessing Model Fit and Hypothesis Testing Required Reading Snijders and Bosker, Chapters 6, 7, and 9 Pinheiro and Bates, pp. 174-196, 81-94 8 Multilevel Models Required Reading Pinheiro and Bates, Section 4.2.3 Snijders and Bosker, pp. 83-85 5 9 Modeling Longitudinal Data Required Reading Snijders and Bosker, Chapter 12 Optional Reading McCulloch and Searle, Chapter 7 Scott, Marc A. and Mark S. Handcock. 2001. Covariance Models for Latent Structure in Longitudinal Data. http://www.csss.washington.edu/Papers/wp14.pdf 10 Extending the Basic Linear Mixed-E ects Model Required Reading Pinheiro and Bates, Chapter 5 Higdon, David. 2001. Space and Space-time Modeling using Process Convolutions. Duke ISDS Discussion Paper 01-03. http://ftp.isds.duke.edu/WorkingPapers/01-03.html. Snijders and Bosker Chapter 8 (skim) Part III Bayesian Hierarchical Modeling 11 Review of Bayesian and Likelihood Inference Required Reading Gelman et al. Chapter 1 12 Bayesian Analysis of the Basic Linear Model with Gaussian Disturbances Required Reading Gelman et al. Chapter 8 13 Bayesian Analysis of the Two-Level Hierarchical Model with Gaussian Disturbances Required Reading Gelman et al. Chapter 13 Optional Reading Lindley, D.V. and A.F.M. Smith. 1972. Bayes Estimates for the Linear Model (with discussion). Journal of the Royal Statistical Society, Series B. 34: 1-41. 6 14 Fitting Bayesian Hierarchical Models with Gaussian Disturbances Required Reading Gelman et al. Chapter 11 Wake eld, J.C., A.F.M. Smith, A. Racine-Poon, and A.E. Gelfand. 1994. Bayesian Analysis of Linear and Non-Linear Population Models by Using the Gibbs Sampler. Applied Statistics, 43: 201-221. Optional Reading Browne, William and David Draper. 1999. Implementation and Performance Issues in the Bayesian and Likelihood Fitting of Multilevel Models. forthcoming in Computational Statistics, also available at: http://www.bath.ac.uk/ masdd/compstat.ps Browne, William and David Draper. 2000. A Comparison of Bayesian and Likelihood-based Methods for Fitting Multilevel Models. University of Bath Working Paper. http://www.bath.ac.uk/ masdd/browne-draper.p 15 Diagnostics and Model Fit Required Reading Hodges, James S. 1998. Some Algebra and Geometry for Hierarchical Models, Applied to Diagnostics (with discussion). Journal of the Royal Statistical Society, Series B. 60: 497-536. Gelman, A. and X.-L. Meng. 1996. Model Checking and Model Improvement. in Markov Chain Monte Carlo in Practice, Gilks, Richardson, and Spiegelhalter (eds.), pp. 189-201. Part IV Additional Topics We Probably Won t Have Time to Cover A Hierarchical Models with Student-t Disturbances Required Reading Wake eld, J.C., A.F.M. Smith, A. Racine-Poon, and A.E. Gelfand. 1994. Bayesian Analysis of Linear and Non-Linear Population Models by Using the Gibbs Sampler. Applied Statistics, 43: 201-221. B Bayesian Analysis of Hierarchical Longitudinal Models Required Reading Carlin, B.P. 1996. Hierarchical Longitudinal Modeling . in Markov Chain Monte Carlo in Practice, Gilks, Richardson, and Spiegelhalter (eds.), pp. 303-319. Lange, Nicholas, Bradley P. Carlin, and Alan E. Gelfand. Hierarchical Bayes Models for the Progression of HIV Infection Using Longitudinal CD4 T-Cell Numbers (with discussion). Journal of the American Statistical Association. 87: 615-632. 7 C Hierarchical Models for Binomial Data Required Reading Rodriquez, G. and N. Goldman. 1995. An Assessment of Estimation Procedures for Multilevel Models with Binary Responses. Journal of the Royal Statistical Society, Series A. 158: 73-89. Yang, Min, Harvey Goldstein, and Anthony Heath. 2000. Multilevel Models for Repeated Binary Outcomes: Attitudes and Voting over the Electoral Cycle. Journal of the Royal Statistical Society, Series A, 163: 49-62. Goldstein, Harvey and Jon Rasbash. 1996. Improved Approximations for Multilevel Models with Binary Responses. Journal of the Royal Statistical Society, Series A. 159: 505-513. D Hierarchical Models for Poisson Data Required Reading Christiansen, Cindy L. and Carl N. Morris. 1997. Hierarchical Poisson Regression Modeling. Journal of the American Statistical Association. 92: 618-631. Cohen, Jacqueline, Daniel Nagin, Garrick Wallstrom and Larry Wasserman. 1998. Hierarchical Bayesian Analysis of Arrest Rates. Journal of the American Statistical Association. 93: 1260-1270. January, 2002
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