Statistics 504 - Spring 2003Analysis of Discrete DataCourse website: http://www.stat.psu.edu/~jls/stat504/2003Instructor: Joe Schafer, 412 Thomas Building (3-4918) and S-156 Henderson (3-9795), [email protected]. Class meets Tuesday and Thursday 9:45–11:00 am in 212Hammond Building. Instructor’s office hours are Monday 3:00–5:00 and by appoint-ment.Who should take this course: Stat 504 is intended primarily for graduate studentsoutside of the Statistics department. It may also be appropriate for first- or second-year graduate students in Statistics. Advanced graduate students in Statisticsshould consider taking Stat 544 instead.Prerequisites: Stat 504 assumes knowledge of basic techniques of applied statistics,including normal-theory confidence intervals and hypothesis tests (i.e.,oneandtwo-sample t-tests, etc.), multiple linear regression and basic analysis of variance.A course in applied probability, or at least some familiarity with discrete probabilityand distributions, expectation, variance, etc. is important. Students are expected tohave basic mathematical ability to deal with summations, square roots, logarithms,etc. and occasionally some simple matrix matrix algebra.Text: The text for Stat 504 is Categorical Data Analysis, Second Edition by AlanAgresti (2002, Wiley). This is a popular and highly cited reference book on cate-gorical data. Some of the lectures will follow this book closely, and others will not.It may be possible to survive without purchasing Agresti (2002), but the book isdefinitely worth owning.Another book that may be useful is Categorical Data Analysis Using the SAS Sys-tem, Second Edition by Stokes, Davis, and Koch (2001, SAS Institute). This book isnot required. However, it can be quite helpful for graduate students who anticipatedoing a lot of categorical data analysis in SAS in their future research. This bookwas written by biostatisticians and has a strong biostatistical flavor. It focuseson the mechanics of performing analyses in SAS, rather than on the underlyingstatistical principles.Computing: We will primarily use SAS. Students who wish to use other packages(S-PLUS, SPSS, Minitab, Stata, etc.) are welcome to do so. Users of these otherpackages, however, will be responsible for teaching themselves how to perform theanalyses in these packages, and for ensuring that the results are consistent with whatthey would obtain from SAS. Sample analyses in SAS will be provided throughoutthe course. Students who use other statistical packages should probably re-workthese examples to make sure that they obtain the same results.The amount of class time that we can devote to computer issues is limited. Studentswho encounter difficulties in computing will be expected to seek help outside of classtime—in office hours with the instructor and grader or, preferably, through workingtogether with other students in the class.Class attendance: This course will cover a broad range of topics, and will frequentlygo beyond material found in the Agresti textbooks. Students will be responsiblefor all material covered in class, whether or not it is found in the textbooks. Henceit is absolutely essential for students to attend class on a regular basis and to takegood notes.Grading: Grades for Stat 504 will be based on homework assignments, which will begiven frequently throughout the semester. The last assignment will be a take-homefinal; it will be more comprehensive and longer than the others, and it will be worth30% of the final grade.Collaborative work: Students in Stat 504 are encouraged to work together—for ex-ample, to help one another with computer issues, to share class notes and discussthe material, etc. On the homework assignments, a reasonable amount of collabo-ration is allowed. Each student, however, must turn in his or her own written workwhich reflects his or her own individual understanding of the material. Because thisis a graduate course, the students will be assumed to have sufficient motivation andmaturity to come to their own understanding of the material without exams or astrict working-alone policy.Outline of course: The following outline is tentative, and may be modified as thesemester progresses, according to the interests of students and the discretion of theinstructor.1. Quick review of discrete probability distributions: binomial, multinomial,Poisson. Introduction to the concept of likelihood. Tests for one-way tablesusing Pearson’s X2and likelihood-ratio G2statistics.2. Introduction to contingency tables. 2 × 2andr × c tables, tests for inde-pendence and homogeneity of proportions, Fisher’s exact test, odds ratio andlogit, other measures of association. Matched pairs and McNemar’s test. In-troduction to 3-way tables, full independence and conditional independence,collapsing and Simpson’s paradox, Mantel-Haenszel tests.3. Introduction to generalized linear models. Poisson regression. Logistic regres-sion for dichotomous response, including interpretation of coefficients, maineffects and interactions, model selection, diagnostics, and assessing goodnessof fit. Adjustments for over-dispersion.4. Polytomous logit models for ordinal and nominal response.5. Loglinear models for multi-way tables.6. Other topics as time permits: repeated measures, generalized least squares,GEE methods, mixed models, latent-class models, missing